{ "response":{"numFound":1173288,"start":0,"docs":[ { "id":"10.1371/journal.pgph.0000293/materials_and_methods", "doc_partial_parent_id":"10.1371/journal.pgph.0000293", "doc_type":"partial", "journal_eissn":"2767-3375", "publisher":"Public Library of Science", "journal":"PLOS Global Public Health", "journal_id_pmc":"plosgph", "journal_id_publisher":"plos", "journal_id_nlm_ta":"PLOS Glob Public Health", "eissn":"2767-3375", "publication_date":"2022-03-31T00:00:00Z", "received_date":"2021-08-01T00:00:00Z", "accepted_date":"2022-03-02T00:00:00Z", "article_type":"Research Article", "article_type_facet":"Research Article", "author":["Sunil Pokharel", "Lisa J White", "Jilian A Sacks", "Camille Escadafal", "Amy Toporowski", "Sahra Isse Mohammed", "Solomon Chane Abera", "Kekeletso Kao", "Marcela De Melo Freitas", "Sabine Dittrich"], "author_facet":["Sunil Pokharel", "Lisa J White", "Jilian A Sacks", "Camille Escadafal", "Amy Toporowski", "Sahra Isse Mohammed", "Solomon Chane Abera", "Kekeletso Kao", "Marcela De Melo Freitas", "Sabine Dittrich"], "editor":["Ana Marcia de Sá Guimarães"], "editor_facet":["Ana Marcia de Sá Guimarães"], "pagecount":16, "volume":2, "issue":3, "elocation_id":"e0000293", "journal_name":"PLOS Global Public Health", "journal_key":"PLOSGlobalPublicHealth", "subject":["/Biology and life sciences/Molecular biology/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction/Reverse transcriptase-polymerase chain reaction", "/Computer and information sciences/Computer applications/Web-based applications", "/Medicine and health sciences/Diagnostic medicine", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Medical conditions/Infectious diseases", "/Medicine and health sciences/Medical conditions/Infectious diseases/Viral diseases/COVID 19", "/Medicine and health sciences/Medical conditions/Parasitic diseases/Malaria", "/Medicine and health sciences/Medical conditions/Tropical diseases/Malaria", "/Physical sciences/Mathematics/Applied mathematics/Algorithms", "/Research and analysis methods/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction/Reverse transcriptase-polymerase chain reaction", "/Research and analysis methods/Simulation and modeling/Algorithms"], "subject_hierarchy":["/Biology and life sciences/Molecular biology/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction/Reverse transcriptase-polymerase chain reaction", "/Computer and information sciences/Computer applications/Web-based applications", "/Medicine and health sciences/Diagnostic medicine", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Medical conditions/Infectious diseases", "/Medicine and health sciences/Medical conditions/Infectious diseases/Viral diseases/COVID 19", "/Medicine and health sciences/Medical conditions/Parasitic diseases/Malaria", "/Medicine and health sciences/Medical conditions/Tropical diseases/Malaria", "/Physical sciences/Mathematics/Applied mathematics/Algorithms", "/Research and analysis methods/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction/Reverse transcriptase-polymerase chain reaction", "/Research and analysis methods/Simulation and modeling/Algorithms"], "subject_facet":["/Biology and life sciences/Molecular biology/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction/Reverse transcriptase-polymerase chain reaction", "/Computer and information sciences/Computer applications/Web-based applications", "/Medicine and health sciences/Diagnostic medicine", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Medical conditions/Infectious diseases", "/Medicine and health sciences/Medical conditions/Infectious diseases/Viral diseases/COVID 19", "/Medicine and health sciences/Medical conditions/Parasitic diseases/Malaria", "/Medicine and health sciences/Medical conditions/Tropical diseases/Malaria", "/Physical sciences/Mathematics/Applied mathematics/Algorithms", "/Research and analysis methods/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction/Reverse transcriptase-polymerase chain reaction", "/Research and analysis methods/Simulation and modeling/Algorithms"], "subject_level_1":["Biology and life sciences", "Computer and information sciences", "Medicine and health sciences", "Physical sciences", "Research and analysis methods"], "striking_image":"10.1371/journal.pgph.0000293.g006", "timestamp":"2026-03-14T09:31:27.210Z", "doc_partial_body":["\nDefinitions\nSingular testing means either one of the two tests is applied alone as the only diagnostic tool for screening and/or diagnostic purposes. This approach is adopted when an optimal diagnostic test is available at the point-of-care, for example, the malaria RDT, which is adopted as a singular test for the diagnosis of malaria [15]. In the present study, singular testing serves as a comparator.\nCombination testing involves two available tests being applied in either a sequential or a simultaneous testing algorithm, as described below. A combination testing strategy is used when the combination enhances the value of the tests in terms of clinical diagnosis and screening. Combination testing has previously been adopted for various infectious diseases, including HIV, HBV and HCV [4, 5].\nSequential testing is considered to be more appropriate than simultaneous testing in terms of the demand for tests, logistics and resources required for its implementation and is preferred in practice; therefore, we have focussed on this approach. Nonetheless, the results of diagnostic outcomes (true and false positives and true and false negatives) described below also hold true for the corresponding simultaneous testing strategies.\n\nSequential testing\nTests are used sequentially, one after the other, with the second test used to confirm the result of the first test. There are two strategies that can be adopted:\nStrategy 1: Confirmatory testing for positive results. When performing confirmatory testing for positive results, the second test is applied only if the first test is positive. This approach optimises the specificity of combination testing at the expense of sensitivity, meaning false positives are minimised (Fig 1A). This approach has been widely used to confirm diagnoses of HIV, HBV and HCV [4, 5].\n\n10.1371/journal.pgph.0000293.g001\nFig 1\n\nTesting strategies.\nA. Confirmatory testing for positives, meaning every positive test triggers a follow up test. B. Confirmatory testing for negatives, meaning that every negative triggers a follow-up test. C. Simultaneous testing, meaning that both tests are performed at the same time and the patient is considered to have a positive result if both are positive. D. Simultaneous testing, meaning that both tests are performed at the same time, and if either test is positive the patient is considered to have a positive result.\n\n\n\n\nStrategy 2: Confirmatory testing for negative results\nWhen performing confirmatory testing for negative results, the second test is applied only if the first test is negative. This approach optimises the sensitivity of combination testing at the expense of specificity, meaning false negatives are minimised (Fig 1B). An example of this approach is the application of the Cepheid GeneXpert® nucleic acid amplification test during tuberculosis screening as a follow-up test for suspected cases who return a negative sputum microscopy result [16].\n\n\nSimultaneous testing\nDuring simultaneous testing, both tests are applied at the same time and the results are interpreted together. There are two possible approaches for the interpretation of test results under simultaneous testing.\n\nStrategy 3\nIf both test results are positive, then the case is considered to be positive for the infection. This approach optimises the specificity of combination testing at the expense of sensitivity, meaning false positives are minimised (Fig 1C).\n\n\nStrategy 4\nIf one of the test results is positive, then the case is considered to be positive for the infection. This approach optimises the sensitivity of combination testing at the expense of specificity, meaning false negatives are minimised (Fig 1D).\nThe average time to results refers to the average turnaround time for a testing strategy, from the time of sample collection to the time of reporting of results to the patient from whom the sample was collected.\n\n\nCalculation of combined sensitivities and specificities of two-test algorithms\nHere, we describe the combined sensitivity and specificity of a two-test algorithm when the application of a confirmatory second test occurs based on either a positive or negative result of the prior test.\nThe combined sensitivity and specificity of two tests with individual test sensitivities of kse1 and kse2, and respective specificities of ksp1 and ksp2 when applied sequentially, with the second test applied as a confirmatory test for patients who test positive by the first test is represented by SET1 and SPT1 and with the second test applied as a confirmatory test for patients who test negative by the first test is represented by SET2 and SPT2, are as follows:\n\n\n\n\nSET1=kse1*kse2\n\n\n\n\n\n\n\nSPT1=1−(1−ksp1)(1−ksp2)\n\n\n\n\n\n\n\nSET2=1−(1−kse1)(1−kse2)\n\n\n\n\n\n\n\nSPT2=ksp1*ksp2\n\n\n\nThe changes in sensitivities and specificities with each of the testing strategies with corresponding changes in specificities and sensitivities compared with singular testing by either of the tests are supplied in the S1 Text. We discuss the impact on the combined accuracies with examples in the Results section. The calculations of test outcomes of true positives, false negatives, true negatives and false negatives for each of the testing approaches are provided in the S1 Text.\nIt is important to note that confirmatory testing for positives using a sequential testing strategy (Strategy 1) and simultaneous testing considering a case to be positive if both test results are positive for the infection (Strategy 3) predict the same sensitivities and specificities and thus the same diagnostic outcomes (true and false positives and true and false negatives). Similarly, confirmatory testing for negatives using a sequential testing strategy (Strategy 2) and simultaneous testing considering a case to be positive if either one of the test results is positive (Strategy 4) predict the same sensitivities and specificities. Nevertheless, sequential testing strategies are preferred to simultaneous testing due to having lower turnaround times and fewer resource requirements. The equations for calculating turnaround times and second test volumes are included in the S1 Text.\n\nConditional dependence between tests\nConditional dependence between test results exists when the agreement of results between two tests differs from those that would be observed by chance alone. Unlike when tests are independent, the sensitivities and specificities of a second test differ according to whether the first test result was positive or negative.\nIf there is positive dependence of one test on the other:\n\nThe sensitivity of the second test among positives from the first test increases.\nThe sensitivity of the second test among negatives from the first test decreases.\n\nThe opposite is true for negative dependence. The influence of test dependence on the outcome of a combination of tests is adopted from a previously described method [17] and is described in detail in the S1 Text.\n\nApplication of tests\n\nAssumptions\nWe make the following assumptions in our model:\n\nThe two tests used in combination were independent of each other, and the likelihood of a positive test was not dependent on the result of another test. The relaxation of this assumption is explored in the S1 Text.\nThe likelihood that an individual tested positive for a disease depended on the test characteristics and disease status, irrespective of the stage of disease and corresponding viral load, presence of symptoms, and status of the host immune response.\n\n\n\nModel\nWe used a simulation approach using R statistical software, version 3.6.2 [18] to compare the outcome of testing strategies when each of the tests was applied singularly or in sequential combination, with further testing occurring for patients with positive or negative prior test results. The model accounted for two tests for COVID-19, with previously defined sensitivity and specificity and turnaround times for results. The code to run the model and generate outputs is available at https://github.com/sunildrp/covid-testing-algo.\n\nScenarios\nWe used two hypothetical examples of use case scenarios.\n\nA high infection prevalence of 20,000/100,000 (20%) in the tested population. The high prevalence scenario represents hospital settings where individuals often present with symptomatic infection, and the primary aim of testing is to obtain a diagnosis of the disease for clinical management and isolation of cases. Available literature suggests a highly variable prevalence of COVID-19 infection in healthcare settings (3–71%, median 21%) [19].\nA low infection prevalence of 50/100,000 (0.05%) in the tested population. The low infection prevalence scenario represents a situation where the tested individuals are usually asymptomatic and tests are used to screen for COVID-19, e.g. rapid mass testing of asymptomatic individuals in England [20] and point-of-entry or border screening programmes.\n\n\nData\nThe tests used for the simulation with their corresponding accuracy values are shown in Table 1. The turnaround times from the time of sample collection to result using Ag-RDT and RT-PCR were assumed to be 30 minutes and 24 hours, respectively. Ag-RDTs are performed at the site of sample collection and produce results within 15–30 minutes [21]. For RT-PCR, samples must be transported to a laboratory, and it usually takes 24 hours or more for the results depending on the testing situation.\n\n10.1371/journal.pgph.0000293.t001\nTable 1 Model inputs: Sensitivities and specificities of COVID-19 tests.\n\n\n\n\n\n\n\n\n\n\n\n\n\nTest\nSensitivity (%)\nSpecificity (%)\nSource\n\n\n\n\n1.\nAg-RDT\n70\n97\n*Assumption\n\n\n2.\nRT-PCR\n90\n98\nSystematic review and meta-analysis of nucleic acid amplification tests on respiratory tract samples [22]\n\n\n\n\n\n*The available sensitivity and specificity values of Ag-RDTs are measured relative to RT-PCR, with no direct information about their true performance in the population; the values vary widely across studies [8, 10, 23]. The input parameters for this analysis were empirically selected based on the available knowledge to reflect their true performance in the population. In the web-application, for pragmatic reasons, sensitivity and specificity of RT-PCR are pre-set to 100% to reflect the relationship between RT-PCR and Ag-RDTs and ease the comparison between two Ag-RDTs where the available test performance data are generated using RT-PCR as the reference standard.\n\n\n\nOutputs\nWe calculated the true positives, true negatives, false positives, and false negatives for each of the single tests and for the sequential algorithms of two tests where further tests were applied to patients who were positive or negative for prior tests. We further calculated the sensitivity and specificity for the combinations of tests, the numbers of each test required and the average turnaround times for results.\n\nWeb-based application\nWe applied the same methods to develop a web-based application using R [18] and an interactive web-based interface using the R “Shiny” package [24]. The web application takes the population size being tested, infection prevalence in the tested population, diagnostic test accuracies and turnaround times for each test as inputs and calculates the test outcomes, the numbers of each test needed and the average turnaround times for each singular test and the two-test algorithms. The application also allows users to explore the impact of conditional dependence between the tests if it exists, given the availability of reliable data. The Foundation for Innovative New Diagnostics (FIND) and other diagnostics partners are already using the tool to provide technical assistance to ministries of health around the world. Feedback from early users of the tool, obtained during the provision of technical assistance to the government of Somalia, has been used to improve subsequent iterations of the tool. Virtual meetings were organized to train the early users (including JAS, CE, AT, SIM, SCA, KK, MDMF) of the web application and subsequent feedbacks were sought through virtual meetings and email correspondences. Revisions were made in the design of the interface to enhance user friendliness and outputs of the tools were modified to meet the need of the users.\n"]}, { "id":"10.1371/journal.pone.0212343/results_and_discussion", "doc_partial_parent_id":"10.1371/journal.pone.0212343", "doc_type":"partial", "journal_eissn":"1932-6203", "publisher":"Public Library of Science", "journal":"PLOS ONE", "journal_id_pmc":"plosone", "journal_id_publisher":"plos", "journal_id_nlm_ta":"PLoS ONE", "eissn":"1932-6203", "publication_date":"2019-02-22T00:00:00Z", "received_date":"2018-08-30T00:00:00Z", "accepted_date":"2019-01-31T00:00:00Z", "article_type":"Research Article", "article_type_facet":"Research Article", "author":["Charlene Harichund", "Pinky Kunene", "Sinenhlanhla Simelane", "Quarraisha Abdool Karim", "Mosa Moshabela"], "author_facet":["Charlene Harichund", "Pinky Kunene", "Sinenhlanhla Simelane", "Quarraisha Abdool Karim", "Mosa Moshabela"], "editor":["Jonathan Garcia"], "editor_facet":["Jonathan Garcia"], "pagecount":12, "volume":14, "issue":2, "elocation_id":"e0212343", "journal_name":"PLOS ONE", "journal_key":"PLoSONE", "subject":["/Biology and life sciences/Microbiology/Medical microbiology/Microbial pathogens/Viral pathogens/Immunodeficiency viruses/HIV", "/Biology and life sciences/Microbiology/Medical microbiology/Microbial pathogens/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Biology and life sciences/Organisms/Viruses/Immunodeficiency viruses/HIV", "/Biology and life sciences/Organisms/Viruses/RNA viruses/Retroviruses/Lentivirus/HIV", "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Immunodeficiency viruses/HIV", "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Medicine and health sciences/Clinical medicine/Clinical trials/Phase I clinical investigation", "/Medicine and health sciences/Clinical medicine/Clinical trials/Phase II clinical investigation", "/Medicine and health sciences/Diagnostic medicine/HIV diagnosis and management", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Epidemiology/Medical risk factors", "/Medicine and health sciences/Health care/Health care facilities", "/Medicine and health sciences/Pathology and laboratory medicine/Pathogens/Microbial pathogens/Viral pathogens/Immunodeficiency viruses/HIV", "/Medicine and health sciences/Pathology and laboratory medicine/Pathogens/Microbial pathogens/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Medicine and health sciences/Pharmacology/Drug research and development/Clinical trials/Phase I clinical investigation", "/Medicine and health sciences/Pharmacology/Drug research and development/Clinical trials/Phase II clinical investigation", "/Medicine and health sciences/Public and occupational health/Preventive medicine/HIV prevention", "/Research and analysis methods/Clinical trials/Phase I clinical investigation", "/Research and analysis methods/Clinical trials/Phase II clinical investigation"], "subject_hierarchy":["/Biology and life sciences/Microbiology/Medical microbiology/Microbial pathogens/Viral pathogens/Immunodeficiency viruses/HIV", "/Biology and life sciences/Microbiology/Medical microbiology/Microbial pathogens/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Biology and life sciences/Organisms/Viruses/Immunodeficiency viruses/HIV", "/Biology and life sciences/Organisms/Viruses/RNA viruses/Retroviruses/Lentivirus/HIV", "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Immunodeficiency viruses/HIV", "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Medicine and health sciences/Clinical medicine/Clinical trials/Phase I clinical investigation", "/Medicine and health sciences/Clinical medicine/Clinical trials/Phase II clinical investigation", "/Medicine and health sciences/Diagnostic medicine/HIV diagnosis and management", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Epidemiology/Medical risk factors", "/Medicine and health sciences/Health care/Health care facilities", "/Medicine and health sciences/Pathology and laboratory medicine/Pathogens/Microbial pathogens/Viral pathogens/Immunodeficiency viruses/HIV", "/Medicine and health sciences/Pathology and laboratory medicine/Pathogens/Microbial pathogens/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Medicine and health sciences/Pharmacology/Drug research and development/Clinical trials/Phase I clinical investigation", "/Medicine and health sciences/Pharmacology/Drug research and development/Clinical trials/Phase II clinical investigation", "/Medicine and health sciences/Public and occupational health/Preventive medicine/HIV prevention", "/Research and analysis methods/Clinical trials/Phase I clinical investigation", "/Research and analysis methods/Clinical trials/Phase II clinical investigation"], "subject_facet":["/Biology and life sciences/Microbiology/Medical microbiology/Microbial pathogens/Viral pathogens/Immunodeficiency viruses/HIV", "/Biology and life sciences/Microbiology/Medical microbiology/Microbial pathogens/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Biology and life sciences/Organisms/Viruses/Immunodeficiency viruses/HIV", "/Biology and life sciences/Organisms/Viruses/RNA viruses/Retroviruses/Lentivirus/HIV", "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Immunodeficiency viruses/HIV", "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Medicine and health sciences/Clinical medicine/Clinical trials/Phase I clinical investigation", "/Medicine and health sciences/Clinical medicine/Clinical trials/Phase II clinical investigation", "/Medicine and health sciences/Diagnostic medicine/HIV diagnosis and management", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Epidemiology/Medical risk factors", "/Medicine and health sciences/Health care/Health care facilities", "/Medicine and health sciences/Pathology and laboratory medicine/Pathogens/Microbial pathogens/Viral pathogens/Immunodeficiency viruses/HIV", "/Medicine and health sciences/Pathology and laboratory medicine/Pathogens/Microbial pathogens/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Medicine and health sciences/Pharmacology/Drug research and development/Clinical trials/Phase I clinical investigation", "/Medicine and health sciences/Pharmacology/Drug research and development/Clinical trials/Phase II clinical investigation", "/Medicine and health sciences/Public and occupational health/Preventive medicine/HIV prevention", "/Research and analysis methods/Clinical trials/Phase I clinical investigation", "/Research and analysis methods/Clinical trials/Phase II clinical investigation"], "subject_level_1":["Biology and life sciences", "Medicine and health sciences", "Research and analysis methods"], "striking_image":"10.1371/journal.pone.0212343.g004", "timestamp":"2026-03-14T06:51:16.715Z", "doc_partial_body":["\nParticipants\nDuring Phase 1 of the study, 12 male and 28 female participants were enrolled across two clinical research cites (Table 1), resulting in 80 IDIs being completed. The average age of the men and women were 25 and 27 years, respectively. The majority of participants were unemployed, and all participants had access to an HIV testing facility in their community (Table 1).\n\n10.1371/journal.pone.0212343.t001\nTable 1 Demographic characteristics of participants during Phase 1.\n\n\n\n\n\n\n\n\n\n\nDemographics\nGender\n\n\nMale\nFemale\n\n\n\n\nParticipants (n)\n12\n28\n\n\nCohorts\n\n\nHIV testing naïve\n3\n7\n\n\nResearch tester(enrolment in a research study)\n0\n12\n\n\nExperienced tester(previously tested for HIV)\n9\n9\n\n\nMean age (years of age) (range)\n25 (23–37)\n29 (18–48)\n\n\nMarital status\n\n\nSingle\n11\n28\n\n\nMarried\n1\n0\n\n\nEmployment status\n\n\n\n\nEmployed\n3\n8\n\n\nUnemployed\n9\n20\n\n\nAccess to HIV testing facility\n\n\nYes\n12\n28\n\n\nNo\n0\n0\n\n\n\n\n\nThirty (n = 30/40) participants were successfully contacted during Phase 2 of the study, approximately three months after their study visit (Fig 1). Ten participants were excluded from the analysis as eight were unreachable and two tested HIV positive at their study visit (Fig 1). Five male experienced testers, from a total of eight participants, were lost to follow-up. Two men and 12 women, who were experienced testers, underwent repeat testing during Phase 2, which included one female HIV testing naïve participant. Of the 16 participants who did not have a repeat test after their study visit, five were male (two HIV testing naïve and three experienced testers) and eleven females (five HIV testing naïve and six experienced testers).\n\n10.1371/journal.pone.0212343.g001\nFig 1\n\nUptake of HIV testing following exposure to two HIV testing approaches during Phase 2 of study and reasons for HIV testing behaviour.\n\n\n\n\nFactors that influence repeat HIV testing practice\nIn Fig 2, data on motivation to test for HIV at three time points including baseline (prior to their participation in the study), after exposure to HCT and HIVST in the study (T0) and during Phase 2, which followed their onsite study visit (T1) are presented. At T0, participant’s overall preference for either HCT or HIVST and motivation to test was examined. Whilst at T1, participants reported on their motivation to test and actual test (HCT or HIVST) used, which provided an important understanding of factors that influence repeat HIV testing behaviour.\n\n10.1371/journal.pone.0212343.g002\nFig 2\n\nOverview of HIV testing behaviour of participants who tested for HIV post study visit.\n\n\n\nData on HIV testing behaviour of participants who did not test for HIV during Phase 2 and analysed at two time points, baseline and following exposure to HCT and HIVST in the study (T0) are presented in Fig 3. HIV testing naïve participants were only assessed at T0 as they had no prior testing history. Overall, motivating factors for HIV testing included 1) HIV status awareness, 2) repeat testing as a precautionary measure in response to risk exposure, 3) extending repeat HIV testing to partners, 4) routine testing as part of ‘normal’ repeat HIV testing behaviour and 5) provider-initiated repeat HIV testing.\n\n10.1371/journal.pone.0212343.g003\nFig 3\n\nOverview of HIV testing behaviour of participants who did not test for HIV during Phase 2.\n\n\n\n\nHIV status awareness\nTwelve experienced testers and five HIV testing naïve participants reported a desire for HIV status awareness as their reason for an initial HIV test (Figs 2 and 3). However, during the study visits (Phase 1), HIV status awareness was not the primary reason for repeat HIV testing among the same participants (Figs 2 and 3). The desire for knowledge of one’s HIV status could be perceived as wanting to take control of their health by managing their HIV positive or negative status earlier. The pattern observed with HIV testing practice expressed in this study indicates HIV status awareness as the primary reason for routinely connecting an individual with HIV testing services, but secondary factors such as risk exposure may intermittently influence future testing (Fig 2). This behaviour may be driven by their desire to always be aware of their HIV status and was also indicative of their autonomy to test, as one participant mentioned.\n\n“I always have to know my HIV status, which is a good thing for me” (IDI, Female, RT, 0026).\n\nAs participants increased their frequency of repeat HIV testing, they may have been better equipped to discern when they required subsequent HIV testing test as HIV status awareness was no longer a primary reason for testing. This practice was evident through phase 2 data analysis (Fig 2),\n\n\nRepeat testing as a precautionary measure in response to risk exposure\nHIV risk exposure influenced initial HIV testing among six experienced testers and two HIV testing naïve participants (Figs 2 and 3). Interestingly, these eight participants were able to understand their risk and seek HIV testing services without prior risk reduction counselling. During the study visits (Phase 1), the majority of participants whose initial HIV test was due to risk exposure, exhibited HIV testing behaviour that ensured they had regular HIV testing (Figs 2 and 3), perhaps as a precautionary measure to ensure that they were aware of their HIV status in light of their risk exposure. Some participants were interested in repeat HIV testing during Phase 1, as they felt they might have been in the window period or as a result of recent exposure to HIV. Despite their regular testing practice, these participants were concerned that their status could change and needed to ensure that they could seek care earlier to manage their result. Protecting oneself by testing for HIV, following risk exposure, is important as it affords an individual the option to manage their result earlier by accessing treatment or prevention services.\n\n“I would need to test because I don’t know maybe at this moment I could still be in the window period” (IDI, Female, RT, 0022).\n“I needed to test, as I engaged in risky sex and the condom burst” (IDI, Male, RT, 0008).\n\n\n\nRoutine testing as part of ‘normal’ repeat HIV testing behaviour\nSeven participants who tested during the post study visit (Phase 2) reported routine testing as their reason for repeat testing upon entry into this study (Fig 2), which may be indicative of ‘normal’ testing behaviour. There was no direct link between reason for initial testing behaviour and routine testing practice during the study visit (Phase 1) testing (Fig 2). Although participants reported routine testing as their primary reason for repeat testing, the primary rationale for routine testing could be in keeping with testing as a precautionary measure linked to HIV status awareness and risk exposure.\n\n\nExtending repeat HIV testing to partners for regular testers\nOne female participant believed that her status had always been HIV negative and she should include her partner in the testing process as this would encourage her to test again for HIV. This highlighted the participant’s ability to be cognisant of the relationship between risk exposure and partner testing, where one should always know their partner’s HIV status.\n\n“I’m so used to testing, maybe if I was testing with my boyfriend I would test again” (IDI, Female, RT, 0028).\n\n\n\nProvider-initiated HIV testing\nOnly two participants reported provider-initiated HIV testing as part of their initial HIV testing practice. One participant underwent HIV testing at her antenatal clinic due to her pregnancy and the second participant tested as a prerequisite to circumcision. Provider-initiated HIV testing was an uncommon testing practice during enrolment into the study (Phase 1) (Figs 2 and 3). However, this testing practice was more frequent during follow-up repeat HIV testing (Phase 2) as six participants displayed this type of testing behaviour (Fig 2). Overall, the participants who accessed health care facilities, post study visit (Phase 2), for pregnancy outcome, contraception-related clinic visits and needle stick injury, reported provider initiated counselling and testing. Door-to-door HIV testing and testing at mobile clinics, and traditional healers who are trained to perform HIV tests and engage with individuals within households, contributed to uptake of HIV testing through community-based testing (Fig 4). Participants viewed community-based testing approaches as convenient opportunities for repeat testing as it was delivered to them and they did not have to leave their homes for testing.\n\n10.1371/journal.pone.0212343.g004\nFig 4\n\nInterrelationship of factors that influence repeat HIV testing practices.\n\n\n\n\n\nReasons for non-uptake of repeat HIV testing\nExperienced testers and HIV testing naïve participants reported no perceived risk and not having time to test, as reasons for not testing during Phase 2 of the study. Risk exposure, as outlined earlier, influenced uptake of repeat testing. Promoting repeat HIV testing behaviour among HIV testing naïve participants would be important to ensure continuity of their HIV status awareness. Perhaps testing during the study was adequate for these participants as time and no desire for repeat HIV testing were highlighted as reasons for non-uptake of HIV testing.\n\n\nInterrelationship of factors that influence repeat HIV testing practices\nWhile four primary factors (Fig 4) influenced HIV testing and repeat testing behaviour among experienced and HIV testing naïve participants, an interrelationship between routine testing, HIV status awareness and risk exposure emerged through which more frequent testing may occur to primarily determine HIV status (Fig 4). Similarly, continuous risk exposure may lead to routine testing for awareness of a person’s HIV status, resulting in repeat testing (Fig 4). Provider-initiated testing (Fig 4) may influence repeat HIV testing but may not be entirely voluntary in high endemic areas where testing is essential to guide clinical management of patients. Therefore, provider-initiated testing may not be linked to voluntary HIV status determination which in turn may limit repeat HIV testing.\n\n\nUptake of HIV self-testing as a repeat testing approach\nAll participants who tested during Phase 2 used traditional testing approaches such as HCT. It can be noted that one participant who regularly tested, purchased an HIVST kit from her pharmacy but did not use it as she gave it to a family member to use following their recent risk exposure (Fig 2). However, six participants who did not have a repeat HIV test reported a desire to test with HIVST for their next HIV test, of which four were HIV testing naïve participants (Fig 3). Accessibility to HIVST kits was influenced by affordability for five participants who did not have a repeat HIV test, as they were not in a financial position to purchase the kits (Fig 3). Importantly, HIVST could be included as a testing approach within the framework outlined in Fig 4 to prevent missed testing opportunities. For most participants who tested, reports that they were comfortable with their current testing approach and did not require testing with HIVST was noted.\nThe repeat HIV testing practice was influenced by the interrelationship between the desire for HIV status awareness, routine testing and risk exposure. Although initial HIV testing behaviour may begin with a desire for knowledge of HIV status, routine or regular testing behaviour may be due to risk exposure. This, in turn, leads to HIV status awareness or routine testing to allow constant awareness of HIV status to manage a HIV positive or negative result. HIV status awareness which has been highlighted as the primary reason for repeat testing, is important in reaching the first 90 of the 90-90-90 targets. Contrary to our study, sexual risk taking was proposed as the primary reason for repeat testing among people within a community in Hlabisa in KwaZulu-Natal [8]. Also, people who tested HIV negative were more likely to have a repeat HIV test, which contradicts evidence from other studies that highlighted that people were more likely not to have repeat testing if they tested negative [8, 10]. Therefore, the importance of repeat HIV testing practices should be encouraged during HIV testing campaigns in addition to first-time testing.The potential of HIVST as a repeat HIV testing approach was highlighted in this study as some participants considered using it despite the availability of HCT; however, missed testing opportunities, mainly among HIV testing naïve participants, were noted due to affordability of HIVST which limited its use. The potential of HIVST can be gleaned from some participants considering use of HIVST for their subsequent HIV test in Phase 2. Several studies advocated for the use of HIVST to increase the frequency of HIV testing [5, 13, 14], and to encourage testing among people who have not tested [9]. Further to this, scale-up of biomedical HIV prevention initiatives such as Pre-Exposure Prophylaxis and microbicides will require regular repeat HIV testing which may cause undue burden on already strained human resources within primary healthcare facilities [15, 16]. Therefore, the potential repeat HIV testing potential of HIV self-testing could be extended to these HIV prevention approaches to reduce the HIV testing burden on primary healthcare facilities. To our knowledge, the use of HIVST as a repeat testing approach with HIV prevention approaches is not yet in existence within sub-Saharan Africa. Thus, future research to evaluate the feasibility of HIVST for repeat HIV testing during implementation of HIV prevention initiatives.In South Africa, HIVST is primarily available from pharmacies at a cost. Thus, in addition to affordability, the accessibility of HIVST plays a role in the uptake of this HIV testing approach, as well as determining its potential effect on increasing the uptake of HIV testing. This study focused on motivation to test for HIV and preference for HCT or HIVST as a testing approach, but did not explore cost and accessibility of HIVST which are characteristic of feasibility studies. As the price of HIVST kits and access to these testing kits factored in participant’s decision to undergo repeat HIV testing, future research should be directed toward feasibility studies evaluating distribution models that will ensure cost-effective and easily accessible HIVST kits which, in turn, may promote the uptake of HIVST.A study in Uganda found that high-risk populations who have high rates of HIV and sexual risk behaviour, displayed an increased preference for HIVST for repeat testing [17]. Since risk exposure was identified as a factor that influences the repeat testing practice, HIVST may be an important addition to the HIV testing framework to increase uptake of repeat HIV testing. This study has several limitations. Firstly, the small sample size together with the use of purposive sampling with its selectiveness bias limits the generalizability of these findings as, the cohort is not representative of the primary target of HIVST. The cohort selected does represent individuals who may have a desire to test for HIV but may face barriers to repeat testing associated with available testing approaches such as HCT. Secondly, the study may have benefited from participants presenting at clinical research sites for follow-up visits to determine their uptake of HIVST which would have enabled us to further explore HIV testing behaviour. Thirdly, the outcome of repeat HIV testing may have been limited by the strict adherence to the three-months follow-up period as participants may have been found to have undergone repeat testing if the follow-up period was extended."]}, { "id":"10.1371/journal.pone.0212343/body", "doc_partial_parent_id":"10.1371/journal.pone.0212343", "doc_type":"partial", "journal_eissn":"1932-6203", "publisher":"Public Library of Science", "journal":"PLOS ONE", "journal_id_pmc":"plosone", "journal_id_publisher":"plos", "journal_id_nlm_ta":"PLoS ONE", "eissn":"1932-6203", "publication_date":"2019-02-22T00:00:00Z", "received_date":"2018-08-30T00:00:00Z", "accepted_date":"2019-01-31T00:00:00Z", "article_type":"Research Article", "article_type_facet":"Research Article", "author":["Charlene Harichund", "Pinky Kunene", "Sinenhlanhla Simelane", "Quarraisha Abdool Karim", "Mosa Moshabela"], "author_facet":["Charlene Harichund", "Pinky Kunene", "Sinenhlanhla Simelane", "Quarraisha Abdool Karim", "Mosa 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investigation", "/Research and analysis methods/Clinical trials/Phase II clinical investigation"], "subject_hierarchy":["/Biology and life sciences/Microbiology/Medical microbiology/Microbial pathogens/Viral pathogens/Immunodeficiency viruses/HIV", "/Biology and life sciences/Microbiology/Medical microbiology/Microbial pathogens/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Biology and life sciences/Organisms/Viruses/Immunodeficiency viruses/HIV", "/Biology and life sciences/Organisms/Viruses/RNA viruses/Retroviruses/Lentivirus/HIV", "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Immunodeficiency viruses/HIV", "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Medicine and health sciences/Clinical medicine/Clinical trials/Phase I clinical investigation", "/Medicine and health sciences/Clinical medicine/Clinical trials/Phase II clinical investigation", "/Medicine and health sciences/Diagnostic medicine/HIV diagnosis and 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and health sciences/Epidemiology/Medical risk factors", "/Medicine and health sciences/Health care/Health care facilities", "/Medicine and health sciences/Pathology and laboratory medicine/Pathogens/Microbial pathogens/Viral pathogens/Immunodeficiency viruses/HIV", "/Medicine and health sciences/Pathology and laboratory medicine/Pathogens/Microbial pathogens/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Medicine and health sciences/Pharmacology/Drug research and development/Clinical trials/Phase I clinical investigation", "/Medicine and health sciences/Pharmacology/Drug research and development/Clinical trials/Phase II clinical investigation", "/Medicine and health sciences/Public and occupational health/Preventive medicine/HIV prevention", "/Research and analysis methods/Clinical trials/Phase I clinical investigation", "/Research and analysis methods/Clinical trials/Phase II clinical investigation"], "subject_level_1":["Biology and life sciences", "Medicine and health sciences", "Research and analysis methods"], "striking_image":"10.1371/journal.pone.0212343.g004", "timestamp":"2026-03-14T06:51:16.715Z", "doc_partial_body":[" Introduction Despite the availability of several HIV testing approaches, HIV counselling and testing (HCT) is most commonly utilized and has utility for people who test for the first time [ 1 , 2 ]. However, the low self-perceived HIV risk, stigma, fear of social exclusion, inconvenient clinic hours and quality of HIV testing services are barriers to uptake of HCT [ 3 ], highlighting the need for additional testing options. The World Health Organization (WHO) recommends HIV self-testing (HIVST) as an additional HIV testing approach, to complement existing services associated with HCT [ 4 ]. The potential of HIVST to improve the uptake of HIV testing, when compared to traditional HIV testing approaches and its ability to increase the frequency of HIV testing among men who have sex with men (MSM) and male partners of heterosexual women, was recently reviewed [ 5 ]. While the uptake of HIV testing is primarily focused on individuals who test for the first time, enabling earlier diagnosis and management of participants, there is little data available on repeat HIV testing [ 6 ]. Repeat HIV testing is important, particularly for individuals in high HIV burden communities, and where partner change is frequent but safer sex practices are limited for multiple reasons [ 1 , 7 ]. Repeat HIV testing is also important as it ensures sustainability and the continued success of prevention programmes [ 8 ]. Survey data from sub-Saharan Africa report repeat testing rates from 26% to 87% [ 8 , 9 ]. Perceptions that a negative HIV result remains unchanged is a major barrier to repeat testing [ 10 ]. Offering HIVST as a testing approach together with HCT, may serve to increase repeat HIV testing rates [ 11 ]. This study assessed repeat HIV testing practices and the potential role of HIVST among repeat HIV testers, following exposure to HIVST. Materials and methods Participant selection Purposive sampling was used to recruit volunteers from either a primary health care clinic offering HIV testing services, which were adjacent to the Centre for the AIDS Programme of Research in South Africa (CAPRISA), or the CAPRISA research clinic. Volunteers recruited from the primary health care clinic were either those who have never had an HIV test (HIV naïve) or who previously had an HIV test (experienced tester). Participants from the CAPRISA clinic who were previously enrolled in a research study with a predetermined frequency of testing based on the study protocol (research tester). Consenting men and women older than 18 years of age, from each of these groups, were eligible for participation in this study. Study design The study was conducted in two phases. Phase 1 included a qualitative assessment of the participants’ HIV testing behaviour at two time points: baseline and after testing with both HIVST and HCT. Participants who tested positive for HIV were referred to appropriate facilities for further care and management. During Phase 2, participants were contacted telephonically, approximately three months after their study visit to determine their uptake of HIV testing and the testing approach used. Ethics approval (reference number: BFC326/15) for the study was obtained from the Biomedical Research Ethics Committee at the University of KwaZulu-Natal. Written informed consent was obtained prior to enrolment into the study. Data collection During study visits, two researchers who were trained in qualitative interviewing, conducted the in-depth interviews (IDIs), using interview guides ( S1 Fig ). Qualitative discussions focused on HIV testing practices and user experience with both HIV testing approaches (HCT and HIVST), and were recorded and transcribed by the study team. The demographic characteristics of each participant were also collected during their study visit at each clinical research site ( S2 Fig ). Telephonic follow-up interviews were undertaken by a research assistant using a structured interview schedule that included the following items: 1) Have you tested for HIV since your study visit? 2) Reason(s) for testing or not testing. 3) Have you considered HIV self-testing? 4) Reason(s) for HIVST or not. Participant responses were recorded in their study files. Four attempts at contacting participants at different time points over four weeks were completed before a participant was considered lost to follow-up. Data analysis The framework analysis method described by Rabiee (2004) was used to analyse the IDI transcripts ( S3 Fig ) [ 12 ]. This method included familiarisation of the data, identification of a thematic framework, indexing, charting, as well as mapping and interpretation [ 4 ]. Researcher one developed an initial list of theoretical and emerging codes from a sub-set of four transcripts. Researcher one, who was well versed with literature around HIV self-testing and HIV testing, employed the assistance of researcher two to assist with coding of transcripts. Researcher two was provided with in-depth training about the project and coding. Thereafter, both researchers independently followed the framework analysis method described by Rabiee in 2004 with two transcripts to verify codes and identify new emerging themes. Thereafter analysis, outcomes were discussed and compared to clarify themes and address inter-code discrepancies before proceeding with data analysis of all available transcripts. Theoretical and emergent thematic frameworks were identified by writing memos in the column of the written transcripts in the form of short phrases, ideas or concepts arising from the transcripts. Highlighting and sorting out quotes and making comparisons both within and between cases was conducted through indexing. Data was then charted, which involved removing quotes from their original context and rearranging them under their appropriate thematic content. The final step of the process, mapping and interpretation, involved axial coding and analysis of the data to identify the relationship between the quotes and the links between the data as a whole. The participants’ telephonic responses were collated, following the review of their study files and univariate analysis completed. Results Participants During Phase 1 of the study, 12 male and 28 female participants were enrolled across two clinical research cites ( Table 1 ), resulting in 80 IDIs being completed. The average age of the men and women were 25 and 27 years, respectively. The majority of participants were unemployed, and all participants had access to an HIV testing facility in their community ( Table 1 ). 10.1371/journal.pone.0212343.t001 Table 1 Demographic characteristics of participants during Phase 1. Demographics Gender Male Female Participants (n) 12 28 Cohorts HIV testing naïve 3 7 Research tester (enrolment in a research study) 0 12 Experienced tester (previously tested for HIV) 9 9 Mean age (years of age) (range) 25 (23–37) 29 (18–48) Marital status Single 11 28 Married 1 0 Employment status Employed 3 8 Unemployed 9 20 Access to HIV testing facility Yes 12 28 No 0 0 Thirty (n = 30/40) participants were successfully contacted during Phase 2 of the study, approximately three months after their study visit ( Fig 1 ). Ten participants were excluded from the analysis as eight were unreachable and two tested HIV positive at their study visit ( Fig 1 ). Five male experienced testers, from a total of eight participants, were lost to follow-up. Two men and 12 women, who were experienced testers, underwent repeat testing during Phase 2, which included one female HIV testing naïve participant. Of the 16 participants who did not have a repeat test after their study visit, five were male (two HIV testing naïve and three experienced testers) and eleven females (five HIV testing naïve and six experienced testers). 10.1371/journal.pone.0212343.g001 Fig 1 Uptake of HIV testing following exposure to two HIV testing approaches during Phase 2 of study and reasons for HIV testing behaviour. Factors that influence repeat HIV testing practice In Fig 2 , data on motivation to test for HIV at three time points including baseline (prior to their participation in the study), after exposure to HCT and HIVST in the study (T 0 ) and during Phase 2, which followed their onsite study visit (T 1 ) are presented. At T 0 , participant’s overall preference for either HCT or HIVST and motivation to test was examined. Whilst at T 1 , participants reported on their motivation to test and actual test (HCT or HIVST) used, which provided an important understanding of factors that influence repeat HIV testing behaviour. 10.1371/journal.pone.0212343.g002 Fig 2 Overview of HIV testing behaviour of participants who tested for HIV post study visit. Data on HIV testing behaviour of participants who did not test for HIV during Phase 2 and analysed at two time points, baseline and following exposure to HCT and HIVST in the study (T 0 ) are presented in Fig 3 . HIV testing naïve participants were only assessed at T 0 as they had no prior testing history. Overall, motivating factors for HIV testing included 1) HIV status awareness, 2) repeat testing as a precautionary measure in response to risk exposure, 3) extending repeat HIV testing to partners, 4) routine testing as part of ‘normal’ repeat HIV testing behaviour and 5) provider-initiated repeat HIV testing. 10.1371/journal.pone.0212343.g003 Fig 3 Overview of HIV testing behaviour of participants who did not test for HIV during Phase 2. HIV status awareness Twelve experienced testers and five HIV testing naïve participants reported a desire for HIV status awareness as their reason for an initial HIV test (Figs 2 and 3 ). However, during the study visits (Phase 1), HIV status awareness was not the primary reason for repeat HIV testing among the same participants (Figs 2 and 3 ). The desire for knowledge of one’s HIV status could be perceived as wanting to take control of their health by managing their HIV positive or negative status earlier. The pattern observed with HIV testing practice expressed in this study indicates HIV status awareness as the primary reason for routinely connecting an individual with HIV testing services, but secondary factors such as risk exposure may intermittently influence future testing ( Fig 2 ). This behaviour may be driven by their desire to always be aware of their HIV status and was also indicative of their autonomy to test, as one participant mentioned. “I always have to know my HIV status , which is a good thing for me” (IDI, Female, RT, 0026). As participants increased their frequency of repeat HIV testing, they may have been better equipped to discern when they required subsequent HIV testing test as HIV status awareness was no longer a primary reason for testing. This practice was evident through phase 2 data analysis ( Fig 2 ), Repeat testing as a precautionary measure in response to risk exposure HIV risk exposure influenced initial HIV testing among six experienced testers and two HIV testing naïve participants (Figs 2 and 3 ). Interestingly, these eight participants were able to understand their risk and seek HIV testing services without prior risk reduction counselling. During the study visits (Phase 1), the majority of participants whose initial HIV test was due to risk exposure, exhibited HIV testing behaviour that ensured they had regular HIV testing (Figs 2 and 3 ), perhaps as a precautionary measure to ensure that they were aware of their HIV status in light of their risk exposure. Some participants were interested in repeat HIV testing during Phase 1, as they felt they might have been in the window period or as a result of recent exposure to HIV. Despite their regular testing practice, these participants were concerned that their status could change and needed to ensure that they could seek care earlier to manage their result. Protecting oneself by testing for HIV, following risk exposure, is important as it affords an individual the option to manage their result earlier by accessing treatment or prevention services. “I would need to test because I don’t know maybe at this moment I could still be in the window period” (IDI, Female, RT, 0022). “I needed to test , as I engaged in risky sex and the condom burst” (IDI, Male, RT, 0008). Routine testing as part of ‘normal’ repeat HIV testing behaviour Seven participants who tested during the post study visit (Phase 2) reported routine testing as their reason for repeat testing upon entry into this study ( Fig 2 ), which may be indicative of ‘normal’ testing behaviour. There was no direct link between reason for initial testing behaviour and routine testing practice during the study visit (Phase 1) testing ( Fig 2 ). Although participants reported routine testing as their primary reason for repeat testing, the primary rationale for routine testing could be in keeping with testing as a precautionary measure linked to HIV status awareness and risk exposure. Extending repeat HIV testing to partners for regular testers One female participant believed that her status had always been HIV negative and she should include her partner in the testing process as this would encourage her to test again for HIV. This highlighted the participant’s ability to be cognisant of the relationship between risk exposure and partner testing, where one should always know their partner’s HIV status. “I’m so used to testing , maybe if I was testing with my boyfriend I would test again” (IDI, Female, RT, 0028). Provider-initiated HIV testing Only two participants reported provider-initiated HIV testing as part of their initial HIV testing practice. One participant underwent HIV testing at her antenatal clinic due to her pregnancy and the second participant tested as a prerequisite to circumcision. Provider-initiated HIV testing was an uncommon testing practice during enrolment into the study (Phase 1) (Figs 2 and 3 ). However, this testing practice was more frequent during follow-up repeat HIV testing (Phase 2) as six participants displayed this type of testing behaviour ( Fig 2 ). Overall, the participants who accessed health care facilities, post study visit (Phase 2), for pregnancy outcome, contraception-related clinic visits and needle stick injury, reported provider initiated counselling and testing. Door-to-door HIV testing and testing at mobile clinics, and traditional healers who are trained to perform HIV tests and engage with individuals within households, contributed to uptake of HIV testing through community-based testing ( Fig 4 ). Participants viewed community-based testing approaches as convenient opportunities for repeat testing as it was delivered to them and they did not have to leave their homes for testing. 10.1371/journal.pone.0212343.g004 Fig 4 Interrelationship of factors that influence repeat HIV testing practices. Reasons for non-uptake of repeat HIV testing Experienced testers and HIV testing naïve participants reported no perceived risk and not having time to test, as reasons for not testing during Phase 2 of the study. Risk exposure, as outlined earlier, influenced uptake of repeat testing. Promoting repeat HIV testing behaviour among HIV testing naïve participants would be important to ensure continuity of their HIV status awareness. Perhaps testing during the study was adequate for these participants as time and no desire for repeat HIV testing were highlighted as reasons for non-uptake of HIV testing. Interrelationship of factors that influence repeat HIV testing practices While four primary factors ( Fig 4 ) influenced HIV testing and repeat testing behaviour among experienced and HIV testing naïve participants, an interrelationship between routine testing, HIV status awareness and risk exposure emerged through which more frequent testing may occur to primarily determine HIV status ( Fig 4 ). Similarly, continuous risk exposure may lead to routine testing for awareness of a person’s HIV status, resulting in repeat testing ( Fig 4 ). Provider-initiated testing ( Fig 4 ) may influence repeat HIV testing but may not be entirely voluntary in high endemic areas where testing is essential to guide clinical management of patients. Therefore, provider-initiated testing may not be linked to voluntary HIV status determination which in turn may limit repeat HIV testing. Uptake of HIV self-testing as a repeat testing approach All participants who tested during Phase 2 used traditional testing approaches such as HCT. It can be noted that one participant who regularly tested, purchased an HIVST kit from her pharmacy but did not use it as she gave it to a family member to use following their recent risk exposure ( Fig 2 ). However, six participants who did not have a repeat HIV test reported a desire to test with HIVST for their next HIV test, of which four were HIV testing naïve participants ( Fig 3 ). Accessibility to HIVST kits was influenced by affordability for five participants who did not have a repeat HIV test, as they were not in a financial position to purchase the kits ( Fig 3 ). Importantly, HIVST could be included as a testing approach within the framework outlined in Fig 4 to prevent missed testing opportunities. For most participants who tested, reports that they were comfortable with their current testing approach and did not require testing with HIVST was noted. Discussion The repeat HIV testing practice was influenced by the interrelationship between the desire for HIV status awareness, routine testing and risk exposure. Although initial HIV testing behaviour may begin with a desire for knowledge of HIV status, routine or regular testing behaviour may be due to risk exposure. This, in turn, leads to HIV status awareness or routine testing to allow constant awareness of HIV status to manage a HIV positive or negative result. HIV status awareness which has been highlighted as the primary reason for repeat testing, is important in reaching the first 90 of the 90-90-90 targets. Contrary to our study, sexual risk taking was proposed as the primary reason for repeat testing among people within a community in Hlabisa in KwaZulu-Natal [ 8 ]. Also, people who tested HIV negative were more likely to have a repeat HIV test, which contradicts evidence from other studies that highlighted that people were more likely not to have repeat testing if they tested negative [ 8 , 10 ]. Therefore, the importance of repeat HIV testing practices should be encouraged during HIV testing campaigns in addition to first-time testing. The potential of HIVST as a repeat HIV testing approach was highlighted in this study as some participants considered using it despite the availability of HCT; however, missed testing opportunities, mainly among HIV testing naïve participants, were noted due to affordability of HIVST which limited its use. The potential of HIVST can be gleaned from some participants considering use of HIVST for their subsequent HIV test in Phase 2. Several studies advocated for the use of HIVST to increase the frequency of HIV testing [ 5 , 13 , 14 ], and to encourage testing among people who have not tested [ 9 ]. Further to this, scale-up of biomedical HIV prevention initiatives such as Pre-Exposure Prophylaxis and microbicides will require regular repeat HIV testing which may cause undue burden on already strained human resources within primary healthcare facilities [ 15 , 16 ]. Therefore, the potential repeat HIV testing potential of HIV self-testing could be extended to these HIV prevention approaches to reduce the HIV testing burden on primary healthcare facilities. To our knowledge, the use of HIVST as a repeat testing approach with HIV prevention approaches is not yet in existence within sub-Saharan Africa. Thus, future research to evaluate the feasibility of HIVST for repeat HIV testing during implementation of HIV prevention initiatives. In South Africa, HIVST is primarily available from pharmacies at a cost. Thus, in addition to affordability, the accessibility of HIVST plays a role in the uptake of this HIV testing approach, as well as determining its potential effect on increasing the uptake of HIV testing. This study focused on motivation to test for HIV and preference for HCT or HIVST as a testing approach, but did not explore cost and accessibility of HIVST which are characteristic of feasibility studies. As the price of HIVST kits and access to these testing kits factored in participant’s decision to undergo repeat HIV testing, future research should be directed toward feasibility studies evaluating distribution models that will ensure cost-effective and easily accessible HIVST kits which, in turn, may promote the uptake of HIVST. A study in Uganda found that high-risk populations who have high rates of HIV and sexual risk behaviour, displayed an increased preference for HIVST for repeat testing [ 17 ]. Since risk exposure was identified as a factor that influences the repeat testing practice, HIVST may be an important addition to the HIV testing framework to increase uptake of repeat HIV testing. This study has several limitations. Firstly, the small sample size together with the use of purposive sampling with its selectiveness bias limits the generalizability of these findings as, the cohort is not representative of the primary target of HIVST. The cohort selected does represent individuals who may have a desire to test for HIV but may face barriers to repeat testing associated with available testing approaches such as HCT. Secondly, the study may have benefited from participants presenting at clinical research sites for follow-up visits to determine their uptake of HIVST which would have enabled us to further explore HIV testing behaviour. Thirdly, the outcome of repeat HIV testing may have been limited by the strict adherence to the three-months follow-up period as participants may have been found to have undergone repeat testing if the follow-up period was extended. Conclusion Repeat testing practice is influenced primarily by desire for HIV status awareness and risk exposure. The potential for HIVST as an additional repeat testing approach exists but is limited due to affordability and accessibility as HIVST is not available within public healthcare facilities. The cost of HIVST requires further consideration to expand its accessibility to individuals whose desire for repeat HIV testing with HIVST is restricted by affordability. This study provided supporting evidence around repeat HIV testing practices that includes HIVST as an additional testing approach within the HIV testing framework. Supporting information S1 Fig Qualitative interview guide. (PDF) S2 Fig Demographic and locator information tool. (PDF) S3 Fig Transcripts from interviews. (DOCX) "]}, { "id":"10.1371/journal.pgph.0000293/body", "doc_partial_parent_id":"10.1371/journal.pgph.0000293", "doc_type":"partial", "journal_eissn":"2767-3375", "publisher":"Public Library of Science", "journal":"PLOS Global Public Health", "journal_id_pmc":"plosgph", "journal_id_publisher":"plos", "journal_id_nlm_ta":"PLOS Glob Public Health", "eissn":"2767-3375", "publication_date":"2022-03-31T00:00:00Z", "received_date":"2021-08-01T00:00:00Z", "accepted_date":"2022-03-02T00:00:00Z", "article_type":"Research Article", "article_type_facet":"Research Article", "author":["Sunil Pokharel", "Lisa J White", "Jilian A Sacks", "Camille Escadafal", "Amy Toporowski", "Sahra Isse Mohammed", "Solomon Chane Abera", "Kekeletso Kao", "Marcela De Melo Freitas", "Sabine Dittrich"], "author_facet":["Sunil Pokharel", "Lisa J White", "Jilian A Sacks", "Camille Escadafal", "Amy Toporowski", "Sahra Isse Mohammed", "Solomon Chane Abera", "Kekeletso Kao", "Marcela De Melo Freitas", "Sabine Dittrich"], "editor":["Ana Marcia de Sá Guimarães"], "editor_facet":["Ana Marcia de Sá Guimarães"], "pagecount":16, "volume":2, "issue":3, "elocation_id":"e0000293", "journal_name":"PLOS Global Public Health", "journal_key":"PLOSGlobalPublicHealth", "subject":["/Biology and life sciences/Molecular biology/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction/Reverse transcriptase-polymerase chain reaction", "/Computer and information sciences/Computer applications/Web-based applications", "/Medicine and health sciences/Diagnostic medicine", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Medical conditions/Infectious diseases", "/Medicine and health sciences/Medical conditions/Infectious diseases/Viral diseases/COVID 19", "/Medicine and health sciences/Medical conditions/Parasitic diseases/Malaria", "/Medicine and health sciences/Medical conditions/Tropical diseases/Malaria", "/Physical sciences/Mathematics/Applied mathematics/Algorithms", "/Research and analysis methods/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction/Reverse transcriptase-polymerase chain reaction", "/Research and analysis methods/Simulation and modeling/Algorithms"], "subject_hierarchy":["/Biology and life sciences/Molecular biology/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction/Reverse transcriptase-polymerase chain reaction", "/Computer and information sciences/Computer applications/Web-based applications", "/Medicine and health sciences/Diagnostic medicine", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Medical conditions/Infectious diseases", "/Medicine and health sciences/Medical conditions/Infectious diseases/Viral diseases/COVID 19", "/Medicine and health sciences/Medical conditions/Parasitic diseases/Malaria", "/Medicine and health sciences/Medical conditions/Tropical diseases/Malaria", "/Physical sciences/Mathematics/Applied mathematics/Algorithms", "/Research and analysis methods/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction/Reverse transcriptase-polymerase chain reaction", "/Research and analysis methods/Simulation and modeling/Algorithms"], "subject_facet":["/Biology and life sciences/Molecular biology/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction/Reverse transcriptase-polymerase chain reaction", "/Computer and information sciences/Computer applications/Web-based applications", "/Medicine and health sciences/Diagnostic medicine", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Medical conditions/Infectious diseases", "/Medicine and health sciences/Medical conditions/Infectious diseases/Viral diseases/COVID 19", "/Medicine and health sciences/Medical conditions/Parasitic diseases/Malaria", "/Medicine and health sciences/Medical conditions/Tropical diseases/Malaria", "/Physical sciences/Mathematics/Applied mathematics/Algorithms", "/Research and analysis methods/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction/Reverse transcriptase-polymerase chain reaction", "/Research and analysis methods/Simulation and modeling/Algorithms"], "subject_level_1":["Biology and life sciences", "Computer and information sciences", "Medicine and health sciences", "Physical sciences", "Research and analysis methods"], "striking_image":"10.1371/journal.pgph.0000293.g006", "timestamp":"2026-03-14T09:31:27.210Z", "doc_partial_body":[" Introduction The accurate and timely diagnosis of numerous infectious diseases is constrained by a lack of optimal diagnostic infrastructure and expertise, particularly at the point-of-care in low- and middle-income countries (LMICs) [ 1 ]. Rapid diagnostic tests (RDTs) provide a platform that is simple to use, cost effective and can provide rapid results; the use of malaria RDTs in malaria endemic settings has been shown to improve health outcomes [ 2 ]. However, outside of the widely used malaria RDT, available RDTs for many infectious diseases are limited by suboptimal accuracies and hence would benefit from being used as part of clearly defined diagnostic algorithms [ 3 ]. Diagnostic tests and their ability to detect a pathogen directly (antigenic or genomic material) or to detect infections by identifying the host response (antibody) have often formed part of diagnostic algorithms, where any decision to apply further tests is based on prior test results [ 4 , 5 ]. This ‘two-test algorithm’ approach to diagnosis has been successfully adopted for HIV and hepatitis B and C [ 4 , 5 ]. The currently recommended HIV testing algorithm includes a combination of two or three reactive tests, depending on the background infection prevalence [ 6 ]. The diagnostic algorithms currently used for hepatitis B virus (HBV) and hepatitis C virus (HCV) require a similar two-test approach, using either an enzyme immunoassay (EIA) or an RDT for the serological detection of hepatitis B surface antigen (HBsAg) or anti-HCV antibodies, with any positive serological results confirmed by viral detection using more expensive tests, such as nucleic acid testing [ 4 , 7 ]. Reverse transcription polymerase chain reaction (RT-PCR) offers high accuracy and remains the ‘gold standard’ for the diagnosis of COVID-19. However, its utility for universal screening and diagnosis is limited by its complexity, cost and turnaround time; it is therefore inaccessible to a large proportion of the global population who live in resource-poor settings [ 8 ]. RDTs to detect antigens of SARS-CoV-2, the virus that causes COVID-19, have been developed and are currently being evaluated, but are less accurate compared with the accuracy of RT-PCR [ 9 – 11 ]. A recent Cochrane review estimated that the sensitivity of antigen RDTs (Ag-RDTs) for COVID-19 is 72% (95% CI 64.7%–79%) in symptomatic patients and 58.1% (95% CI 40.2–74.1) in asymptomatic patients compared with RT-PCR tests [ 8 ]. Nevertheless, these RDTs are used at border screening points, for screening asymptomatic individuals who have been in contact with a case, and for mass population screening programmes [ 12 , 13 ]. The World Health Organization (WHO) recommends the use of Ag-RDTs for SARS-CoV-2 with >80% sensitivity and >97% specificity compared with RT-PCR for individuals who are symptomatic, meet the suspected case definition and/or are in a setting with a suspected outbreak, where the reference test (RT-PCR) is not available or has limited usefulness due to long turnaround times [ 14 ]. Nevertheless, confirmatory testing of an Ag-RDT result with RT-PCR should be performed wherever possible and a cautious interpretation of the result where confirmatory testing is not feasible is recommended. To optimise testing algorithms for different scenarios, it is critical to consider the trade-offs between the good accuracy but high costs and turnaround times of RT-PCR and the low costs and turnaround times but suboptimal accuracy of Ag-RDTs. Sequential testing algorithms for multiple causes of acute febrile illnesses using a diagnostic test for each aetiology have been explored previously [ 3 ]. The implementation of adaptive algorithms based on local epidemiology (disease prevalence) was found to predict better diagnosis and add value to available tests. In the current study, we build on this approach to compare the impact of two-test algorithms versus singular testing for COVID-19-testing use cases. We tested the diagnostic abilities of Ag-RDTs and RT-PCR when these tests were combined in a two-test algorithm and compared this with singular testing. Comparisons of diagnostic outcomes (true positives and true negatives) were made when the tests were applied in a high-prevalence scenario, akin to diagnostic testing of symptomatic cases in hospital settings, and a low-prevalence scenario, to represent point-of-entry or border screening for infections. We then compared the average turnaround times to receive results and the demand for tests for each of the testing strategies. A web-based application was also developed, which can help to optimise testing strategies in different use cases, depending on the expected testing demand, prevalence of infection in the population and available resources. Methods Definitions Singular testing means either one of the two tests is applied alone as the only diagnostic tool for screening and/or diagnostic purposes. This approach is adopted when an optimal diagnostic test is available at the point-of-care, for example, the malaria RDT, which is adopted as a singular test for the diagnosis of malaria [ 15 ]. In the present study, singular testing serves as a comparator. Combination testing involves two available tests being applied in either a sequential or a simultaneous testing algorithm, as described below. A combination testing strategy is used when the combination enhances the value of the tests in terms of clinical diagnosis and screening. Combination testing has previously been adopted for various infectious diseases, including HIV, HBV and HCV [ 4 , 5 ]. Sequential testing is considered to be more appropriate than simultaneous testing in terms of the demand for tests, logistics and resources required for its implementation and is preferred in practice; therefore, we have focussed on this approach. Nonetheless, the results of diagnostic outcomes (true and false positives and true and false negatives) described below also hold true for the corresponding simultaneous testing strategies. Sequential testing Tests are used sequentially, one after the other, with the second test used to confirm the result of the first test. There are two strategies that can be adopted: Strategy 1: Confirmatory testing for positive results. When performing confirmatory testing for positive results, the second test is applied only if the first test is positive. This approach optimises the specificity of combination testing at the expense of sensitivity, meaning false positives are minimised ( Fig 1A ). This approach has been widely used to confirm diagnoses of HIV, HBV and HCV [ 4 , 5 ]. 10.1371/journal.pgph.0000293.g001 Fig 1 Testing strategies. A. Confirmatory testing for positives, meaning every positive test triggers a follow up test. B. Confirmatory testing for negatives, meaning that every negative triggers a follow-up test. C. Simultaneous testing, meaning that both tests are performed at the same time and the patient is considered to have a positive result if both are positive. D. Simultaneous testing, meaning that both tests are performed at the same time, and if either test is positive the patient is considered to have a positive result. Strategy 2: Confirmatory testing for negative results When performing confirmatory testing for negative results, the second test is applied only if the first test is negative. This approach optimises the sensitivity of combination testing at the expense of specificity, meaning false negatives are minimised ( Fig 1B ). An example of this approach is the application of the Cepheid GeneXpert ® nucleic acid amplification test during tuberculosis screening as a follow-up test for suspected cases who return a negative sputum microscopy result [ 16 ]. Simultaneous testing During simultaneous testing, both tests are applied at the same time and the results are interpreted together. There are two possible approaches for the interpretation of test results under simultaneous testing. Strategy 3 If both test results are positive, then the case is considered to be positive for the infection. This approach optimises the specificity of combination testing at the expense of sensitivity, meaning false positives are minimised ( Fig 1C ). Strategy 4 If one of the test results is positive, then the case is considered to be positive for the infection. This approach optimises the sensitivity of combination testing at the expense of specificity, meaning false negatives are minimised ( Fig 1D ). The average time to results refers to the average turnaround time for a testing strategy, from the time of sample collection to the time of reporting of results to the patient from whom the sample was collected. Calculation of combined sensitivities and specificities of two-test algorithms Here, we describe the combined sensitivity and specificity of a two-test algorithm when the application of a confirmatory second test occurs based on either a positive or negative result of the prior test. The combined sensitivity and specificity of two tests with individual test sensitivities of k se 1 and k se 2 , and respective specificities of k sp 1 and k sp 2 when applied sequentially, with the second test applied as a confirmatory test for patients who test positive by the first test is represented by SE T 1 and SP T 1 and with the second test applied as a confirmatory test for patients who test negative by the first test is represented by SE T 2 and SP T 2 , are as follows: S E T 1 = k s e 1 * k s e 2 S P T 1 = 1 − ( 1 − k s p 1 ) ( 1 − k s p 2 ) S E T 2 = 1 − ( 1 − k s e 1 ) ( 1 − k s e 2 ) S P T 2 = k s p 1 * k s p 2 The changes in sensitivities and specificities with each of the testing strategies with corresponding changes in specificities and sensitivities compared with singular testing by either of the tests are supplied in the S1 Text . We discuss the impact on the combined accuracies with examples in the Results section. The calculations of test outcomes of true positives, false negatives, true negatives and false negatives for each of the testing approaches are provided in the S1 Text . It is important to note that confirmatory testing for positives using a sequential testing strategy (Strategy 1) and simultaneous testing considering a case to be positive if both test results are positive for the infection (Strategy 3) predict the same sensitivities and specificities and thus the same diagnostic outcomes (true and false positives and true and false negatives). Similarly, confirmatory testing for negatives using a sequential testing strategy (Strategy 2) and simultaneous testing considering a case to be positive if either one of the test results is positive (Strategy 4) predict the same sensitivities and specificities. Nevertheless, sequential testing strategies are preferred to simultaneous testing due to having lower turnaround times and fewer resource requirements. The equations for calculating turnaround times and second test volumes are included in the S1 Text . Conditional dependence between tests Conditional dependence between test results exists when the agreement of results between two tests differs from those that would be observed by chance alone. Unlike when tests are independent, the sensitivities and specificities of a second test differ according to whether the first test result was positive or negative. If there is positive dependence of one test on the other: The sensitivity of the second test among positives from the first test increases. The sensitivity of the second test among negatives from the first test decreases. The opposite is true for negative dependence. The influence of test dependence on the outcome of a combination of tests is adopted from a previously described method [ 17 ] and is described in detail in the S1 Text . Application of tests Assumptions We make the following assumptions in our model: The two tests used in combination were independent of each other, and the likelihood of a positive test was not dependent on the result of another test. The relaxation of this assumption is explored in the S1 Text . The likelihood that an individual tested positive for a disease depended on the test characteristics and disease status, irrespective of the stage of disease and corresponding viral load, presence of symptoms, and status of the host immune response. Model We used a simulation approach using R statistical software, version 3.6.2 [ 18 ] to compare the outcome of testing strategies when each of the tests was applied singularly or in sequential combination, with further testing occurring for patients with positive or negative prior test results. The model accounted for two tests for COVID-19, with previously defined sensitivity and specificity and turnaround times for results. The code to run the model and generate outputs is available at https://github.com/sunildrp/covid-testing-algo . Scenarios We used two hypothetical examples of use case scenarios. A high infection prevalence of 20,000/100,000 (20%) in the tested population. The high prevalence scenario represents hospital settings where individuals often present with symptomatic infection, and the primary aim of testing is to obtain a diagnosis of the disease for clinical management and isolation of cases. Available literature suggests a highly variable prevalence of COVID-19 infection in healthcare settings (3–71%, median 21%) [ 19 ]. A low infection prevalence of 50/100,000 (0.05%) in the tested population. The low infection prevalence scenario represents a situation where the tested individuals are usually asymptomatic and tests are used to screen for COVID-19, e.g. rapid mass testing of asymptomatic individuals in England [ 20 ] and point-of-entry or border screening programmes. Data The tests used for the simulation with their corresponding accuracy values are shown in Table 1 . The turnaround times from the time of sample collection to result using Ag-RDT and RT-PCR were assumed to be 30 minutes and 24 hours, respectively. Ag-RDTs are performed at the site of sample collection and produce results within 15–30 minutes [ 21 ]. For RT-PCR, samples must be transported to a laboratory, and it usually takes 24 hours or more for the results depending on the testing situation. 10.1371/journal.pgph.0000293.t001 Table 1 Model inputs: Sensitivities and specificities of COVID-19 tests. Test Sensitivity (%) Specificity (%) Source 1. Ag-RDT 70 97 * Assumption 2. RT-PCR 90 98 Systematic review and meta-analysis of nucleic acid amplification tests on respiratory tract samples [ 22 ] *The available sensitivity and specificity values of Ag-RDTs are measured relative to RT-PCR, with no direct information about their true performance in the population; the values vary widely across studies [ 8 , 10 , 23 ]. The input parameters for this analysis were empirically selected based on the available knowledge to reflect their true performance in the population. In the web-application, for pragmatic reasons, sensitivity and specificity of RT-PCR are pre-set to 100% to reflect the relationship between RT-PCR and Ag-RDTs and ease the comparison between two Ag-RDTs where the available test performance data are generated using RT-PCR as the reference standard. Outputs We calculated the true positives, true negatives, false positives, and false negatives for each of the single tests and for the sequential algorithms of two tests where further tests were applied to patients who were positive or negative for prior tests. We further calculated the sensitivity and specificity for the combinations of tests, the numbers of each test required and the average turnaround times for results. Web-based application We applied the same methods to develop a web-based application using R [ 18 ] and an interactive web-based interface using the R “Shiny” package [ 24 ]. The web application takes the population size being tested, infection prevalence in the tested population, diagnostic test accuracies and turnaround times for each test as inputs and calculates the test outcomes, the numbers of each test needed and the average turnaround times for each singular test and the two-test algorithms. The application also allows users to explore the impact of conditional dependence between the tests if it exists, given the availability of reliable data. The Foundation for Innovative New Diagnostics (FIND) and other diagnostics partners are already using the tool to provide technical assistance to ministries of health around the world. Feedback from early users of the tool, obtained during the provision of technical assistance to the government of Somalia, has been used to improve subsequent iterations of the tool. Virtual meetings were organized to train the early users (including JAS, CE, AT, SIM, SCA, KK, MDMF) of the web application and subsequent feedbacks were sought through virtual meetings and email correspondences. Revisions were made in the design of the interface to enhance user friendliness and outputs of the tools were modified to meet the need of the users. Results Sensitivity and specificity of two-test algorithms Sensitivities and specificities of two-test algorithms are unaffected by disease prevalence and are thus applicable in both high- and low-prevalence scenarios. Also, the sensitivities and specificities of the two-test algorithms are the same irrespective of the order in which the tests are performed. That is to say, the algorithm of an Ag-RDT followed by RT-PCR and that of RT-PCR followed by an Ag-RDT have the same diagnostic performance. In practice, however, the cheaper and easier test would likely be chosen as the primary test, rather than the more resource intensive test. As an Ag-RDT is the preferred first test followed by confirmatory testing with RT-PCR, we focussed on the algorithm comprising an Ag-RDT followed by RT-PCR testing. The sensitivity and specificity of the algorithm when RT-PCR is performed on patients who received a negative Ag-RDT result are 97% and 95.06%, respectively ( Fig 3 ). By using this approach to maximise the sensitivity of testing, there is a gain in sensitivity of 27% compared with that of the Ag-RDT alone, with a loss of specificity of 1.94%. Compared with that of the RT-PCR test alone, there is a gain in sensitivity of 7% and a loss of specificity of 2.94%. The sensitivity and specificity of the algorithm when RT-PCR is performed on patients who received a positive Ag-RDT result are 63% and 99.94%, respectively. With this approach to maximise the specificity of testing, there is a gain in specificity of 2.94% compared with that of the Ag-RDT alone, with a loss of sensitivity of 7%. Compared with that of the RT-PCR test alone, there is a gain in specificity of 1.94% and a loss of sensitivity of 27% ( Fig 2 ). 10.1371/journal.pgph.0000293.g002 Fig 2 Sensitivity and specificity of combination testing compared with singular testing. The sensitivities and specificities of two-test algorithms are independent of the order of testing. Test outcomes in high- and low-prevalence scenarios We simulated the application of tests as standalone diagnostics or in two-test algorithms in 100,000 individuals and predicted the test outcomes for hospital use-cases with a high prevalence of infection and public health screening use-cases with a low prevalence of infection. Hospital use-case with a high prevalence of infection The aim of testing in hospital settings is to confirm the diagnosis of suspected cases, optimise the correct identification of cases, and minimise false-positive results. The application of an Ag-RDT or RT-PCR as standalone tests in a population of 100,000 with 20,000 infected individuals (infection prevalence of 20,000/100,000, or 20%) resulted in the correct identification of 14,000 and 18,000 individuals with infections, respectively, with corresponding false-positive results of 2,400 individuals using Ag-RDT alone and 1,600 individuals using RT-PCR alone. The application of both tests in the two-test algorithm, when RT-PCR was applied as a confirmatory test in patients who tested positive by Ag-RDT, resulted in the correct identification of 12,600 individuals and missed 7,400 individuals with infection. This approach minimised the false-positive results to 48 individuals ( Fig 3A ). In contrast, application of RT-PCR in patients who tested negative by Ag-RDT resulted in the correct identification of 19400 individuals with infection, but generated false positive results in 3952 in patients without infection. The population undergoing testing in a day, or a week may be much smaller in an actual hospital setting, but the trade-off between the correct identification of cases (true positives) and false positives holds a similar relationship, where the application of RT-PCR as a confirmatory test for individuals who test positive by Ag-RDT can largely minimise false-positive results, and prevent unnecessary treatment and distress among patients without infection. However, this should be cautiously weighted with the impact on community transmission with high number of missed cases. 10.1371/journal.pgph.0000293.g003 Fig 3 Test outcomes by testing strategy in (A) a high-prevalence scenario and (B) a low-prevalence scenario. Public health screening use-case with a low prevalence of infection The low-prevalence scenario represents a public health screening use-case, for example, border screening programmes, where the aim of testing is to maximise the identification of individuals with asymptomatic infections and minimise false-negative results to reduce the importation of cases and subsequent transmission of infection. The application of an Ag-RDT or RT-PCR as standalone screening tests in a population of 100,000 with 50 infected individuals (infection prevalence of 50/100000, or 0.05%) resulted in the correct identification of 35 and 45 individuals with infections, respectively, with corresponding false-negative results of 15 and 5 individuals, and false positives of 2999 and 1999 individuals, respectively. The application of both tests in the two-test algorithm, when RT-PCR was applied as a second screening test in patients who tested negative by Ag-RDT, resulted in the correct identification of 48 individuals with infection, reducing the false-negative results to 2 individuals ( Fig 3B ). This approach however generated false positive results in 4938 individuals without infections. In contrast, application of RT-PCR in individuals who tested positive with Ag-RDT resulted in correct identification of 32 individuals with infection and produced false negative and false positive results in 18 and 60, individuals, respectively. Implications for test logistics and turnaround times for results The predicted number of second tests required and the turnaround times for results for the algorithm involving an Ag-RDT followed by RT-PCR are shown in Figs 5 and 6 , respectively. Noting that the number of Ag-RDTs would be equal to the total population size being tested, the different number of RT-PCR tests required to carry out different testing strategies is the major impact on cost and access to testing. For example, demand for RT-PCR tests when applied as a confirmatory test in patients who test positive by Ag-RDT is limited to 16,400 and 3,034 tests in the high- and low-prevalence scenarios, respectively ( Fig 4 ), rather than 100,000 tests from each scenario when it was used as a standalone test. For the other side, only a small decrease in the number of RT-PCR tests would be observed if this test were needed to confirm negative results. 10.1371/journal.pgph.0000293.g004 Fig 4 Number of RT-PCR tests. The required quantity of RT-PCR tests when applied as a second test in the two-test algorithm differed by testing strategy and infection prevalence. It corresponds to the population being tested (100,000) when used as a single test. 10.1371/journal.pgph.0000293.g005 Fig 5 Average time taken to receive results (hours), based on assumed turnaround times of individual tests. The turnaround time for a testing strategy is the duration from sample collection to reporting of results to the patient from whom the samples were collected. 10.1371/journal.pgph.0000293.g006 Fig 6 Bar diagrams showing the assessment of test algorithms in various scenarios. A. Confirmatory testing for positives in a high prevalence scenario. B. Confirmatory testing for negatives in a high prevalence scenario. C. Confirmatory testing for positives in a low prevalence scenario. D. Confirmatory testing for negatives in a low prevalence scenario. Interpretation: the darker the graph, the better the algorithm; TP = true positive, TN = true negative, FP = false positive, FN = false negative; the percentage of the test population who do not require a second test is a proxy for the cost-effectiveness of the algorithm; speed of results = number of tests per 100 people per hour i.e., 100/average time to results. A substantial reduction in the average turnaround time for results was observed when RT-PCR was applied as a confirmatory test in patients who tested positive by Ag-RDT, i.e., 4.44 and 1.23 hours in the high- and low-prevalence scenarios, respectively, compared with 24 hours when the RT-PCR test was used alone ( Fig 5 ).However, when applied the other way around to confirm negative results, only a small decrease in the number of RT-PCR tests required was observed. The impact of sensitivity, specificity, test results, percentage of the population not needing a second test (based on the second test’s requirements), and speed of test results (based on the average time to receive results) for each algorithm–scenario pair on choosing an appropriate algorithm is illustrated in Fig 6 . The methodology presented here has also been used as part of ongoing country consultations as part of the COVID-19 ACT-Accelerator Diagnostic Pillar to support countries with the implementation of the Ag-RDT ( Box 1 ). Box 1. A real life use case, describing the utilisation of the app as part of ongoing support activities with partners in Sub-Saharan Africa. The example presented represents the situation in Somalia and serves only as an example to illustrate the utility of this work to support global implementation of simple tools to mitigate the impact of COVID-19. How to utilise the Ag-RDTs in Somalia : In discussions with a team from the Ministry of Health in Somalia, the application was used to demonstrate the differences in the outcomes when the RT-PCR and various Ag-RDTs were used. The specific use case the team from the MoH were aiming to address was mass testing to a “target population” as well as testing of the “general population”. The target population was defined as symptomatic people, health care workers, high risk groups in confirmed outbreaks and contacts of confirmed cases. The general population was defined as non-symptomatic people, people at schools, workplaces, religious institutions, and port of entry. Although, an algorithm of Ag-RDT and RT-PCR was found to be the most sensitive approach, alternatives had to be found as RT-PCR capacity is currently limited in Somalia. To compensate of the limited access to molecular testing capacity, the team explored the use of multiple Ag-RDTs as a pragmatic alternative. The available estimates on the diagnostic performance characteristics of two Ag-RDTs were used to compare the possible testing strategies, combining the tests in a sequential order (SD Biosensor–SD Biosensor, SD Biosensor–Panbio, Panbio–Panbio). To allow a simple and pragmatic assessment of the times the testing strategy will give the wrong results the team established a simple error rate—measure. This was defined as the percentage of false diagnoses, either false positives or false negatives, out of the total population undergoing testing. These error rates together with positive and negative predictive values were used as the key outcomes. The app was used to calculate the aforementioned values and output was compared by the team to inform the testing strategy and its pros and cons in the local context. This iterative, data driven approach ensured that informed decisions could be taken and recommendation on the choice of algorithms were made based on the outcomes and error rate as well as final test availability. Even if the best options (RT-PCR) were limited to the team in Somalia, the simple web-application presented here allowed the team to make informed decisions and be aware of the bottle necks of their strategies. Disclosure of this consultation in scientific publication has been done in accordance with approval from the MoH in Somalia. Discussion To better understand the application of multiple available tests in the diagnosis of and screening for a disease, this work explored strategies for combining tests in various use cases. The intention was to assist health authorities in choosing an appropriate combination testing strategy for infectious diseases such as COVID-19, optimising strategies for high sensitivity or specificity as needed and making the best possible use of available resources. The high-prevalence scenario is representative of testing in hospitals to confirm diagnoses of symptomatic patients and inform their clinical management. The current recommendation for diagnostic testing in hospital settings is restricted to RT-PCR in most countries [ 25 ]; however, such capacity is often limited to central laboratories [ 26 , 27 ]. The prolonged sample to result time for RT-PCR can propagate the dissemination of infection, particularly if testing is highly centralised [ 13 , 28 ]. Screening programmes aim to promptly identify infected, often asymptomatic individuals in community settings or limit the importation of cases across borders and isolate any infected individuals to suppress transmission [ 29 ]. The high cost and complexity of RT-PCR and the limited sensitivity of the available Ag-RDTs discourages the application of either when screening large populations. The application of a two-test algorithm in the hospital use-cases using an Ag-RDT followed by confirmatory RT-PCR testing of positive samples substantially reduced the false-positive rates, average turnaround times for results and RT-PCR test volumes compared with these values for RT-PCR testing alone. Reduction in false positives prevents unnecessary treatment and distress among patients without infection, reduction in average turnaround time benefits rapid identification of cases and curbs community transmission, and reduction in RT-PCR testing requirement has great value in optimizing scarce resources, especially in low resource settings. Nevertheless, given the negative impact of such a combination strategy on the sensitivity of testing, this approach increases false negative rate with potential impact on community transmission due to missed cases. Any negative test results should be interpreted with care, taking into consideration the pre-test probability of disease [ 8 , 30 ]. As there exists an association of various COVID-19 symptoms and course of illness with test results, the application of two-test algorithm cannot occur in isolation, rather, decision for testing needs to be individualized to patients and account for their clinical presentation and course of infection. Similarly, application of the tests in a confirmatory algorithm to optimise the sensitivity of screening programmes, where RT-PCR was used for samples that tested negative by Ag-RDT, increased the correct identification of cases, but at the cost of an increased number of false-positive results. A positive result with such an algorithm should be interpreted cautiously, as increased false-positive results in such a strategy can lead to the unnecessary isolation of individuals and distress among the wider population. When formulating a testing strategy for a particular use case, we must weigh the contextual value of the sensitivity and specificity of testing against the turnaround time for results and available resources [ 13 ]. A ‘one-size fits all’ approach is inappropriate [ 31 ]. When developing context-specific optimisation, multiple tests in an algorithm should be considered, to obtain the most productive output. For example, COVID-19 presents as a syndrome, showing fever and respiratory symptoms and can often not be clinically differentiated from the spectrum of other pathogens that cause respiratory infections or undifferentiated fevers [ 32 ]. While currently all focus is on COVID-19, going forward an integrated approach to the application of diagnostics for febrile illnesses should include other prevalent aetiologies [ 3 ]. The present analysis and the associated web application allow users to combine two tests for COVID-19 but also other infectious diseases and estimate the outcomes of algorithms for a combination of tests. Despite the utility, our study has some limitations given the assumptions made in the analysis. In the absence of reliable data, the current analysis assumes that tests used in combination were independent of each other, and the likelihood of testing positive by a test was not dependent on the result of another test, which might have missed interactions between test results. Our analysis did not account for potential differences in test performances depending on the test population (e.g. asymptomatic versus symptomatic; acute versus screening). The input data for the test accuracy estimates were obtained from independent clinical studies of symptomatic infections, yet data are emerging that suggest a lower performance of Ag-RDTs in asymptomatic populations [ 8 ]. The analysis did not incorporate the possible effects of the stage of disease, corresponding viral load, and the status of host-immune responses on the test outcomes. Nevertheless, the web application allows users to run their own analysis with a context-specific, relevant test combination (e.g. Ag-RDT and RT-PCR or two different RDTs) with more realistic input data for their testing population and incorporate test-dependence in their analysis. We did not include any economic analysis of the algorithms; rather, we focussed on the test volumes. Nevertheless, end users can directly calculate the cost of tests for their specific scenario based on output test volumes. Available diagnostic tests against various infectious diseases, including COVID-19, have limitations in their utility as standalone diagnostics at the point-of-care. A combination of available tests, using appropriate algorithms, should be considered to enhance the utility of these tests in clinical and public health decision-making [ 33 ]. The implications of the performance characteristics of a test, their availability for use, and turnaround times for results should be weighed cautiously against the contextual priorities of use cases when determining testing strategies [ 34 , 35 ]. The algorithm and the web tool we have developed will assist in making these decisions. Supporting information S1 Text (DOCX) "]}, { "id":"10.1371/journal.pone.0058732/body", "doc_partial_parent_id":"10.1371/journal.pone.0058732", "doc_type":"partial", "journal_eissn":"1932-6203", "publisher":"Public Library of Science", "journal":"PLoS ONE", "journal_id_pmc":"plosone", "journal_id_publisher":"plos", "journal_id_nlm_ta":"PLoS ONE", "eissn":"1932-6203", "publication_date":"2013-03-20T00:00:00Z", "received_date":"2012-11-29T00:00:00Z", "accepted_date":"2013-02-05T00:00:00Z", "article_type":"Research Article", "article_type_facet":"Research Article", "author":["Nicholas J Wald", "Jonathan P Bestwick"], "author_facet":["Nicholas J Wald", "Jonathan P Bestwick"], "editor":["Cees Oudejans"], "editor_facet":["Cees Oudejans"], "pagecount":6, "volume":8, "issue":3, "elocation_id":"e58732", "journal_name":"PLOS ONE", "journal_key":"PLoSONE", "subject":["/Biology and life sciences/Molecular biology/Molecular biology techniques/Marker genes/Selection markers", "/Biology and life sciences/Molecular biology/Molecular biology techniques/Sequencing techniques/DNA sequencing", "/Biology and life sciences/Neuroscience/Reflexes", "/Medicine and health sciences/Clinical genetics/Chromosomal disorders/Down syndrome", "/Medicine and health sciences/Diagnostic medicine/Diagnostic radiology/Ultrasound imaging", "/Medicine and health sciences/Diagnostic medicine/Prenatal diagnosis/Amniocentesis", "/Medicine and health sciences/Epidemiology/Medical risk factors", "/Medicine and health sciences/Radiology and imaging/Diagnostic radiology/Ultrasound imaging", "/Medicine and health sciences/Surgical and invasive medical procedures/Obstetric procedures/Amniocentesis", "/Medicine and health sciences/Women's health/Maternal health/Pregnancy", "/Medicine and health sciences/Women's health/Obstetrics and gynecology/Pregnancy", "/Research and analysis methods/Imaging techniques/Diagnostic radiology/Ultrasound imaging", "/Research and analysis methods/Molecular biology 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sciences/Women's health/Maternal health/Pregnancy", "/Medicine and health sciences/Women's health/Obstetrics and gynecology/Pregnancy", "/Research and analysis methods/Imaging techniques/Diagnostic radiology/Ultrasound imaging", "/Research and analysis methods/Molecular biology techniques/Marker genes/Selection markers", "/Research and analysis methods/Molecular biology techniques/Sequencing techniques/DNA sequencing"], "subject_facet":["/Biology and life sciences/Molecular biology/Molecular biology techniques/Marker genes/Selection markers", "/Biology and life sciences/Molecular biology/Molecular biology techniques/Sequencing techniques/DNA sequencing", "/Biology and life sciences/Neuroscience/Reflexes", "/Medicine and health sciences/Clinical genetics/Chromosomal disorders/Down syndrome", "/Medicine and health sciences/Diagnostic medicine/Diagnostic radiology/Ultrasound imaging", "/Medicine and health sciences/Diagnostic medicine/Prenatal diagnosis/Amniocentesis", "/Medicine and health sciences/Epidemiology/Medical risk factors", "/Medicine and health sciences/Radiology and imaging/Diagnostic radiology/Ultrasound imaging", "/Medicine and health sciences/Surgical and invasive medical procedures/Obstetric procedures/Amniocentesis", "/Medicine and health sciences/Women's health/Maternal health/Pregnancy", "/Medicine and health sciences/Women's health/Obstetrics and gynecology/Pregnancy", "/Research and analysis methods/Imaging techniques/Diagnostic radiology/Ultrasound imaging", "/Research and analysis methods/Molecular biology techniques/Marker genes/Selection markers", "/Research and analysis methods/Molecular biology techniques/Sequencing techniques/DNA sequencing"], "subject_level_1":["Biology and life sciences", "Medicine and health sciences", "Research and analysis methods"], "striking_image":"10.1371/journal.pone.0058732.g002", "timestamp":"2026-03-14T01:56:22.950Z", "doc_partial_body":[" Introduction The testing of cell-free DNA circulating in maternal plasma offers an effective means of screening for Down's syndrome with detection rates (proportion of affected pregnancies with positive results) of 98% or more and false-positive rates (proportion of unaffected pregnancies with positive results) of about 0.2% or less [1] – [7] . At present such DNA testing tends to be expensive (cited as being charged $795 to $2762 in the United States [6] ) and requires specialist expertise available in only a few laboratories. In about 2–13% of pregnancies a result cannot be obtained for various reasons including insufficient fetal DNA in the maternal plasma. These can be referred to as test failures and tend to be ignored in describing the efficacy of the test. One study [1] reported 11.5% (compromised sample, haemolyzed sample, inadequate volume, failed quality control). Another reported a test failure rate of 3.4% (0.88% assay failure and 2.50% of samples inadequate [2] ). A third study reported that 16 out of 532 pregnancies (3%) yielded insufficient fetal DNA and could not be tested and 4 out of 96 Down's syndrome pregnancies (4.2%; 3 mosaics) yielded an unidentifiable result as well as 24 out of 426 unaffected pregnancies (5.6%) suggesting a test failure rate of 7% [3] . A fourth study reported that in one group 5% did not meet “QC criteria”, but none in a second group of the same size [4] . In a fifth study based on women undergoing routine screening, results were not obtained on 4.9% of samples [5] . In a sixth study, based on a mixture of women with positive conventional screening tests for Down's syndrome and women undergoing routine screening, 1.6% failed the quality control criteria [5] . In a seventh study 21 out of 166 samples did not pass the DNA quality test (13%) [7] . We here propose a screening protocol arising from, and improving on, an idea previously reported [8] , that merges existing methods based on fetal ultrasound measurements and immunoassays with the newer DNA techniques in a way that would substantially reduce the cost compared with the cost of universal DNA testing and still achieve a high screening performance, that is, a high detection rate for a low false-positive rate. The proposed protocol, which is outlined in Figure 1 , uses the first trimester stage of an Integrated test (late first trimester measurement of the ultrasound marker nuchal translucency [NT] and the serum markers free β-human chorionic gonadotropin [hCG] and pregnancy associated plasma protein-A [PAPP-A] with maternal age; the Combined test) to determine which women would receive an automatic DNA sequencing test on the sample already collected. The automatic application of a second test in this way can be referred to as “reflex” DNA testing, ie. one triggered by the result of the first test. All women who do not receive a DNA test result proceed to have the second part of the Integrated test which includes the re-use of maternal age and the NT, free β-hCG and PAPP-A measurements together with early second trimester measurement of the serum markers alphafetoprotein [AFP], unconjugated estriol [uE 3 ] and inhibin-A. Typically the Integrated test uses an hCG (total or the free β) measurement in the second trimester, but in the proposed protocol it is measured in the first trimester instead. 10.1371/journal.pone.0058732.g001 Figure 1 Protocol for reflex DNA testing in conjunction with Integrated test screening. The proposal provides a practical solution to the problem that while DNA testing is an effective screening method it is expensive and can be done only at a small number of laboratories. We offer a solution to this by using the existing screening tests based on serum markers and an ultrasound marker used at a very low false-positive rate to identify a higher risk group, such that only the higher risk women need to have the DNA testing. Importantly, this entails little loss in screening performance. Methods Screening performance of the protocol was estimated as follows. Multivariate Gaussian distribution parameters (means, standard deviations and correlation coefficients) of the screening markers from a large cohort study (the Serum Urine and Ultrasound Screening Study [SURUSS]) [9] , revised to incorporate subsequent improvements [10] , were used to simulate 500,000 Down's syndrome pregnancies and 500,000 unaffected pregnancies, each with a set of marker values (first trimester marker values measured at 11 completed weeks' gestation). Each simulated pregnancy was assigned a maternal age based on the distribution of maternities in England and Wales from 2006 to 2008 inclusive (the latest available at the time the study was performed) [11] and the maternal age-specific odds of an affected livebirth [12] – [14] . For each simulated pregnancy, a risk of being affected with Down's syndrome based on the first stage of the Integrated test (NT, free β-hCG and PAPP-A) was calculated by multiplying the maternal age-specific odds of having an affected live birth (adjusted to early second trimester by multiplying by 1/0.77 to allow for the general fetal loss in Down's syndrome pregnancies from this time in pregnancy until term [14] ) by the likelihood ratio for being affected (for the simulated set of marker values) which was calculated from the multivariate Gaussian distributions of NT, free β-hCG and PAPP-A levels in affected and unaffected pregnancies. The risk cut-offs that yielded initial false-positive rates of 10%, 20%, 40%, 60%, 80% and 90% were determined. A DNA result for those with a risk greater than or equal to the calculated risk cut-off levels was generated. The test failure rate was taken as 3% (towards the lower range of estimates because in some instances a repeat sample may be obtained and provide a test result and these are not considered as test failures in our analyses). 97% were assigned a successfully completed DNA test and 3% were not. Of those in which DNA testing was assumed to have been successfully completed, screening performance was taken from Palomaki et al. [2] as being typically within the range of estimates, so 98.6% of the simulated Down's syndrome pregnancies and 0.2% of the simulated unaffected pregnancies were randomly classified as being screen positive based on DNA sequencing. For those initially classified low risk, and for those in whom DNA testing failed, an Integrated test risk of being affected with Down's syndrome was calculated re-using the first trimester markers together with the second trimester markers. Those with an Integrated test risk greater than 1 in 50 were classified as being screen positive. Overall detection and false-positive rates were estimated, and compared with estimates based on all women having a DNA test. The estimated screening performance was compared with universal DNA testing based on (i) offering women with failed tests a diagnostic test, treating them as screen positive, so yielding a 3.0% false-positive rate, which with the 0.2% test false-positive rate sums to 3.2% or (ii) offering women a second trimester Quadruple test (AFP, uE 3 , hCG and inhibin-A; 85% detection rate for a 5% false-positive rate) [10] . A similar analysis was done based on using the Combined test (NT, free β-hCG and PAPP-A) only. We estimated the cost of the screening protocol per woman as a multiple of the cost of an Integrated test. If C IT is the cost of an Integrated test, C DNA the cost of a DNA test, a the proportion of the Integrated test cost incurred in the first trimester, b the proportion of the Integrated test cost incurred in the second trimester and P the proportion of women who have DNA testing (i.e. the positive rate of the initial stage of the Integrated test), the cost per woman screened is:- i.e. the cost of the first stage of an Integrated test, plus the cost of a DNA test in women who have a DNA test plus the cost of the second stage of the Integrated test in women who do not have a DNA test plus the cost of the second stage of the Integrated test in women who have a DNA test, but the test failed. Because a + b  = 1, b  = 1- a , and after dividing throughout by C IT and rearranging, the cost per woman screened as a multiple of the cost of the Integrated test is given by the following equation So if a is 75%, P is 10% and the DNA test is 20 times more expensive than the Integrated test, the cost per woman screened as a multiple of the Integrated test cost is 1+[0.97×0.1×(0.75−1)]+20×0.1 = 3.0. A similar analysis was performed using the protocol applied to the Combined test. The cost per woman screened as a multiple of the Combined test is Results Figure 2 is a flow diagram showing an example of the effect of DNA sequencing in conjunction with the Integrated test in 100,000 pregnancies (including 286 with Down's syndrome based on the early second trimester prevalence [11] – [15] ). The first trimester risk cut-off to achieve an initial false-positive rate of 20% based on NT, free β-hCG, and PAPP-A was 1 in 1,600. Women with a risk estimate greater than or equal to this risk cut-off have a reflex DNA test. A test result is not reported at this stage. The remaining women continue to have the second part of the Integrated test. The figure shows 275 (96%) affected and 19,943 (20%) unaffected pregnancies have a reflex DNA test. For 3% of these women the DNA test fails (8 affected, 598 unaffected). These women have second trimester markers measured and an Integrated test risk is reported. Among women who have a completed DNA test, 263 affected and 38 unaffected pregnancies have a positive result. Among the women whose DNA test failed and the women who were not selected for DNA testing after the first trimester stage of the Integrated test, 8 affected and 44 unaffected pregnancies are positive based on the completed Integrated test (risk ≥1 in 50). The overall screening performance is an estimated detection rate of 95% (271/286) with a false-positive rate of 0.1% (82/99,714). 10.1371/journal.pone.0058732.g002 Figure 2 Protocol for reflex DNA testing in conjunction with Integrated test screening in which 20% of women at highest risk using NT, PAPP-A, and free β-hCG (first part of the Integrated test) receive a DNA sequencing test. Table 1 shows the screening performance of this approach according to the percentage of women selected for a reflex DNA test based on the first stage of the Integrated test. As the percentage increases from 10% to 90% the detection rate increases from about 92% to 98% and the false-positive rate initially decreases from 0.11% (10% have a DNA test) to 0.08% (20% have a DNA test) then increases to 0.20% (90% have a DNA test). Table 1 also shows the screening performance of routine DNA testing without an Integrated test if (i) women with a DNA test failure have a diagnostic amniocentesis or (ii) women with a DNA test failure have a second trimester screening Quadruple test, the two practical options available. In the first case DNA test failures are regarded as screen-positive and the detection rate is 98.6% with a false-positive rate of 3.2%. In the second case, in which women with a failed test have a Quadruple test, the detection rate is 98.0% with a false-positive rate of 0.3%. 10.1371/journal.pone.0058732.t001 Table 1 Screening performance of reflex DNA tests with the Integrated test according to percentage of women having reflex DNA test (Integrated test risk cut-off 1 in 50). Women selected for reflex DNA test after first stage of Integrated test Risk cut-off for first stage of Integrated test Overall screening performance Detection rate (%) False-positive rate (%) 10% 1 in 630 92.4 0.11 20% 1 in 1600 94.8 0.08 40% 1 in 4900 96.9 0.10 60% 1 in 12000 97.7 0.14 80% 1 in 27000 98.1 0.18 90% 1 in 47000 98.2 0.20 All women have a DNA test (no Integrated test):- test failures classified as positive 98.6 3.19 test failures have a Quadruple test, risk cut-off 1 in 100 98.0 0.29 Table 2 shows, in a similar way to Table 1 , the cost per woman screened expressed as a multiple of the cost of an Integrated test. As the percentage of women having reflex DNA testing increases from 10% to 90% the cost increases from double to ten-fold if the cost of the DNA test is ten times the cost of the Integrated test. Table 2 also shows how the cost per woman screened changes as the cost of the DNA test decreases. For example if the cost of the DNA test were 20 times the cost of the Integrated test, and 20% of women classified as higher risk at the first stage of the Integrated test, the cost per woman screened would be 5.0 times greater than the cost of the Integrated test. If the cost of the DNA test were 10 times the cost of the Integrated test, the cost per woman screened would be 3.0 times greater. The estimates in Table 2 are based on 75% of the cost of the Integrated test being incurred at the first trimester stage but are robust to different proportions. For example with the cost being split equally between the first and second trimesters the cost per woman screened would be 4.9 instead of 5.0 and 2.9 instead of 3.0 times greater in the examples above. 10.1371/journal.pone.0058732.t002 Table 2 Illustration of the cost per woman screened according to the cost of the DNA test, expressed as a multiple of the cost of an Integrated test, and the proportion of women who have a DNA test (i.e. positive based on a the first trimester stage of the Integrated test, 75% of the cost of the Integrated test incurred in the first trimester). Women selected for reflex DNA test after first stage of Integrated test DNA test cost as a multiple of Integrated test cost 2.5 5 10 20 40 10% 1.2 1.5 2.0 3.0 5.0 20% 1.5 2.0 3.0 5.0 9.0 40% 1.9 2.9 4.9 8.9 17 60% 2.4 3.9 6.9 13 25 80% 2.8 4.8 8.8 17 33 90% 3.0 5.3 9.8 19 37 Figures S1 and S2 illustrate the effect of using the reflex DNA testing approach with the Combined test in the same way that figures 1 and 2 do with the Integrated test, and Tables S1 and S2 present the corresponding estimates in the same way as tables 1 and 2 . The screening performance is similar to that with the Integrated test. Discussion The reflex DNA testing protocol proposed here, in which the first part of an Integrated test is used to determine who should receive a DNA test, has a number of advantages. First, it has a high screening performance; while the detection rate may be about five percentage points lower than routine DNA testing, the false-positive rate is about 30 times lower if DNA test failures are considered positive and these women have a diagnostic amniocentesis, or about 3 times lower if these women have a second trimester Quadruple test. Second, all women receive a screening result; there are no failed tests and there is no need to tell some women that they had a failed DNA test and needlessly cause them anxiety. Third, the cost of DNA sequencing for the programme is reduced by 80 or 90%, depending on which of the options is adopted. The cost of continuing the Integrated test would remain, which in a public service context is available at the Wolfson Institute of Preventive Medicine, London, for £35 (about $50), but at present this is substantially less than all women having a DNA test. Fourth, the very low false positive rate means that only about 3 per 1000 women screened would need a diagnostic amniocentesis and in about 2 in 3 a Down's syndrome pregnancy would be diagnosed. Fifth, such a protocol allows for the screening of other pregnancy complications such as pre-eclampsia, identified using immunoassays or heart defects using ultrasound markers. In our analysis we used the results of Palomaki and colleagues (DNA test detection rate of 98.6% and false-positive rate of 0.2% [1] ) and a DNA test failure rate of 3%. A sensitivity analysis showed that our estimated overall detection rate of 94.8% and overall false-positive rate of 0.08% is robust to reported variations in the DNA test detection rates, false-positive rates, and test failure rates. For DNA detection rates between 97.5% and 99.5%, and false-positive rates between 0.1% and 0.3%, and DNA test failure rates between 1% and 5%, the overall detection rates were between 93.6% and 95.8% and the overall false-positive rate between 0.05% and 0.12%. In a typical Integrated test free β-hCG is not measured in the first trimester, but either total or free β-hCG is measured in the second trimester. In the proposed protocol, the overall screening performance is marginally better by measuring hCG earlier; if total hCG were measured in the second trimester and only an NT and PAPP-A measured in the first trimester, the overall detection rate would be 93.8% (instead of 94.8%) and the overall false-positive rate 0.12% (instead of 0.08%) if 20% of women were selected for a reflex DNA test. There is no advantage in measuring hCG in both the first and second trimesters. The measurement of additional markers such as serum placental growth factor, or ultrasound ductus venosus blood flow or nasal bone would improve the screening performance of the proposed protocol, but these are not routinely used, and therefore are not considered here. Most of the published studies on DNA sequencing as a screening test for Down's syndrome were performed on women who were, for one reason or another, at higher than average risk, but this is not a source of bias as the detection rate and false-positive rate of screening tests using markers that are the consequence of the disorder are independent of the prevalence of the disorder. As experience is gained with the screening protocol proposed in this paper, and if the cost of DNA testing falls, with a lower rate of failed tests, DNA testing could be offered to a larger proportion of pregnancies. At the same time the need for immunoassays and ultrasound measurements currently used to screen for Down's syndrome can be reviewed to assess their value in screening for other disorders such as pre-eclampsia. Table 2 provides an indication of the costs of the proposed protocol with varying proportions having a DNA test. Expressing cost in multiples of the cost of the Integrated test makes the table generally applicable, so that, if a 4 to 5 fold greater cost per woman screened were acceptable, a 20% DNA testing percentage could be done if the DNA test were 20 times more costly than the Integrated test, or 40% if 10 times more costly. As can be seen from figure 2 , the marginal cost of detecting the extra 4% (from 95% to 99%) of Down's syndrome pregnancies that would be detected if all women had DNA testing rather than adopting the proposed protocol would be extremely high, requiring about 80,000 extra DNA tests (100,000 – 20,000) for each extra Down's syndrome pregnancy detected (if 20% have reflex DNA testing). This would remain the case unless the cost of a DNA test were substantially reduced. Collecting plasma samples for DNA testing that may not be used is, of course, an expense, but a small one compared with routine DNA testing. Reflex DNA testing with the Combined test rather than the Integrated test yields a similar screening performance (see Table S1 ) with a similar overall cost (see Table S2 ). The principal disadvantage in using reflex DNA testing with the first trimester Combined test instead of the first stage of the Integrated test is that it would generate a burden of anxiety in a significant number of women. This is because a negative Combined test result would be informed immediately if testing were done at the time of the ultrasound NT measurement or within a day or two if done in a central laboratory. However, because many would regard it to be wrong to artificially delay the reporting of a negative screening result, a “positive” would trigger a DNA test that would take 1–2 weeks, so if women did not receive a prompt result they would realize that they were in a higher risk category. If 20% were selected for a DNA test, as shown in Figure S2 , this would apply to 20% of women in the population. If, however, as we suggest DNA testing were conducted together with the Integrated test the corresponding proportion would be substantially less than 1%. A feature of the proposed screening protocol is that it applies equitably to all pregnant women with the cost averaged over all women screened, regardless of who has a DNA test. This is a practical approach in the context of a screening programme, which is the appropriate way of delivering the service to a population. Our proposed protocol could usefully be linked to interpretive software that would automatically modify the proportion of women selected for reflex DNA testing and provide the appropriate risk cut-off to achieve this. Also, all women who have a DNA test could receive an estimate of the risk of having a Down's syndrome pregnancy, based on a combination of the DNA test result and the first stage of the Integrated test, so the results would be quantitative and not simply be based on a qualitative DNA result. In deriving this risk, the DNA result could be adjusted for relevant factors such as the fetal DNA fraction and maternal weight. In summary, the proposed protocol combines current screening methods with the newer DNA sequencing methods to provide a cost effective strategy for all pregnant women with a very high level of efficacy and safety. Supporting Information Figure S1 Protocol for reflex DNA testing in conjunction with Combined test screening. (TIF) Figure S2 Protocol for reflex DNA testing in conjunction with Combined test screening in which 20% of women at highest risk using the Combined test receive a DNA sequencing test. (TIF) Table S1 Screening performance of reflex DNA tests with the Combined test according to percentage of women having reflex DNA test. (Combined test risk cut-off 1 in 50 for DNA test failures). (DOCX) Table S2 Illustration of the cost per woman screened according to the cost of the DNA test, expressed as a multiple of the cost of a Combined test, and the proportion of women who have a DNA test (i.e. positive based on the Combined test). (DOCX) "]}, { "id":"10.1371/journal.pone.0246285/body", "doc_partial_parent_id":"10.1371/journal.pone.0246285", "doc_type":"partial", "journal_eissn":"1932-6203", "publisher":"Public Library of Science", "journal":"PLOS ONE", "journal_id_pmc":"plosone", "journal_id_publisher":"plos", "journal_id_nlm_ta":"PLoS ONE", "eissn":"1932-6203", "publication_date":"2021-02-08T00:00:00Z", "received_date":"2020-07-09T00:00:00Z", "accepted_date":"2021-01-18T00:00:00Z", "article_type":"Research Article", "article_type_facet":"Research Article", "author":["Douglas R Bish", "Ebru K Bish", "Hussein El-Hajj", "Hrayer Aprahamian"], "author_facet":["Douglas R Bish", "Ebru K Bish", "Hussein El-Hajj", "Hrayer Aprahamian"], "editor":["Casian Pantea"], "editor_facet":["Casian Pantea"], "pagecount":15, "volume":16, "issue":2, "elocation_id":"e0246285", "journal_name":"PLOS ONE", "journal_key":"PLoSONE", "subject":["/Biology and life sciences/Evolutionary biology/Population genetics/Gene pool", "/Biology and life sciences/Genetics/Population genetics/Gene pool", "/Biology and life sciences/Population biology/Population genetics/Gene pool", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Epidemiology/Medical risk factors", "/Medicine and health sciences/Epidemiology/Pandemics", "/Medicine and health sciences/Medical conditions/Infectious diseases/Viral diseases/COVID 19", "/Medicine and health sciences/Public and occupational health/Health screening", "/People and places/Geographical locations/Europe/Iceland", "/Physical sciences/Mathematics/Probability theory/Random variables"], "subject_hierarchy":["/Biology and life sciences/Evolutionary biology/Population genetics/Gene pool", "/Biology and life sciences/Genetics/Population genetics/Gene pool", "/Biology and life sciences/Population biology/Population genetics/Gene pool", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Epidemiology/Medical risk factors", "/Medicine and health sciences/Epidemiology/Pandemics", "/Medicine and health sciences/Medical conditions/Infectious diseases/Viral diseases/COVID 19", "/Medicine and health sciences/Public and occupational health/Health screening", "/People and places/Geographical locations/Europe/Iceland", "/Physical sciences/Mathematics/Probability theory/Random variables"], "subject_facet":["/Biology and life sciences/Evolutionary biology/Population genetics/Gene pool", "/Biology and life sciences/Genetics/Population genetics/Gene pool", "/Biology and life sciences/Population biology/Population genetics/Gene pool", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Epidemiology/Medical risk factors", "/Medicine and health sciences/Epidemiology/Pandemics", "/Medicine and health sciences/Medical conditions/Infectious diseases/Viral diseases/COVID 19", "/Medicine and health sciences/Public and occupational health/Health screening", "/People and places/Geographical locations/Europe/Iceland", "/Physical sciences/Mathematics/Probability theory/Random variables"], "subject_level_1":["Biology and life sciences", "Medicine and health sciences", "People and places", "Physical sciences"], "striking_image":"10.1371/journal.pone.0246285.g005", "timestamp":"2026-03-14T08:44:59.831Z", "doc_partial_body":[" Introduction With around 46.8 million confirmed cases and 1.2M deaths in at least 188 countries (as of 11/2/2020) [ 1 ], the COVID-19 pandemic continues to be the cause of considerable suffering and economic disruption. Effective mitigation requires laboratory-based testing to identify COVID-19 positive subjects. As the WHO Director-General Ghebreyesus puts it, \"The most effective way to prevent infections and save lives is breaking the chains of transmission, and to do that you must test and isolate. We cannot stop this pandemic if we don’t know who is infected. We have a simple message for all countries: test, test, test” [ 2 ]. Testing is essential not only for symptomatic individuals, but also for asymptomatic individuals [ 3 ], because they are a major source of transmission [ 4 ]. Unfortunately, a major impediment to mitigation efforts in the United States (US), and in other parts of the world, has been the limited testing capacity for COVID-19, which, in the US, has constrained the number of tests that could be conducted, mostly restricting testing to those with symptoms for case identification, and less on mass screening and contact tracing efforts. Countries that were able to ramp up their COVID-19 testing capacity quickly and follow an aggressive testing strategy earlier during the epidemic were considerably more effective than others. For example, South Korea was able to curb the growth of the disease mainly through expanded testing, without a strong imposition of social distancing measures. By testing over 300,000 people out of its population of 52 million [ 5 ], South Korea was able to implement highly effective interventions early on, including contact tracing, followed by enforced quarantines and isolations. Another example is Iceland, which is able to offer free COVID-19 testing to the general population [ 6 ], and as of June 14, 2020, was able to test around 17% of its population [ 7 ]. The current mode of COVID-19 testing worldwide is individual testing , that is, each subject’s specimen is tested with a single test. An alternative to individual testing, proposed by Dorfman in 1943 [ 8 ], is pooled testing , in which samples, sufficient for testing, are extracted from the specimens (e.g., nasopharyngeal swabs) from multiple subjects, and combined in a pool , and tested via a single test; if the pooled test’s outcome is positive, then all subjects in the pool are individually tested (with the same type of test, using a new sample extracted from the previously collected specimen); and if the pooled test’s outcome is negative, then all subjects in the pool are classified as disease-negative. Pooled testing does not require any additional resources beyond individual testing [ 9 ], and can substantially expand testing capacity over individual testing, especially when prevalence rates are low. Pooled testing, and in particular the Dorfman pooling method, is currently used in public health screening, including screening for sexually-transmitted diseases and screening donated blood for transfusion-transmittable infections [ 10 – 13 ]. An important design decision in pooled testing is the pool size (i.e., number of specimens in each pool) so as to maximize the efficiency of testing (i.e., minimize the number of tests per subject) [ 11 ] provides a rigorous analysis on the selection of an optimal pool size for Dorfman pooling. Because pooling has obvious application to COVID-19 testing, there have been several recent pooling papers focused on COVID-19, for example [ 14 – 16 ], offer various simplifications of the analysis in [ 11 ], with a focus on COVID-19. Unlike [ 14 – 16 ], this paper considers uncertainty in the prevalence rate, which is a defining feature of COVID-19; in other public health screening applications, the disease spread is less dynamic and prevalence changes at a much slower rate (e.g., sexually-transmitted diseases). For COVID-19, disease prevalence changes quickly, and there is high uncertainty around its prevalence at any point in time. Considering pooled testing design, one concern is accuracy, in particular a potential increase in the number of false-negatives as a result of pooling. Pooling does not increase the number of false-positives over individual testing [ 11 ]. With imperfect tests, pooling will increase the false-negative rate (e.g., see [ 11 ]), because a disease-positive subject must be tested twice (first in a pool, then individually) to be classified as positive. Further, pooling may lead to the “dilution” of the infected specimen(s) in the pool, reducing the sensitivity of the pooled test, thus increasing the false-negative rate, especially for larger pools [ 13 ]. A common method for reducing dilution is to set a maximum pool size for, e.g., see [ 10 , 12 ]. There are several lab-based studies that investigate the impact of pooling on the sensitivity of a PCR test for COVID-19, which is the most common type of test for COVID-19 screening. This preliminary research indicates that pooled testing leads only to a minor reduction in PCR sensitivity for larger pool sizes. For example, [ 9 ] shows that the PCR test was able to detect an infected specimen in pools of size of 32 in nine out of the ten pools tested. [ 17 ] shows a similar result for pools of size 30. In addition, several other studies find no loss of sensitivity for smaller pools, e.g., [ 18 – 20 ] use pool sizes of 5, 8, and 10, respectively. Not surprisingly [ 21 , 22 ], show that the dilution effect is more pronounced when the infected specimens in the pool have low viral loads; the window period analysis in [ 21 ] indicates that the low viral load typically occurs for specimens that are collected either too early or too late after infection. Related to the overall pooled testing design [ 23 ], proposes a design where the pooled test is repeated to reduce false-negatives, and shows that such a design is still efficient compared to individual testing. On the other hand [ 24 ], explores, via simulation, different pooling designs (e.g., adaptive and non-adaptive) and different metrics (e.g., efficiency and accuracy). A PCR test run takes in the order of 2 hours [ 25 , 26 ] to complete, thus, pooled testing, followed by individual testing as needed, is viable from a time perspective, and does not significantly increase the testing time for a particular subject. Further, testing machines have a capacity, which limits their throughput (e.g., number of completed tests per testing day), e.g., a limit of 96 samples per testing cycle (run) is common [ 25 ]. Because pooled testing increases the number of specimens tested per testing cycle, it also increases the throughput, shortening the average time to get the test results. The expanded testing capacity provided by pooling could enable more extensive testing for COVID-19. This paper builds on previously published mathematical models by the authors; develops a robust approach for pooled testing design that can be customized for different testing populations and for a dynamic and uncertain disease prevalence; and demonstrates that the proposed pooled testing approach has the potential to substantially increase COVID-19 testing capacity. Further, we explore the impact of test sensitivity, and provide insight on how to manage the uncertainty in test sensitivity. This research is timely as limited COVID-19 testing capacity remains a serious problem, and more testing capacity is urgently needed, especially given the increasing number of infections, and the efforts to return to some form of “normalcy.” Methods We study case identification via pooled testing; develop an easily implementable method for robust pooling design under prevalence uncertainty [ 27 , 28 ], and for risk-stratified groups; and illustrate the benefits through a case study on mass screening for COVID-19. Our model builds on our earlier work, in particular, we take the analytically complex models and results from [ 10 ], which uses risk-based pooling (to determine pool sizes and pool assignments for subjects given their individual disease risk), from [ 11 ], which uses robust optimization (to determine pool sizes under prevalence uncertainty), and from [ 29 ], which develops sequential pooling design for surveillance; and we develop a novel method for designing a simple, robust pooling strategy, which can be incorporated into a sequential pooling design framework to consider infection dynamics and prevalence uncertainty. For practical relevance, we develop a companion COVID-19 pooling design tool (through a spread sheet), which will be available online. We consider a PCR test, which can be used for both individual and pooled testing. For pooled testing, we consider the Dorfman method [ 8 ] (hereafter, “pooling”). The test produces a binary outcome, with a positive (negative) outcome indicating the presence (absence) of the infection in the pool (for pooled testing) or in the individual specimen (for individual testing). We let Se and Sp respectively denote the test sensitivity (true positive probability) and specificity (true negative probability), and assume that pooling does not change the test’s efficacy up to a maximum allowable pool size . The terms “subject” and “specimen” respectively refer to the individual to be tested, and specimen collected from the individual, and are used interchangeably. We assume that each specimen has sufficient material (samples) for multiple tests, thus, if an individual follow-up test is needed for a subject, it is conducted on a new sample extracted from the subject’s previously collected specimen. Model We design a pooling strategy for a testing population divided into risk groups based on each group’s estimated disease prevalence, by determining, for each group, a robust pool size . The objective is to maximize the efficiency of testing (minimize the expected number of tests per subject) under unknown prevalence. In the following, we detail the derivation of the robust pool size, discuss its extension to sequential pooling design, and derive the false-negative rate of pooling. To simplify the subsequent notation, we omit the group index. Consider a given group, and let P denote the unknown prevalence for the group, with uncertainty set (range) S(P) = [ L , U ], which consists of discrete prevalence scenarios , each with probability, Pr(P = p) , p ϵ S(P) ; our method extends to any user-specified discrete or continuous distribution for P . The uncertainty set S(P) is estimated by the tester, and does not necessarily correspond to the true support of random variable P , which is unknown in practice. Testing efficiency Let n max denote the maximum allowable pool size (due to technological limitation, dilution effect, etc.). If a pool with n specimens tests negative, then only 1/n tests are needed per subject; and if the pool tests positive, then each subject requires an individual “follow-up” test, leading to 1+1/n total tests per subject ( Table 1 displays the probability of each possible event). Then, for any pool size n and prevalence scenario p , the expected number of tests per subject tested (“expected tests”) under pooling, denoted by E[ T ( n , p )], follows: E [ T ( n , p ) ] = 1 + n [ S e − ( S e + S p − 1 ) ( 1 − p ) n ] n . (1) 10.1371/journal.pone.0246285.t001 Table 1 Probabilities of all possible events in pooled testing (for a Pool of n Subjects). Pooled Test Outcome True Subject Status in Pool Pooled Test Negative Pooled Test Positive (Pooled Test Only) (Pooled Test Plus n Individual Tests) All Subjects Negative Sp (1− p ) n (1− Sp )(1− p ) n At Least One Subject Positive (1− Se )(1−(1− p ) n Se (1−(1− p ) n ) The probabilities for the intersections of all possible pooled test outcomes and subject status in pooled testing. A key characteristic of COVID-19 is dynamic and uncertain prevalence rates, thus during testing the actual prevalence rate is unknown. To develop a pool size that is robust under prevalence uncertainty, we use the Regret measure (e.g., [ 11 ]), which can be computed for any pool size n and prevalence scenario p as follows: R e g r e t ( n , p ) = E [ T ( n , p ) ] − E [ T ( n ( p ) , p ) ] , (2) where n ( p ) is the pool size that minimizes E[T( n , p )] for prevalence scenario p (i . e ., the minimizer of Eq ( 1 ) under perfect information on p , the prevalence rate), and can be approximated as follows [ 11 ]: n ( p ) ≈ a r g m i n ( n ∈ ( ⌊ n ˜ ( p ) ⌋ , ⌈ n ˜ ( p ) ⌉ , n m a x ) [ E [ T ( n , p ) ] ] , (3) where n ˜ ( p ) = 1 p ( S e + S p − 1 ) . In Eq ( 3 ), we evaluate the expected tests, E[T( n , p )], at the ceiling and floor of n ˜ ( p ) , and at the maximum allowable pool size, n max , and select the value that yields a lower expected number of tests, in order to obtain an integer pool size, n ( p ). A complex algorithm that derives the (exact) optimal pool size for scenario p is provided in our previous work [ 11 ]. The perfect information assumption used in Eq ( 3 ), which implies a known prevalence rate, is obviously not realistic, and is utilized for the purpose of deriving a robust pool size when the prevalence rate is uncertain. Specifically, we determine a robust pool size , n *, so as to minimize the expected Regret over the uncertainty set S(P) of random variable P , that is: n * = a r g m i n ( n ∈ Z + , n ≤ n m a x ) [ ∑ p ∈ S ( P ) P r ( P = p ) × R e g r e t ( n , p ) ] . (4) Utilizing the Regret objective in Eq ( 4 ) requires the determination of a set of perfect information pool sizes a priori via Eq ( 3 ). The Regret objective leads to a robust solution that is not overly conservative, and a simple method for determining a robust pool size, compared to the analytically complex algorithm of [ 11 ]. In summary, to design a robust pooling strategy under prevalence uncertainty, we use Eqs ( 3 ) and ( 4 ) with each risk group’s respective parameters. Specifically, using Eq ( 3 ), we first calculate a set of perfect information pool sizes , n ( p ), for each scenario p in the range of P ; and then use Eq ( 4 ) to determine the robust pool size for the group under prevalence uncertainty, n *. This process is automated in our spread sheet, and the user needs to only input the problem parameters, including any user-specified probability distribution (discrete or continuous) for random variable P . Sequential pooling design Due to infection dynamics, we allow for updates to pooling design in each testing period (see, e.g., [ 29 ] for sequential pooling design for surveillance). To present our framework for sequential pooling design, we use index t to denote testing period t ∈ Z + . At the beginning of each testing period t , we update the uncertainty set of random variable P based on the testing data obtained in periods 1, … , t -1 , compute each group’s pool size in period t (Eqs ( 3 ) and ( 4 )), and use the updated pool sizes in testing period t . We repeat this process through the testing horizon. False-negative rate We determine the expected false-negatives ( FN s) per subject tested under pooling. When a pool contains infected specimen(s), FN (s) occurs if the pool tests negative, or the pool tests positive but the individual follow-up test for an infected specimen is negative, leading to: E [ F N P o o l ] = ( 1 − S e 2 ) p . (5) On the other hand, for individual testing, when a subject is infected (with probability p ), the test falsely provides a negative outcome (with probability 1- Se ), leading to: E [ F N I n d i v i d u a l ] = ( 1 − S e ) p . (6) Data We demonstrate the efficiency of robust pooling for mass screening using published data for COVID-19, which is stratified into low- and high-risk groups based on symptom class. To this end, we construct each group’s uncertainty set for the prevalence random variable to correspond to the 95% confidence interval (CI) from the dataset, with 100 equally-spaced prevalence scenarios (each with equal probability) within each uncertainty set; and develop a robust pooling design for each group (via Eqs ( 3 ) and ( 4 )). We consider the PCR test for COVID-19 testing. In [ 9 ], ten pools of size 32 were constructed, where each pool contained one specimen infected with COVID-19 and 31 infection-free specimens. Using the PCR test, nine pools tested positive and one pool tested negative (due to dilution). Other studies suggest that the sensitivity of the PCR test for COVID-19 can be as low as 0.71 and as high as 0.98 [ 30 ]. As a result, we perform a one-way sensitivity analysis on the test sensitivity parameter, Se , over a wider range, of [0.70, 1.00], discuss the specific results for the published values (i.e., Se values of 0.71 and 0.98) in detail, and qualitatively discuss the results for other test sensitivity values. We also assume that the test has perfect specificity, i.e., Sp = 1 [ 31 ], which is not subject to the dilution effect, and n max = 32 [ 9 ]. Case study data The case study focuses on mass screening of high- and low-risk subjects based on Iceland’s COVID-19 testing dataset [ 7 ]. This dataset includes 63,134 subjects, and reports the number of subjects screened and the number of positive test outcomes for COVID-19 per day, based on testing data from two laboratories, which collectively conduct all COVID-19 screening in Iceland: 1) 21,576 high-risk subjects with “severe symptoms and/or are at high risk of infection because of close contact with a diagnosed individual” [ 32 ], tested by the National University Hospital of Iceland (NUHI) between February-28-2020 and June-14-2020, leading to 1,628 positive-testing subjects; and 2) 41,558 low-risk subjects in the general population who have requested screening on a voluntary basis, tested by deCODE genetics between March-15-2020 and June-14-2020, leading to 182 positive-testing subjects. We implement sequential pooling design, and compute the robust pool sizes for every week between March-05-2020 and June-14-2020 (high-risk group), and between March-19-2020 and June-14-2020 (low-risk group), i.e., after obtaining a number of days of testing data for each group. In particular, at the beginning of each week, we use the previous week’s testing data for each of the low- and high-risk groups, and the Wald’s method [ 33 ], to construct a 95% CI for each group’s prevalence: L ( p ^ ) = p ^ − z 0.975 p ^ ( 1 − p ^ ) / T , and U ( p ^ ) = p ^ + z 0.975 p ^ ( 1 − p ^ ) / T , where p ^ is the point estimate, z 0.975 is the inverse of the CDF of the standard normal distribution at point 0.975, and T is the number of subjects tested in the previous week. Results For illustrative purposes, Fig 1 reports the perfect information pool sizes (i.e., ( n(p) ) from Eq ( 3 ) for prevalence scenario p ) and expected number of tests per subject (simply, expected tests), for various prevalence scenarios between 0.01 and 0.292, and test sensitivity values ( Se = 0.71, 0.98, 1), considering that the test has perfect specificity. The expected tests under perfect information on prevalence rate provides a lower bound ( LB ) on the number of tests achievable via pooling, but is not realistic due to the inherent uncertainty in the prevalence rate (i.e., the lack of perfect information), which is typically the case for a highly contagious disease like COVID-19. Pooling is not more efficient than individual testing for prevalence scenarios above 0.292, due to the large number of individual follow-up tests. Relatedly, Fig 2 shows the expected tests ( E[T(n(p) , p)] ) for various prevalence scenarios between 0.025 and 0.30, and test sensitivity values of 0.98 ( Fig 2(A)) and 0.71 ( Fig 2(B)) over a range of pool sizes, and thus shows the impact of pool size on efficiency for each prevalence scenario and test sensitivity. 10.1371/journal.pone.0246285.g001 Fig 1 Perfect information pool size and expected number of tests per subject versus prevalence rate for various test sensitivity values. The perfect information pool size, n(p) , and expected number of tests per subject, E[T(n(p) , p)] , for each prevalence scenario p between 0.01–0.292 for test sensitivity values, Se = 0.71, 0.98, 1. 10.1371/journal.pone.0246285.g002 Fig 2 Expected number of tests per subject versus pool size for various prevalence rates for test sensitivity values (a) Se = 0.98 and (b) Se = 0.71. The expected number of tests per subject, E[T(n(p) , p)] , for various prevalence scenarios p between 0.01–0.25 for test sensitivity values (a) Se = 0.98 and (b) Se = 0.71 for pool sizes from 2–32. Based on the Iceland dataset [ 7 ], we develop a robust pooling design within a sequential framework for the high-risk (those tested by NUHI) and low-risk (those tested by deCODE) groups, updated every week during the study period. We consider that the weekly robust pool sizes are used each day of that week, and examine the daily testing results. Fig 3 depicts the weekly robust pool sizes ( n *) for two test sensitivity values ( Se = 0.71, 0.98) as well as the optimal pool size for each prevalence scenario (i.e., the perfect information pool size for each p , n(p) , from Eq ( 3 )) within the 95% CI on the weekly prevalence forecast (with each CI discretized into 100 equally-spaced prevalence scenarios), along with the actual weekly prevalence rate. Note that n(p) decreases as the prevalence rate p increases (Eq ( 3 )). Thus, the robust pool size ( n *) is bounded from above by the optimal pool size for the lower limit of the CI on prevalence, and from below by the optimal pool size for the upper limit of the CI. We see that the robust pool size tends to be closer to the optimal pool size for the upper limit of the CI, that is, closer to the lower bound pool size. This figure also shows that as the test sensitivity increases, the robust pool size decreases. 10.1371/journal.pone.0246285.g003 Fig 3 Weekly robust pool size and 95% confidence interval pool sizes for (a) High-risk and (b) Low-risk groups for two test sensitivity values, and actual weekly prevalence rates for (c) High-risk and (d) Low-risk groups. The robust pool size, n *, for each week along with pool sizes corresponding to the 95% confidence interval of the prevalence forecast for (a) high-risk and (b) low-risk groups for test sensitivity values, Se = 0.71 and 0.98, and the actual weekly prevalence rates for (c) high-risk and (d) low-risk groups. Fig 4 reports the daily number of tests for individual testing (i.e., the actual number of tests conducted per day in the dataset), and the expected number of tests for robust pooling (i.e., using n *) and the perfect information lower bound ( LB , i.e., using n(p) ) for (a) high-risk and (b) low-risk subjects for a test sensitivity of 0.98, and (c) high-risk and (d) low-risk subjects for a test sensitivity of 0.71. Recall that the perfect information lower bound is unattainable, because the prevalence rate is uncertain, and a prevalence rate forecast is required due to changing disease dynamics. Considering test sensitivity values of 0.71 and 0.98, the total reduction in the number of tests, over individual testing, is 61.9% and 54.2% respectively for robust pooling (62.7% and 55.6% respectively under perfect information) for the high-risk group during the period of March-05-June-14; and 90.2% and 88.5% respectively for robust pooling (91.0% and 89.5% respectively under perfect information) for the low-risk group during the period of March-19–June-14. 10.1371/journal.pone.0246285.g004 Fig 4 Daily expected number of tests for the high-risk group for test sensitivity values of (a) 0.98 and (c) 0.71 and for the low-risk group for test sensitivity values of (b) 0.98 and (d) 0.71. The daily expected number of tests required for the (a) high-risk group with Se = 0.98, (b) low-risk group with Se = 0.98, (c) high-risk group with Se = 0.71, and (d) low-risk group with Se = 0.71 for the perfect information lower bound, robust pooling, and individual testing. In the above analysis, we use a maximum allowable pool size, n max , of 32, to limit the dilution effect, which is set based on preliminary studies (see Introduction ), hence we next study how the value of n max affects the results. Table 2 reports the efficiency of robust pooling, that is, the percent reduction in the number of tests that can be achieved via robust pooling compared to individual testing, for lower values of n max , and for test sensitivity values of Se = 0.71 and 0.98, and the high- and low-risk groups. As expected, very low n max values impact the efficiency of testing more for the low-risk group compared to the high-risk group, because the latter group already uses small pool sizes due to their high prevalence. 10.1371/journal.pone.0246285.t002 Table 2 The percent reduction in the expected number of tests via robust pooling compared to individual testing for high-risk and low-risk groups and two test sensitivity values for various maximum allowable pool sizes, n max . Maximum Allowable Pool Size ( n max ) High-risk Group Low-risk Group Se = 0.98 Se = 0.71 Se = 0.98 Se = 0.71 32 54.2% 61.9% 88.5% 90.2% 30 54.1% 61.8% 88.5% 90.1% 20 54.0% 61.7% 88.2% 89.8% 10 53.4% 61% 86.2% 87.4% 5 51.3% 58.8% 79.8% 80.8% By requiring, on average, fewer tests per subject, robust pooling can substantially expand testing capacity. To illustrate this concept, we select a week during the study period, i.e., the week spanning April-2 to April-8 of 2020, during which 7,967 low-risk subjects were tested via 7,967 tests, of which 54 subjects tested positive. We report the expected number of subjects that could be tested using the 7,967 tests under the different strategies. For this measure, the perfect information lower bound on the expected tests per subject provides a perfect information upper bound ( UB ) on the expected number of subjects tested. Fig 5(A) displays the expected number of low-risk subjects that could be tested via 7,967 tests for the individual testing and robust pooling ( n* ) strategies, and the perfect information upper bound ( UB ), for a test sensitivity range [0.70, 1.00]. For each pooling strategy, the number of low-risk subjects screened reduces as test sensitivity increases. For example, as test sensitivity increases from 0.70 to 1.00, the number of low-risk subjects screened reduces from 66,010 to 54,898 under perfect information, and from 60,140 to 49,822 under robust pooling. This follows because a higher test sensitivity implies a higher likelihood that a pool containing an infected specimen will test positive, necessitating further individual testing for all subjects in the pool. As a result, optimal pool sizes are non-increasing in test sensitivity ( Fig 1 ). 10.1371/journal.pone.0246285.g005 Fig 5 Expected number of low-risk subjects screened with 7,967 tests (a) under different strategies and (b) under different assumed test sensitivities, versus true test sensitivity, and the expected number of (c) False-negative cases and (d) Missed and False-negative Cases versus Test Sensitivity. The expected number of low-risk subjects screened with 7,967 tests (a) for the perfect information upper bound, robust pooling, n *, and individual testing versus test sensitivity, (b) assuming a prevalence rate, p , of 0.0065 and a test sensitivity, Se , of 0.70, 0.85, and 1 versus true test sensitivity, (c) FN s (out of the 7,967 low-risk subjects tested under both strategies), and (d) missed cases plus FN s for robust pooling and individual testing (out of 52,173 subjects, which corresponds to the expected number of low-risk subjects tested via robust pooling) versus test sensitivity. The sensitivity of the test may not be known with certainty. To examine the effect of the test sensitivity estimate, we calculate the robust pool sizes for the low-risk group for the week spanning April-2 to April-8, using three assumed test sensitivity values, of 0.70, 0.85, and 1. Fig 5(B) depicts the expected number of low-risk subjects that would be screened with 7,967 tests under a range of true test sensitivity values, Se , in [0.70, 1]. At the extremes, when the true sensitivity is 0.70 and the pooling strategy is based on a sensitivity of 1, 837.2 fewer subjects can be tested in expectation compared to using the true sensitivity; and when the true sensitivity is 1 and the pooling strategy is based on a sensitivity of 0.70, 540.4 fewer subjects can be tested in expectation. Next, we study the effect of pooling on the expected number of FN s for various test sensitivity values. While pooling increases the number of FN s over individual testing for the same number of subjects (Eqs ( 5 ) and ( 6 )), it also allows for expanded testing, thus reducing potential missed cases over individual testing (i.e., infected subjects not tested by individual testing, who could have been tested under pooling). To illustrate this point, we consider again the low-risk subjects tested during the week spanning April-2 to April-8 in the Iceland dataset. Fig 5(C) displays the number of FN s for both robust pooling and individual testing (for the 7,967 subjects tested under both strategies), as a function of test sensitivity, while Fig 5(D) displays the FN s for robust pooling, and the sum of FN s and missed cases for individual testing, for 52,173 subjects that would have been screened under robust pooling (with 7,967 tests). Discussion In this paper, we provide a robust pooled testing approach to screen for COVID-19 and demonstrate its value for overcoming difficulties associated with COVID-19 testing. These difficulties include dynamic disease prevalence, which leads to high uncertainty in current prevalence, a wide range of possible test sensitivity values, different risk groups, and limited testing resources. For illustrative purposes, we use the Iceland dataset [ 7 ], in which the risk groups are based on whether the subject was tested by NUHI (high-risk due to symptoms and/or potential contacts) or by deCODE (low-risk, voluntary testing). The proposed robust pooling strategy significantly reduces the expected number of tests required to accomplish the screening conducted in Iceland for COVID-19 compared to individual testing, and the differences are more pronounced for the low-risk group, see Fig 3 . Overall, the reductions in the number of tests are 54.2% to 61.9% for the high-risk group, for test sensitivity of 0.98 and 0.71, respectively, and 88.5% to 90.2% for the low-risk group, for test sensitivity of 0.98 and 0.71, respectively. These reductions are based on weekly forecasted point estimates and confidence intervals for the prevalence. The robust pooling strategy based on these forecasts does nearly as well as having perfect prevalence information (for which the respective reductions are 55.6% to 62.7% and 89.5% to 91.0%, for the high-risk and low-risk groups, for test sensitivity of 0.98 and 0.71), which, of course, we only have in hindsight. Thus, the proposed robust pooling strategy can be used to substantially expand COVID-19 testing capacity. This expansion is more pronounced at lower prevalence rates (due to fewer follow-up tests and larger pool sizes). Dilution is an important issue when considering pooling, especially for large pools. In our models, we use a maximum allowable pool size, n max , to limit the dilution effect, which is a viable practice in pooled testing, especially when lab-based data on the magnitude of the dilution effect for different pool sizes is scarce (as is the case with COVID-19). Informed by the research that describes pool sizes for which pooling does not significantly affect the test sensitivity for the PCR test for COVID-19 (see Introduction ), we consider that n max is 32. Our analysis ( Table 2 ) indicates that reducing n max , and thus further reducing the potential for dilution, does decrease the efficiency of robust poolng, but even at low values of n max , e.g., n max = 5, robust pooling is still much more efficient than individual testing. As an alternative, if comprehensive data on the dilution effect for COVID-19 become available, one can derive a pooled sensitivity function, as a function of pool size, and use this function in the analytical expressions (Eqs ( 1 ), ( 3 ) and ( 5 )) to model dilution (e.g., see [ 21 , 34 ]). This will be an important future research direction once such data become available. We demonstrate the benefits of pooling in more detail using the week of April-2 to April-8 of 2020 for the low-risk group (with 7,967 low-risk subjects individually tested) considering a test sensitivity of 0.85. In contrast to the 7,967 tests required for individual testing, robust pooling uses a pool size of 14, thus requiring ⌈ 7,967 14 ⌉ = 570 pools. Given the true prevalence of 0.68% (calculated from the dataset), the probability that any pool will test positive (thus requiring individual follow-up tests for the subjects in the pool) is given by Se (1−(1− p ) n ) = 0.07722 (see Table 1 ). Therefore, for the 570 pools, we have, on average, 0.07722×570×14 = 616.2 individual follow-up tests. Thus, with pooling, the 7,967 subjects would require 1,186.2 (= 570+616.2) tests in expectation, an 85.1% reduction over individual testing. This reduction is closely related to a cumulative reduction in testing time, which we illustrate using the same week assuming a PCR testing machine that has a capacity of 96 tests, that is, 96 tests can run at the same time [ 25 ], and assuming that a test run takes 2 hours. Under individual testing, the number of machine runs is ⌈ 7,967 96 ⌉ = 83 , thus requiring 166 hours to complete testing. For the pooled strategy, ⌈ 570 96 ⌉ = 6 runs are required for the pools, plus ⌈ 616 96 ⌉ = 7 runs for the expected individual follow-up tests, thus requiring 26 hours of testing in expectation, compared to 166 hours for individual testing. Next we discuss the effect of test sensitivity on pooling by examining Fig 5 , which again considers the week of April-2 to April-8 of 2020 for the low-risk group of 7,967 subjects. If the 7,967 tests were used in the pooled strategy, between 49,822 (at a sensitivity of 1.00) and 60,140 (at a sensitivity of 0.70) subjects could have been tested (in expectation), see Fig 5(A) . This is a considerable difference, and as Fig 5(B) depicts, even if the pooling strategy is derived under the wrong test sensitivity, pooling still does well, e.g., at a true sensitivity of 0.70, a strategy derived based on perfect sensitivity (of 1.00) tests 59,122 subjects, equivalently, 89.6% of those that could be tested if the true test sensitivity were known (i.e., derived using a test sensitivity of 0.70). This reduction is due to using pools that are too small (13 versus 15 under the true sensitivity of 0.70), which results in loss of efficiency, but this is somewhat mitigated by a lower probability that subjects in a pool will need individual follow-up testing. Fig 5(B) suggests that a good strategy to handle uncertainty in test sensitivity is to pick the mid-point of the potential sensitivity range. Next, we compare the FN s under the different strategies. FN rate is larger under pooling than individual testing (Eqs ( 5 ) and ( 6 )). For instance, Fig 5(C) shows that for a test sensitivity of 0.70, individual testing has 16 expected FN s, while pooling has 28 (for the 7,976 subjects). Of course, pooling uses many fewer tests for these 7,976 subjects, thus allowing for expanded testing. Considering this expanded testing population, Fig 5(D) shows that at a test sensitivity of 0.70, there are 171 FN s from pooling, and 16 FN s plus 335 missed cases from individual testing. As the test sensitivity increases, the FN s decrease fairly fast compared to the reduction in missed cases. As we demonstrate in this study, robust pooling can substantially expand the testing capacity, and allow the testing of many more subjects for COVID-19. However, to achieve the maximum benefits of pooled testing, it is important to use pool sizes that are customized for the different risk groups in the population, and pool sizes that are designed to hedge against prevalence that is dynamic and uncertain; these are the key features of the robust pooling approach developed in this paper. Limitation One limitation is the complex nature of the test sensitivity function for the PCR test for COVID-19. PCR tests tend to have high sensitivity, but for COVID-19, the clinical sensitivity may be lower [ 35 ] (due, for example, to low quality specimens), and the reasons for this lower clinical sensitivity, and ways for improving the clinical sensitivity, have implications for pooling. "]}, { "id":"10.1371/journal.pone.0285083/body", "doc_partial_parent_id":"10.1371/journal.pone.0285083", "doc_type":"partial", "journal_eissn":"1932-6203", "publisher":"Public Library of Science", "journal":"PLOS ONE", "journal_id_pmc":"plosone", "journal_id_publisher":"plos", "journal_id_nlm_ta":"PLoS ONE", "eissn":"1932-6203", "publication_date":"2023-06-05T00:00:00Z", "received_date":"2022-11-24T00:00:00Z", "accepted_date":"2023-04-16T00:00:00Z", "article_type":"Research Article", "article_type_facet":"Research Article", "author":["Afschin Gandjour"], "author_facet":["Afschin Gandjour"], "editor":["Ernesto Iadanza"], "editor_facet":["Ernesto Iadanza"], "pagecount":8, "volume":18, "issue":6, "elocation_id":"e0285083", "journal_name":"PLOS ONE", "journal_key":"PLoSONE", "subject":["/Biology and life sciences/Molecular biology/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction", "/Medicine and health sciences/Critical care and emergency medicine", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Epidemiology", "/Medicine and health sciences/Epidemiology/Pandemics", "/Medicine and health sciences/Medical conditions/Infectious diseases/Viral diseases/COVID 19", "/Physical sciences/Mathematics/Probability theory/Probability distribution", "/Research and analysis methods/Mathematical and statistical techniques/Mathematical models", "/Research and analysis methods/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction"], "subject_hierarchy":["/Biology and life sciences/Molecular biology/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction", "/Medicine and health sciences/Critical care and emergency medicine", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Epidemiology", "/Medicine and health sciences/Epidemiology/Pandemics", "/Medicine and health sciences/Medical conditions/Infectious diseases/Viral diseases/COVID 19", "/Physical sciences/Mathematics/Probability theory/Probability distribution", "/Research and analysis methods/Mathematical and statistical techniques/Mathematical models", "/Research and analysis methods/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction"], "subject_facet":["/Biology and life sciences/Molecular biology/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction", "/Medicine and health sciences/Critical care and emergency medicine", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Epidemiology", "/Medicine and health sciences/Epidemiology/Pandemics", "/Medicine and health sciences/Medical conditions/Infectious diseases/Viral diseases/COVID 19", "/Physical sciences/Mathematics/Probability theory/Probability distribution", "/Research and analysis methods/Mathematical and statistical techniques/Mathematical models", "/Research and analysis methods/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction"], "subject_level_1":["Biology and life sciences", "Medicine and health sciences", "Physical sciences", "Research and analysis methods"], "striking_image":"10.1371/journal.pone.0285083.g002", "timestamp":"2026-03-14T10:42:49.973Z", "doc_partial_body":[" Introduction During the surge in COVID-19 cases due to the highly transmissible Omicron variant, many countries were facing a shortage of rapid antigen tests (RATs) or polymerase chain reaction (PCR) laboratory tests. For example, Germany faced challenges in terms of shortages of PCR machines, in available labor to use the machines, and PCR testing materials since the beginning of 2022. However, these constraints were not solvable within the short-term. Therefore, the German Federal Ministry of Health announced its prioritization of PCR tests that are reimbursed by public funds. Specifically, it decided to prioritize symptomatic individuals [ 1 ]. In contrast, a positive RAT in asymptomatic patients was not recommended for follow-up with a PCR test when the incidence was high (> 1%) [ 1 ]. Moreover, to end isolation, a negative RAT was generally considered as sufficient [ 1 ]. Conversely, some experts argued that isolation should only be terminated using PCR testing because RATs are less accurate [ 2 ]. Moreover, some experts reasoned that symptomatic contacts of COVID-19 patients who had a positive RAT test result could be spared further testing [ 3 ]. Given the controversies around the prioritization of PCR tests, this study developed a mathematical model that defined priority groups for lab-based PCR testing. The model was applied in a German setting. Methods To find a solution to the aforementioned prioritization problem, this study constructed a mathematical model. This model considers situations of limited PCR testing capacity but with an unlimited availability of RATs. The model assumes that PCR lab tests are the gold standard. Nevertheless, false negative test results could arise, for example, because the sample was taken too early or too late [ 4 ]. In addition, false positive test results have been reported. The PCR test value is thus determined as follows: V p = - 1 - S P P C R ∙ V T N + p ∙ 1 - p ∙ S E P C R ∙ V T P , (1) where SP denotes specificity, V TN is the value of a true-negative diagnosis, p denotes the pre-test (i.e., a priori) probability of COVID-19, SE refers to sensitivity, and V TP is the value of detecting (and isolating) a true-positive case. The first term defines the value of avoiding the costs of not diagnosing a true-negative case correctly. Costs are caused by an unnecessary isolation. The second term defines the positive value of diagnosing a true-positive case correctly. The value of identifying a true-positive case lies in preventing the transmission of COVID-19. The pre-test probability of a true-positive case is multiplied by its complimentary probability because the complimentary probability signifies the value created by PCR testing in a true-positive case (i.e., the value that goes above the pre-test probability). Hence, PCR testing yields a higher value when identifying a true-positive case with a low pre-test probability. Given that RATs are an alternative to PCR testing, the model calculates the incremental value of PCR tests over RATs: V p = - 1 - S P P C R ∙ V T N + p ∙ 1 - p ∙ S E P C R ∙ V T P - - 1 - S P R A T ∙ V T N + p ∙ 1 - p ∙ S E R A T ∙ V T P , (2) where SP PCR > SP RAT and SE PCR > SE RAT . I considered estimates of sensitivity and specificity to be independent, because estimates of specificity even for RATs are typically very high. That is, the correlation between sensitivity and specificity was considered negligible. Eq 2 was differentiated with respect to p to determine the pre-test probability, which yields an optimal incremental value: V ' p = 1 - 2 p ∙ S E P C R ∙ V T P - 1 - 2 p ∙ S E R A T ∙ V T P = 0 (3) ⇔ 1 - 2 p = 0 (4) ⇔ p * = 0.5 . (5) Given that the second derivate of V ( p ) is negative, the value of PCR testing is maximized at a pre-test probability of 0.5. Based on the negative quadratic terms of Eq 2 , the value function with respect to the pre-test probability is bell-shaped (see Fig 1 ). To determine lower and upper bounds for the pre-test probability, I analyzed two cases in which the lab-based PCR test-positivity rate in the population μ is either smaller or larger, respectively, than the value-maximizing probability p *. 10.1371/journal.pone.0285083.g001 Fig 1 Relationship between the value of polymerase chain reaction testing and the pre-test probability. Expanding the number of available PCR tests would allow testing individuals with a lower a priori probability, which reduces the test-positivity rate in the population μ . However, the expansion is constrained by the number of available PCR tests. The objective is thus to maximize the value of testing given the current test-positivity rate. The optimal pre-test probability interval includes the value-maximizing probability p * because testing at p * is most efficient. In general, the interval includes all individuals in whom testing value is larger than at the test-positivity rate. Assuming the case where μ < p * yields the following lower and upper bounds for the threshold pre-test probability ( λ L and λ U , respectively): λ L = μ + x μ - p * , μ ≥ - x μ - p * 0 , μ < - x μ - p * (6) λ U = p * + p * - μ = 2 p * - μ , (7) where x ]0, ∞) is a scaling factor that defines the share of the pre-test probability range below μ . If x = 1, one third of the pre-test probability range is below μ (if not bounded by zero) and covers half of the tested population. If x = 2, there is an equal share of the range above and below μ . The latter is justified by a lack of information about the distribution of a priori probabilities. Based on Eqs 6 and 7 it follows that decreasing the availability of PCR tests or increasing the demand for testing (both resulting in a higher test-positivity rate) leads to an increase in the lower bound and a decrease in the upper bound of the pre-test probability. Additionally, assuming the case where μ > p *, the following lower and upper bounds for the threshold pre-test probability are obtained: λ L = 1 - μ (8) λ U = μ + x μ - p * , μ + x μ - p * ≤ 1 1 , μ + x μ - p * > 1 . (9) If x = 1, one third of the pre-test probability range is above μ (if not bounded by one) and covers half of the tested population. If x = 2, there is an equal share of the pre-test probability range above and below μ . If λ U − λ L < μ − ( μ − λ L ), the range for the a priori probability is narrower than that for a uniform distribution of a priori probabilities. If the intention is not to strict access and if the same distribution as in Eqs 6 to 9 is assumed, the share of the population from which positive cases are drawn is set equal to μ − ( μ − λ L ). To satisfy λ U − λ L < μ − ( μ − λ L ), the updated upper threshold probability λ U u was calculated as follows: λ U u = μ + μ - ( μ - p * ) 2 , μ + μ - ( μ - p * ) 2 ≤ 1 1 , μ + μ - ( μ - p * ) 2 > 1 . (10) The updated lower threshold probability λ L u becomes: λ L u = μ - y μ 2 - p * 4 , μ - y μ 2 - p * 4 ≥ 0 0 , μ - y μ 2 - p * 4 < 0 , (11) where y ]0,1] is a scaling factor that defines the size of the testing population with a pre-test probability below μ relative to x . If y = 1, the portion of the tested population below μ is the same as in Eq 6 . That is, expanding the range of the pre-test probability does not lead to a more skewed distribution. If the distribution becomes more skewed, then y < 1 holds and the share of the population from which positive cases are drawn is still smaller than μ − ( μ − λ L ). Fig 2 shows the lower and upper bounds for the threshold pre-test probability depending on the PCR test-positivity rate. It is assumed that two thirds of the tested population have a pre-test probability below μ . 10.1371/journal.pone.0285083.g002 Fig 2 Lower and upper bounds for the threshold pre-test probability depending on the polymerase chain reaction test-positivity rate. (A) Contacts at normal risk. (B) Contacts at +100% risk. Given that V TP depends on the individual’s number of contacts, their age, and various other risk factors, we are able to derive equivalent threshold probabilities for a higher number of contacts or contacts at higher risk for complications. If V TP increases, the lower threshold probability decreases because PCR testing is then more valuable, even with a lower pre-test probability. The adjusted lower threshold probability λ L u u was calculated as follows: V λ L , V T P = λ L u ∙ 1 - λ L u ∙ V T P = λ L u u ∙ 1 - λ L u u ∙ V T P h i g h , (12) where V T P h i g h denotes the value of diagnosing a true-positive case with a higher number of contacts or contacts at higher risk for complications. Rearranging Eq 12 yields the following: - ( λ L u u ) 2 + λ L u u - λ L u ∙ 1 - λ L u ∙ V T P V T P h i g h = 0 . (13) Solving for λ L u u yields: λ L u u = - 1 ± 1 - 4 ∙ λ L u ∙ 1 - λ L u ∙ V T P V T P h i g h - 2 . (14) Following the reasoning for the lower threshold probability, if V TP increases, the higher threshold probability increases because PCR testing is then more valuable even at a higher pre-test probability. Thus, the adjusted higher threshold probability λ H u u is calculated as follows: λ H u u = - 1 ± 1 - 4 ∙ λ H u ∙ 1 - λ H u ∙ V T P V T P h i g h - 2 . (15) Fig 2B shows the lower and upper bounds for the threshold pre-test probability depending on the PCR test-positivity rate and assuming contacts at 100% risk. Results During the fifth calendar week of 2022, a total of 450,588 PCR tests for the diagnosis of COVID-19 were conducted daily in Germany [ 5 ]. The daily COVID-19 incidence was 133,173 on February 6, 2022 [ 6 ]. Therefore, the test-positivity rate was 30%. Based on Eqs 6 and 7 and assuming that at least two thirds of the tested population have a pre-test probability below the test-positivity rate, I obtained λ L ≥ 0.1 and λ U = 0.7. Hence, the minimum a priori probability of PCR testing in the general population was 10%. Next, I determined priority groups based on symptoms, exposure to COVID-19, and prior RAT results (see Table 1 ). I defined symptomatic people as having a 25% likelihood of testing positive. Even without a prior RAT, they would be eligible for PCR testing. However, if they test negative on an RAT, their negative predictive value is larger than 90% [ 7 ]; hence, they would be excluded from PCR testing. Furthermore, given that symptomatic individuals with a positive RAT have a positive predictive value of above 90% [ 7 ], they would also be excluded from PCR testing and could thus receive a second RAT instead. With the increasing scarcity of PCR tests and a lower threshold probability of above 25%, symptomatic people should only be tested by using RATs. 10.1371/journal.pone.0285083.t001 Table 1 Priorities for polymerase chain reaction (PCR) testing based on a PCR test-positivity rate of 30%. Asymptomatic Symptomatic General population Contacts at +100% risk Contacts of confirmed cases General population Contacts at +100% risk RAT positive + + + - - RAT negative - - - - - No RAT - - - + + RAT, rapid antigen test; + priority;—no priority For asymptomatic individuals with no known exposure to someone with COVID-19, a 1% pre-test probability approximating the 7-day incidence on February 7, 2022, was assumed. In this population, PCR testing would be valuable only after a positive RAT result. Health-care workers, those working in care homes with older patients, first responders (i.e., police officers, firefighters, military personnel, paramedics, medical evacuation pilots, dispatchers, nurses, doctors, emergency medical technicians, and emergency managers), and contacts of confirmed cases (especially family members) were assumed to have a 5–10% likelihood of testing positive [ 7 ]. Herein, PCR testing after a positive RAT result would only be valuable in individuals with a 5% likelihood of testing positive prior to RAT testing. For individuals who have twice the number of contacts or who have contacts with twice the usual risk, the lower testing threshold is 4.7%. In other words, the lower testing threshold is reduced to less than half. Conversely, the upper testing threshold increases to 88%. However, the recommendations for PCR testing for the defined prior probabilities do not change (see Table 1 ). The only exception are contacts of confirmed cases with a 10% likelihood of testing positive as positive RAT results should then be confirmed using PCR testing. Discussion To address lab-based PCR test bottlenecks resulting from high COVID-19 incidence rates, the model developed in this study maximizes the value of positive testing. Fundamentally, merely maximizing the number of positive tests in the testing population does not consider the pre-test probability of COVID-19 and hence the additional value of positive testing. Specifically, the model recommends using RATs to test asymptomatic individuals with no known exposure to COVID-19 and PCR testing in symptomatic people (in accordance with Du et al. [ 8 ]). Furthermore, positive RAT results from asymptomatic individuals with no known exposure to COVID-19 should be confirmed using a PCR test. Hence, using RATs among asymptomatic individuals with no known exposure to COVID-19 would be considered a triage tool that enriches the population taking a PCR test (cf. [ 9 ]). The notion of using PCR as a confirmatory test is corroborated with that of another COVID-19 testing model [ 10 ]. In contrast to previous models, however, this study defines the value-maximizing pre-test probability, shape of the value function, and upper and lower probability thresholds for priority PCR testing. Hence, individuals with pre-test probabilities outside the probability thresholds are not prioritized. This supports the idea that the “opportunity cost of a test exceeds the value of information for individuals with pre-test probabilities close to 0 or 1, and thus near certain types are left untested” [ 10 ]. The study by Smits et al. [ 11 ] made a valuable contribution by presenting a utility function for a diagnostic test. In contrast to my study, their research measured the value (utility) of obtaining outcomes such as a true-negative or true-positive diagnosis. However, their value (utility) function does not determine the incremental value of one diagnostic test compared to another. As a word of caution, the analysis implicitly assumes that the value of a positive PCR test is the same both for asymptomatic and symptomatic individuals. The value of a positive PCR test lies in reducing the transmission rate by isolating infectious individuals [ 12 ]. While the U.S. Centers for Disease Control and Prevention [ 13 ] considered infectiousness of asymptomatic individuals to be 25% lower relative to symptomatic patients (in the pre-Omicron era), asymptomatic individuals may transmit more than symptomatic individuals if they are unaware of their infection [ 14 ]. It is not clear to what degree these factors cancel out, that is, yield a value of a positive PCR test that is different for asymptomatic and symptomatic individuals. To incorporate transmission probability in the model would require adjusting the pre-test probabilities. In any case, the fundamental notion that the value of PCR testing is maximized at a pre-test probability of 0.5 remains. Changes in incidence lead to changes in the PCR test-positivity rate and, hence, influence the threshold for PCR testing. Therefore, the results of the application study present a snapshot and should not be extrapolated to different incidences. Nevertheless, for the same PCR test-positivity rate, results are transferable to different settings and countries. This study assumed an unlimited availability of RATs. Future research may thus address a simultaneous RAT testing constraint. "]}, { "id":"10.1371/journal.pone.0266197/results_and_discussion", "doc_partial_parent_id":"10.1371/journal.pone.0266197", "doc_type":"partial", "journal_eissn":"1932-6203", "publisher":"Public Library of Science", "journal":"PLOS ONE", "journal_id_pmc":"plosone", "journal_id_publisher":"plos", "journal_id_nlm_ta":"PLoS ONE", "eissn":"1932-6203", "publication_date":"2022-03-29T00:00:00Z", "received_date":"2021-10-12T00:00:00Z", "accepted_date":"2022-03-16T00:00:00Z", "article_type":"Research Article", "article_type_facet":"Research Article", "author":["Masashi Kamo", "Michio Murakami", "Wataru Naito", "Jun-ichi Takeshita", "Tetsuo Yasutaka", "Seiya Imoto"], "author_facet":["Masashi Kamo", "Michio Murakami", "Wataru Naito", "Jun-ichi Takeshita", "Tetsuo Yasutaka", "Seiya Imoto"], "editor":["Asep K Supriatna"], "editor_facet":["Asep K Supriatna"], "pagecount":14, "volume":17, "issue":3, "elocation_id":"e0266197", "journal_name":"PLOS ONE", "journal_key":"PLoSONE", "subject":["/Biology and life sciences/Molecular biology/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction", "/Biology and life sciences/Psychology/Behavior/Recreation/Games", "/Biology and life sciences/Psychology/Behavior/Recreation/Sports", "/Biology and life sciences/Sports science/Sports", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Epidemiology/Disease dynamics", "/Medicine and health sciences/Epidemiology/Medical risk factors", "/Medicine and health sciences/Medical conditions/Infectious diseases/Viral diseases/COVID 19", "/Medicine and health sciences/Pharmacology/Pharmacologic analysis/Pharmacokinetic analysis/Compartment models", "/Research and analysis methods/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction", "/Social sciences/Psychology/Behavior/Recreation/Games", "/Social sciences/Psychology/Behavior/Recreation/Sports"], "subject_hierarchy":["/Biology and life sciences/Molecular biology/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction", "/Biology and life sciences/Psychology/Behavior/Recreation/Games", "/Biology and life sciences/Psychology/Behavior/Recreation/Sports", "/Biology and life sciences/Sports science/Sports", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Epidemiology/Disease dynamics", "/Medicine and health sciences/Epidemiology/Medical risk factors", "/Medicine and health sciences/Medical conditions/Infectious diseases/Viral diseases/COVID 19", "/Medicine and health sciences/Pharmacology/Pharmacologic analysis/Pharmacokinetic analysis/Compartment models", "/Research and analysis methods/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction", "/Social sciences/Psychology/Behavior/Recreation/Games", "/Social sciences/Psychology/Behavior/Recreation/Sports"], "subject_facet":["/Biology and life sciences/Molecular biology/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction", "/Biology and life sciences/Psychology/Behavior/Recreation/Games", "/Biology and life sciences/Psychology/Behavior/Recreation/Sports", "/Biology and life sciences/Sports science/Sports", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Epidemiology/Disease dynamics", "/Medicine and health sciences/Epidemiology/Medical risk factors", "/Medicine and health sciences/Medical conditions/Infectious diseases/Viral diseases/COVID 19", "/Medicine and health sciences/Pharmacology/Pharmacologic analysis/Pharmacokinetic analysis/Compartment models", "/Research and analysis methods/Molecular biology techniques/Artificial gene amplification and extension/Polymerase chain reaction", "/Social sciences/Psychology/Behavior/Recreation/Games", "/Social sciences/Psychology/Behavior/Recreation/Sports"], "subject_level_1":["Biology and life sciences", "Medicine and health sciences", "Research and analysis methods", "Social sciences"], "striking_image":"10.1371/journal.pone.0266197.g006", "timestamp":"2026-03-14T09:31:27.210Z", "doc_partial_body":["\nGroup A: The effect of PCR testing every 2 weeks\nFig 1 shows the infection dynamics for a group of 100 players without any countermeasures against infection (no checking for symptoms, no tests at all). The total number of infected individuals at day 9 is about 4 (agreeing well with the assumption of R0 = 4), and the total number of infected individuals at about day 14 is about 10, implying that 10% of the individuals in a group are infected in 2 weeks, if no countermeasures are implemented.\n\n10.1371/journal.pone.0266197.g001\nFig 1\n\nInfection dynamics without any countermeasures.\nThe initial values are S(0) = 99, E(0) = 1, and the others are 0. The average of 10,000 replicates. Total number of infected individuals is the sum of E, P1, P2, Ia, and Is.\n\n\n\nIf the starting point of the simulation is taken to be the timing that an individual in the group becomes infected, then the day on which PCR testing is conducted is a random event, and the tests are conducted on day 0 to 13 with equal probability. Simulations were performed for each of all possible days with 10,000 replicates. The results are summarized in Table 3.\n\n10.1371/journal.pone.0266197.t003\nTable 3 Summary of simulation results. Averages of 10,000 repetitions each from day 0 to day 13 when the test is performed (140,000 replicates total).\n\n\n\n\n\n\n\n\n\nAverage days until the first positive confirmation (day) 1\n6.117\n\n\nNumber of positive individuals quarantined from the population due to positive confirmation 1\n1.147\n\n\nNumber of infected individuals remaining in the group after quarantine of detected infected individuals (number among them with E status).1 This is the risk.\n1.970 (1.211)\n\n\nPercentage of 140,000 repetitions in which positive cases were confirmed by symptom checking (%) 2\n62.50\n\n\nPercentage of 140,000 repetitions in which positive cases were confirmed by PCR testing (%) 2\n22.97\n\n\nPercentage of 14-day simulations with no positive confirmation (%) 2\n14.53\n\n\n\n\n\n1 Averages exclude cases where infected individuals were not confirmed within 14 days of simulation\n2 Sum of these three percentages becomes 100%\n\n\nFig 2A shows whether the detection of infected individuals was made by routine testing or by checking for symptomatic, for each day the test was conducted. When the first infected individual appeared on the day that PCR testing was conducted (day 0 on the horizontal axis), all detection of infected individuals was made by checking for symptoms (a black dot). The detection rate by PCR test (gray dots) was always lower than that by the checking for symptoms. When the PCR testing was conducted at day 4 after the first infection, about 45% of infected individuals were detected by the test (about 55% were detected by the checking for symptoms). This result implies that the infected individuals were mostly detected through the checking for symptoms rather than by the PCR test.\n\n10.1371/journal.pone.0266197.g002\nFig 2\n\n\nDetection rate of infected individuals (a) and waiting time for infection detection (b). (a) The ratio of infected individuals detected by checking for symptoms (black dots) with respect to those detected by routine PCR testing (gray dots). (b) The average waiting time until detection of infected individuals after the first infection occurred in the group. The overall average is 6.1 days. This implies that the first infected individual in the group occurs about 6 days (on average) before subsequently infected individuals are found.\n\n\n\nFig 2B shows the average waiting time until infected individuals were detected. If an infected individual appeared in the group on the day of the PCR test (day 0), it took an average of 6.5 days to detect subsequently infected individuals, and all detection was made by checking for symptomatic individuals. If the PCR test was conducted 4 days after the first infected individual appeared in the group, the average waiting time was shorter than that of testing at day 0. This is because the detection by PCR test was maximum (Fig 2A), but the difference from testing at day 0 is just about 1 day.\nThe fraction of infected individuals that were detected by checking for symptoms was 73.13% [= 100 × 62.50 / (62.50 + 22.97)] (Table 3). In this test system, it can be concluded that the role that routine PCR testing plays in detecting infected individuals is not as significant as checking for symptoms.\n\nGroup B: The effect of daily tests and daily checking for symptomatic individuals\nFig 3 shows the infection dynamics for a test system involving a daily antigen test and additional PCR test for those who test positive for antigens (the number of infected individuals excluding the individuals in state E are shown). Infected individuals were quarantined from the group, and the simulation continued for 14 days. The dynamics with various test error rates are shown. When there is no error, the number of infected individuals rises once but then decreases at around day 3 or 4. The dynamics indicates that the effective reproductive number is less than 1 in this test system with no error. In contrast, when the error rates are above 10%, the number of infected individuals keeps rising, indicating that the effective reproductive number is greater than 1.\n\n10.1371/journal.pone.0266197.g003\nFig 3\n\nInfection dynamics in Group B with the test system including an additional PCR test for individuals who test positive for antigens.\nThe initial condition of the dynamics is S(0) = 99, E(0) = 1, and all others are 0. The number of infected individuals in state E is excluded in the figure (see Eq 4 for the number of infected individuals). This is because individuals in state E are not infective and have no effect even if they participate in games.\n\n\n\nWe assume that an infectious disease is brought into the group from the outside only once. Under this assumption, if the infection is brought into the group 2 days after arrival at the destination, the infection spreads within the group for 12 days. The number of infected individuals is given by the number at day 12 in Fig 3. We define the total number of individuals infective at day t after the first infection as\n\n\n\n\nI(t)=P1(t)+P2(t)+Ia(t)+Is(t),(0≤t≤14).\n\n\n(4)\n\nThe probability that infection is brought into the group at day t is given by Eq 3, and hence the average number of infected individuals playing in the games (Im) is\n\n\n\n\nIm=∑t=014p(t)I(14−t).\n\n\n(5)\n\nThe dynamics of the test system with antigen and PCR tests can be solved in the same way as in Fig 3. Using the result of the dynamics and Eq 5, the risk of infected individuals participating in games after isolation can be obtained.\nThe results are shown in Fig 4A. Although it is almost obvious, the risk becomes higher as the error rate rises in any system. The risk is the lowest in the test system with PCR testing only, the second lowest in the test system with antigen testing only, and highest in the test system with an additional PCR test for individuals testing positive for antigens. The combination of two tests leads to increased risk, because infection is determined only when both tests are positive. This order was kept for all test error rates except when the rate was 1.0 which corresponds to no tests (ideally, risk by all test systems should be the same at this situation, but they were different due to variability caused by stochastic simulations).\n\n10.1371/journal.pone.0266197.g004\nFig 4\n\nRisks in Group B in various measurement scenarios.\n(a) Risks in Group B with different test systems and different test error rates. The risk with the test system with daily PCR testing only (○) was the lowest, that with daily antigen testing only (△) was the second lowest, and that with an additional PCR test for individuals testing positive for antigens (◇) was the highest. In all simulations, infected individuals showing symptoms (state Is) are quarantined daily. (b) The risk with different test frequency. Only PCR testing with 0% error was used for the test. Numbers on the horizontal axis indicate the number of days to the next test. For example, a number 2 means that the test frequency was every 2 days. In all test frequencies, the first test on arrival (day 0) at the destination is conducted at day 0. At up to 7-day frequencies, more than two tests were conducted within the 14 days’ isolation. After 8 days, tests were conducted two times, and at 15 days, testing is only once at day 0.\n\n\n\nWhen the error rate is 0, the risk of the test system with an additional PCR test for individuals testing positive for antigens was about 0.5×10−3. In the test system with the PCR test only, the risk reaches 0.5×10−3 when the error rate is about 0.4. Thus, the risk with the test system with an additional PCR test for individuals testing positive for antigens with zero error rate is equivalent to the risk with the test system that with a PCR test only with error rate of 0.4.\nFig 4B shows the risk by only PCR testing at different test frequencies, with test error rate of zero. Not surprisingly, the risk increased as the test frequency was reduced. Numbers along the horizontal axis represent the days to the next test, and hence a number 1, for example, means that the test is conducted daily. The risk for the “1 day to next test” in Fig 4B is equal to the risk with zero error rate of the daily PCR test in Fig 4A (○ on the vertical axis). The risk for the “15 days to next test” in Fig 4B is equal to the risk with 100% error rate, implying no test in Fig 4A. In all results in Fig 4B, PCR tests were conducted at least once on arrival (day 0) at the destination. The reason why the number of tests is different but the risk is the same is that the individuals already infected on arrival at the destination are in state E, which is a state that cannot be detected by testing. Furthermore, by comparing Fig 4A and 4B, we can understand the risk equivalency between test error and test frequency. In the test system with PCR only (○ in Fig 4A), the risk was 0.319×10−3 when the error rate was 0.2. The risk with PCR testing every 2 days was 0.347×10−3. These values imply that daily PCR testing with 20% error and PCR testing every 2 days with 0% error are risk equivalent.\nThe number of infected individuals at each time t in Eq 5 is shown in a stacked bar graph in Fig 5. This figure shows the contribution of the day the infected individual appeared in the group to the risk. In addition to the three test systems shown in Fig 4A, the risk with no tests but with daily checking for symptoms is also shown. Fig 5A shows risks with pp (probability that an individual is infected on arrival) is 1.0×10−4 (the value we have investigated so far, see Table 2). Fig 5B shows risks with pp = 1.0×10−3 (10 times higher). In Fig 5A, the risk without testing was 1.673×10−3. By conducting tests, the risk became 0.491×10−3 (antigen+PCR), 0.263×10−3 (antigen only), and 0.1480×10−3 (PCR only), and rates of reduction were respectively 70.65%, 84.25%, and 91.15%. When pp is 10 times higher (Fig 5B), risk without testing was 3.78×10−3, and the risk was reduced by 0.795×10−3 (antigen+PCR), 0.374×10−3 (antigen only), and 0.189×10−3 (PCR only). The contribution of pp (the brightest gray area) on all risks with no tests in Fig 5A was just 13.00%, but the contribution was 61.95% in Fig 5B. These results indicate that it is important to keep the risk of infection as low as possible at the point of arrival at the destination.\n\n10.1371/journal.pone.0266197.g005\nFig 5\n\nThe contribution of the day on which the infected individual appeared.\n(a) Results with parameters in Table 2. (b) Results when the probability that an individual was infected at arriving (pp) was 10 times higher (other parameters were the same). Test error rates were assumed to be 0%.\n\n\n\nSo far, we have defined the risk as the number of infected individuals participating in games after 14 days’ isolation. The number of individuals quarantined from the group as infected during the 14 days’ isolation (the number of individuals who cannot participate in games) might also be considered as a risk. Fig 6 shows the results of adding the number of individuals quarantined from the group due to the infection during the 14 days’ isolation to the number of infected individuals participating in the games in Fig 5. In contrast to Group A, removal due to infection mainly occurs by testing positive (except in the case of no tests, where of course there is no positive test result). The numbers of infected persons during the 14 days (i.e., the number of infected individuals playing in the games plus the number of individuals quarantined from the group) were 1.74×10−3, 1.93×10−3, 2.20×10−3, and 2.89×10−3 for PCR only, antigen only, antigen + PCR, and no test, respectively with pp = 10−4. If the probability that there is an infected individual on arrival increases tenfold, the numbers of individuals quarantined because of infection become about double in all test systems and were 3.38×10−3, 3.89×10−3, 4.66×10−3, and 6.94×10−3 for PCR only, antigen only, and antigen + PCR, and no test, respectively.\n\n10.1371/journal.pone.0266197.g006\nFig 6\n\nNumber of infected and quarantined individuals.\nNumber of infected individuals playing in the games (in Fig 5) plus the number of individuals quarantined from the group owing to infection. Black shows the number quarantined by checking for symptom, dark gray shows the number quarantined by routine testing, and light gray is the number in Fig 5 (number of infected individuals participating in the games). In the left panel, the probability that there is an infected individual at arrival (pp) is 1.0×10−4, and in the right panel the probability is 1.0×10−3.\n\n\n\nThe risk of infectious diseases and the effectiveness of countermeasures in two sports groups of different nature were investigated by using a stochastic compartment model. One group (Group A) is a professional sports team, which spends a season playing several games within a relatively small area. The other (Group B) is a group of players leaving their country to play an international match in a certain destination. They cross a border and are isolated there for a while, have a limited number of games, and then go home just after the games are over.\nRisk in Group A\nThe countermeasures for the group were a regular PCR test (every 2 weeks) for all players (and staff) and checking for symptomatic individuals. The individuals identified as infected (either by test or by checking for symptoms) are quarantined from the group. After the removal of these identified individuals, some unidentified infected individuals remain in the group, and the number of remaining infected individuals was defined as the risk in this group.\nIn this group, most of the infected individuals were identified by checking for symptoms, and the efficiency of the PCR test once per 2 weeks in identifying infected individuals was only about 1/3 of that of checking for symptoms (Table 3), indicating that the efficiency of the PCR tests to detect the infected individuals was not high. The reason is almost obvious: testing every 2 weeks is not frequent enough. In our parameterization, a susceptible individual becomes uninfected again 12 days after infection, and hence the dynamics of this infection has 12-day cycles. Identification of infected individuals by routine PCR testing can be thought of as a kind of sample survey. In order to reproduce the 12-day cyclic dynamics, samples must be taken at least every 6 days [21]. In other words, for higher efficiency, the frequency of testing should be increased.\nIn the test system in Group A, as shown in Table 3, after removal of infected individuals detected by testing and symptom confirmation, an average of 1.970 infected individuals remains in the group, of which 1.211are in state E, which cannot be detected by tests. Additional testing may be useful to detect these remaining infected individuals. However, because most of the remaining infected individuals in the group are of E status, few infected individuals would be detected by immediate additional testing. It may be more effective to wait a few days (for state E to become state P) before conducting additional tests after strict isolation for preventing new infections while waiting.\n\nRisk in Group B\nIn this population, we defined the risk as the number of infected individuals remaining in the group at the end of 2 weeks of isolation (the number of individuals participating in games in an infected state) and calculated the risk under several test systems. As can be seen from Fig 3, when there are no test errors, the effective reproduction number is below 1, and if a test system of daily antigen testing plus additional PCR testing for individuals who test positive for antigens (dual test system) is used, an outbreak of infection within the group can be prevented. However, if the error rate is more than 10%, the effective reproduction number will be more than 1, and the infection will spread within the group.\nAmong the three test systems (PCR test only, antigen test only, and dual test), the dual test system had the highest risk. Although PCR testing is costly and the number of tests is often limited, antigen testing is prone to false positives. The dual testing system helps reduce the number of PCR tests while also reducing the number of false positives that can occur with antigen testing. At the same time, however, a false-negative result on the second PCR test leads to the missing of infected individuals detected by the first antigen test. The second PCR test can serve as a relief measure for individuals who are identified as infected by false-positive results on the first antigen test. Providing relief measures for false-positive individual is an important task, but because relief measures increase the risk of infection, it is not easy to find out what the best system is. Further careful discussion on this point is needed. Note that we have assumed that the sensitivity of dual testing is a simple multiplication of the sensitivities of these two tests (assuming that the sensitivities of the tests are independent), but this assumption may not be valid in some cases (for example, where there is a possibility that a positive case by the first antigen test is likely to be positive again by the second PCR test).\nIn Fig 4B, we examined how the risk changed when the frequency of testing was reduced. The risk (the number of infected individuals playing games) was 0.347×10−3 when the test frequency was every 2 days. The risk with dual testing with no error (◇ in Fig 4A) was 0.491×10−3, and the value is higher than the risk with PCR testing every 2 days (0.347×10−3). This implies that PCR testing every 2 days had a lower risk than daily dual testing. If PCR testing can be performed on all subjects in terms of cost and availability of testing resources, then performing only the PCR test thoroughly on the subjects may be the most promising option for reducing the risk of infection.\nComparison of Fig 4A and 4B indicates that the risk with daily PCR testing only at an error rate of 20% was similar to the risk with PCR testing every 2 days at an error rate of 0%. This result shows the importance of collecting accurate and appropriate samples. Finding such a risk equivalence relationship is important for decision making, not only for infectious disease control but also for general risk assessment studies.\nDaily testing reduced the number of infected individuals after 14 days (i.e., those who participate in games while infected) by nearly 80% (Fig 5, dual test with pp = 1.0×10−3) and reduced the number of infected individuals during 14 days by nearly 30% (Fig 6, dual test with pp = 1.0×10−3), highlighting that daily testing is effective in reducing the number of infected players who go to games. Furthermore, keeping the initial number of infected individuals low is important to reduce the risk. The result is consistent with the result by Ndii et al. [22] who found that finding infected individuals as early as possible is important to reduce the number of undetected infected individuals. If infection control measures are taken before departure, any infected individuals will arrive at the destination in state E, a state that cannot be detected by tests. Although it is very important to reduce the initial number of infected individuals, testing immediately after entry into the country is not very useful. At the Tokyo Olympic and Paralympic Games, the athletes were generally tested twice, 96 hours before departure and once on the arrival. They were allowed to participate in Games-related activities for the first 3 days after their arrival if they tested negative for COVID-19 every day and operated under a higher level of supervision. Thorough testing before and after the arrival may have been a useful approach to reduce the risk of infection in the athlete village, but it will need to be verified separately whether only the 3-day testing and supervision after arrival was sufficient.\n"]}, { "id":"10.1371/journal.pone.0013721/supporting_information", "doc_partial_parent_id":"10.1371/journal.pone.0013721", "doc_type":"partial", "journal_eissn":"1932-6203", "publisher":"Public Library of Science", "journal":"PLoS ONE", "journal_id_pmc":"plosone", "journal_id_publisher":"plos", "journal_id_nlm_ta":"PLoS ONE", "eissn":"1932-6203", "publication_date":"2010-10-29T00:00:00Z", "received_date":"2010-03-18T00:00:00Z", "accepted_date":"2010-10-05T00:00:00Z", "article_type":"Research Article", "article_type_facet":"Research Article", "author":["Junwei Wang", "Meiwen Jia", "Liping Zhu", "Zengjin Yuan", "Peng Li", "Chang Chang", "Jian Luo", "Mingyao Liu", "Tieliu Shi"], "author_facet":["Junwei Wang", "Meiwen Jia", "Liping Zhu", "Zengjin Yuan", "Peng Li", "Chang Chang", "Jian Luo", "Mingyao Liu", "Tieliu Shi"], "editor":["Mary Bryk"], "editor_facet":["Mary Bryk"], "pagecount":13, "volume":5, "issue":10, "elocation_id":"e13721", "journal_name":"PLOS ONE", "journal_key":"PLoSONE", "subject":["/Biology and life sciences/Genetics/Gene expression", "/Computer and information sciences/Systems science/Nonlinear systems", "/Medicine and health sciences/Oncology/Cancers and neoplasms/Breast tumors/Breast cancer", "/Physical sciences/Mathematics/Probability theory/Probability distribution/Normal distribution", "/Physical sciences/Mathematics/Probability theory/Probability distribution/Skewness", "/Physical sciences/Mathematics/Probability theory/Statistical distributions", "/Physical sciences/Mathematics/Probability theory/Statistical distributions/Distribution curves", "/Physical sciences/Mathematics/Systems science/Nonlinear systems", "/Research and analysis methods/Bioassays and physiological analysis/Microarrays"], "subject_hierarchy":["/Biology and life sciences/Genetics/Gene expression", "/Computer and information sciences/Systems science/Nonlinear systems", "/Medicine and health sciences/Oncology/Cancers and neoplasms/Breast tumors/Breast cancer", "/Physical sciences/Mathematics/Probability theory/Probability distribution/Normal distribution", "/Physical sciences/Mathematics/Probability theory/Probability distribution/Skewness", "/Physical sciences/Mathematics/Probability theory/Statistical distributions", "/Physical sciences/Mathematics/Probability theory/Statistical distributions/Distribution curves", "/Physical sciences/Mathematics/Systems science/Nonlinear systems", "/Research and analysis methods/Bioassays and physiological analysis/Microarrays"], "subject_facet":["/Biology and life sciences/Genetics/Gene expression", "/Computer and information sciences/Systems science/Nonlinear systems", "/Medicine and health sciences/Oncology/Cancers and neoplasms/Breast tumors/Breast cancer", "/Physical sciences/Mathematics/Probability theory/Probability distribution/Normal distribution", "/Physical sciences/Mathematics/Probability theory/Probability distribution/Skewness", "/Physical sciences/Mathematics/Probability theory/Statistical distributions", "/Physical sciences/Mathematics/Probability theory/Statistical distributions/Distribution curves", "/Physical sciences/Mathematics/Systems science/Nonlinear systems", "/Research and analysis methods/Bioassays and physiological analysis/Microarrays"], "subject_level_1":["Biology and life sciences", "Computer and information sciences", "Medicine and health sciences", "Physical sciences", "Research and analysis methods"], "striking_image":"10.1371/journal.pone.0013721.g003", "timestamp":"2026-03-14T00:56:06.421Z", "doc_partial_body":["File S1\nFormula of T-test and F-test, proof of independence between skewness, kurtosis, mean, and variance, transform of moments, biological model\n(0.23 MB DOC)\nFile S2\nProof of SWang test\n(0.06 MB DOC)\nFile S3\nGeneral inverse of matrix,relation between SWang test and T-test\n(0.05 MB DOC)\nFile S4\nThe pseudo codes of simulation on SWang test, T-test, F-test, SAM, Fold-change to calculate false positive rate and statistics power, and the SAS/iml code for calculate SWang\n(0.05 MB DOC)\nFile S5\nThis file contains supporting information tables and a list of reference\n(0.18 MB DOC)\nFigure S1\nFalse positive rate of T-test, F-test, Fold-change, SAM(0.3), and SWang respectively, with 5 Case-control Samples from Uniform distribution. Under Complex distribution for case and control. A: False positive rate of SWang(1,2) and other methods. B: False positive rate of SWang(1,3) and other methods. C: False positive rate of SWang(1,4) and other methods. D: False positive rate of SWang(2,3) and other methods. E: False positive rate of SWang(2,4) and other methods. F: False positive rate of SWang(1,3) and other methods. The false positive rate of T-test(black spotline), F-test(gray spotline), Fold change(green spotline), SWang(blue spotline), and SAM(0.3)(red spotline) with cutoff of p-value.\n(4.80 MB TIF)\nFigure S2\nFalse positive rate of T-test, F-test, Fold-change, SAM(0.3), and SWang, respectively, with 5 Case-control Samples from complex distribution, respectively. Under Normal distribution for case and control. A: False positive rate of SWang(1,2) and other methods. B: False positive rate of SWang(1,3) and other methods. C: False positive rate of SWang(1,4) and other methods. D: False positive rate of SWang(2,3) and other methods. E: False positive rate of SWang(2,4) and other methods. F: False positive rate of SWang(1,3) and other methods. The false positive rate of T-test(black spotline), F-test(gray spotline), Fold change(green spotline), SWang(blue spotline), and SAM(0.3)(red spotline) with cutoff of p-value.\n(4.80 MB TIF)\nFigure S3\nFalse positive rate of T-test, F-test, Fold-change, SAM(0.3), and SWang, respectively, with different Samples from Uniform distribution. Under Uniform distribution for case and control. A: False positive rate of SWang(1,2) and other methods. B: False positive rate of SWang(1,3) and other methods. C: False positive rate of SWang(1,4) and other methods. D: False positive rate of SWang(2,3) and other methods. E: False positive rate of SWang(2,4) and other methods. F: False positive rate of SWang(1,3) and other methods. SS = 3, 6, 8, 12, 20, 40, 100, and 200 mean that there exist 3, 6, 8, 12, 20, 40, 100, and 200 case-control samples, respectively. The false positive rate of T-test(black spotline), F-test(gray spotline), Fold change(green spotline), SWang(blue spotline), and SAM(0.3)(red spotline) with cutoff of p-value. (Note: FPR of SAM and Fold-change for large sample sizes are similar to those of SAM and Fold-change for 3 samples. To better display the FPR of methods, the graphs will not plot the FPR of SAM and Fold-change when the sample size is greater than 3.)\n(9.06 MB TIF)\nFigure S4\nFalse positive rate of T-test, F-test, Fold-change, SAM(0.3), and SWang, respectively, with different Samples from Normal distribution. Under Normal distribution for case and control. A: False positive rate of SWang(1,2) and other methods. B: False positive rate of SWang(1,3) and other methods. C: False positive rate of SWang(1,4) and other methods. D: False positive rate of SWang(2,3) and other methods. E: False positive rate of SWang(2,4) and other methods. F: False positive rate of SWang(1,3) and other methods. SS = 3, 6, 8, 12, 20, 40, 100, and 200 mean that there exist 3, 6, 8, 12, 20, 40, 100, and 200 case-control samples, respectively. The false positive rate of T-test(black spotline), F-test(gray spotline), Fold change(green spotline), SWang(blue spotline), and SAM(0.3)(red spotline) with cutoff of p-value.\n(9.06 MB TIF)\nFigure S5\nFalse positive rate of T-test, F-test, Fold-change, SAM(0.3), and SWang, respectively, with different Samples from Complex distribution. Under complex distribution for case and control. A: False positive rate of SWang(1,2) and other methods. B: False positive rate of SWang(1,3) and other methods. C: False positive rate of SWang(1,4) and other methods. D: False positive rate of SWang(2,3) and other methods. E: False positive rate of SWang(2,4) and other methods. F: False positive rate of SWang(1,3) and other methods. SS = 3, 6, 8, 12, 20, 40, 100, and 200 mean that there exist 3, 6, 8, 12, 20, 40, 100, and 200 case-control samples, respectively. The false positive rate of T-test(black spotline), F-test(gray spotline), Fold change(green spotline), SWang(blue spotline), and SAM(0.3)(red spotline) with cutoff of p-value.\n(9.06 MB TIF)\nFigure S6\nFalse positive rate of T-test, F-test, Fold-change, SAM(0.3), and SWang, respectively, with different Samples from Exponential distribution. Under Exponential distribution for case and control. A: False positive rate of SWang(1,2) and other methods. B: False positive rate of SWang(1,3) and other methods. C: False positive rate of SWang(1,4) and other methods. D: False positive rate of SWang(2,3) and other methods. E: False positive rate of SWang(2,4) and other methods. F: False positive rate of SWang(1,3) and other methods. SS = 3, 6, 8, 12, 20, 40, 100, and 200 mean that there exist 3, 6, 8, 12, 20, 40, 100, and 200 case-control samples, respectively. The false positive rate of T-test(black spotline), F-test(gray spotline), Fold change(green spotline), SWang(blue spotline), and SAM(0.3)(red spotline) with cutoff of p-value.\n(9.06 MB TIF)\nFigure S7\nFalse positive rate of T-test, F-test, Fold-change, SAM(0.3), and SWang, respectively, with different Samples from Cauchy distribution. Under Cauchy distribution for case and control. A: False positive rate of SWang(1,2) and other methods. B: False positive rate of SWang(1,3) and other methods. C: False positive rate of SWang(1,4) and other methods. D: False positive rate of SWang(2,3) and other methods. E: False positive rate of SWang(2,4) and other methods. F: False positive rate of SWang(1,3) and other methods. SS = 3, 6, 8, 12, 20, 40, 100, and 200 mean that there exist 3, 6, 8, 12, 20, 40, 100, and 200 case-control samples, respectively. The false positive rate of T-test(black spotline), F-test(gray spotline), Fold change(green spotline), SWang(blue spotline), and SAM(0.3)(red spotline) with cutoff of p-value.\n(9.06 MB TIF)\nFigure S8\nFalse positive rate of T-test, F-test, Fold-change, SAM(0.3) in ‘Spike-in’ dataset. A: False positive rate of SWang(1,2) and other methods. B: False positive rate of SWang(1,3) and other methods. C: False positive rate of SWang(1,4) and other methods. D: False positive rate of SWang(2,3) and other methods. E: False positive rate of SWang(2,4) and other methods. F: False positive rate of SWang(1,3) and other methods. The false positive rate of T-test(black spotline), F-test(grey spotline), Fold change(yellow spotline), SWang(blue spotline), and SAM(0.3)(red spotline) with cutoff of p-value.\n(6.41 MB TIF)\nFigure S9\nStatistical power of T-test, F-test, Fold change, SAM(0.3), and SWang(1,4) with small sample sizes. A: Statistics power of those methods are under Normal distribution for case. B: under Exponetial distribution for case. C: under Uniform distribution for case. D: under Gamma distribution for case. E: under mixture of gamma and normal distribution of case group. F: under complex distribution which is a combination of various distribution for case.The statistical power of T-test (black spotline), F-test(gray spotline), Fold change(green spotline), SWang(blue spotline), and SAM(0.3)(red spotline) under simulation. (Note: the Size is equal to product of (Total-2)*m+n-3*Total+4, the total is the largest sample size is simulation.)\n(9.06 MB TIF)\nFigure S10\nStatistical power of T-test, F-test, Fold change, SWang (1, 4), SAM(0.3) on Normal distribution and Normal distribution. The statistical power of T-test (black spotline), F-test(gray spotline), Fold change(green spotline), SWang(blue spotline), and SAM(0.3)(red spotline) under simulation. A: SWang(1,2), T-test, F-test, SAM(0.3) and Fold change. B: SWang(1,3), T-test, F-test, SAM(0.3) and Fold change. C: SWang(1,4), T-test, F-test, SAM(0.3) and Fold change; D: SWang(2,3), T-test, F-test, SAM(0.3) and Fold change. E: SWang(2,4), T-test, F-test, SAM(0.3) and Fold change. F: SWang(3, 4), T-test, F-test, SAM(0.3) and Fold change. (Note: the Size is equal to product of (Total-2)*m+n-3*Total+4, the total is the largest sample size is simulation.)\n(9.06 MB TIF)\nFigure S11\nStatistical power of T-test, F-test, Fold change, SAM(0.3), and SWang based on Normal distribution and Normal distribution with small sample size. The statistical power of T-test (black spotline), F-test(gray spotline), Fold change(green spotline), SWang(blue spotline), and SAM(0.3)(red spotline) under simulation. A: SWang(1,2), T-test, F-test, SAM(0.3) and Fold change. B: SWang(1,3), T-test, F-test, SAM(0.3) and Fold change. C: SWang(1,4), T-test, F-test, SAM(0.3) and Fold change; D: SWang(2,3), T-test, F-test, SAM(0.3) and Fold change. E: SWang(2,4), T-test, F-test, SAM(0.3) and Fold change. F: SWang(3, 4), T-test, F-test, SAM(0.3) and Fold change. (Note: the Size is equal to the product of (Total-2)*m+n-3*Total+4, the total is the largest sample size is simulation.)\n(9.06 MB TIF)\nFigure S12\nStatistical power of T-test, F-test, Fold-change, SWang (1, 4), SAM(0.3) on Exponential distribution and Normal distribution. The statistical power of T-test (black spotline), F-test(gray spotline), Fold change(green spotline), SWang(blue spotline), and SAM(0.3)(red spotline) under simulation. A: SWang(1,2), T-test, F-test, SAM(0.3) and Fold change. B: SWang(1,3), T-test, F-test, SAM(0.3) and Fold change. C: SWang(1,4), T-test, F-test, SAM(0.3) and Fold change; D: SWang(2,3), T-test, F-test, SAM(0.3) and Fold change. E: SWang(2,4), T-test, F-test, SAM(0.3) and Fold change. F: SWang(3, 4), T-test, F-test, SAM(0.3) and Fold-change. (Note: the Size is equal to the product of (Total-2)*m+n-3*Total+4, the total is the largest sample size is simulation.)\n(9.06 MB TIF)\nFigure S13\nStatistical power of T-test, F-test, Fold change, SWang (1, 4), SAM(0.3) under Uniform distribution and Normal distribution. The statistical power of T-test (black spotline), F-test(gray spotline), Fold change(green spotline), SWang(blue spotline), and SAM(0.3)(red spotline) under simulation. A: SWang(1,2), T-test, F-test, SAM(0.3) and Fold change. B: SWang(1,3), T-test, F-test, SAM(0.3) and Fold change. C: SWang(1,4), T-test, F-test, SAM(0.3) and Fold change; D: SWang(2,3), T-test, F-test, SAM(0.3) and Fold change. E: SWang(2,4), T-test, F-test, SAM(0.3) and Fold change. F: SWang(3, 4), T-test, F-test, SAM(0.3) and Fold change. From figures, it shows that when the distribution of the case group's gene expression is complex distributions which is simple addition of Normal, Uniform, and Triangual distribution, the statistics power of SWang are decentralized. (Note: the Size is equal to the product of (Total-2)*m+n-3*Total+4, the total is the largest sample size is simulation.)\n(9.06 MB TIF)\nFigure S14\nStatistical power of T-test, F-test, Fold change, SWang (1, 4), SAM(0.3) under Gamm distribution and Normal distribution. The statistical power of T-test (black spotline), F-test(gray spotline), Fold change(green spotline), SWang(blue spotline), and SAM(0.3)(red spotline) under simulation. A: SWang(1,2), T-test, F-test, SAM(0.3) and Fold change. B: SWang(1,3), T-test, F-test, SAM(0.3) and Fold change. C: SWang(1,4), T-test, F-test, SAM(0.3) and Fold change; D: SWang(2,3), T-test, F-test, SAM(0.3) and Fold change. E: SWang(2,4), T-test, F-test, SAM(0.3) and Fold change. F: SWang(3, 4), T-test, F-test, SAM(0.3) and Fold change. (Note: the Size is equal to the product of (Total-2)*m+n-3*Total+4, the total is the largest sample size is simulation.)\n(9.06 MB TIF)\nFigure S15\nStatistical power of T-test, F-test, Fold change, SWang (1, 4), SAM(0.3) under mixture of Gamm & Normal distribution and Normal distribution. The statistical power of T-test (black spotline), F-test(gray spotline), Fold change(green spotline), SWang(blue spotline), and SAM(0.3)(red spotline) under simulation. A: SWang(1,2), T-test, F-test, SAM(0.3) and Fold change. B: SWang(1,3), T-test, F-test, SAM(0.3) and Fold change. C: SWang(1,4), T-test, F-test, SAM(0.3) and Fold change; D: SWang(2,3), T-test, F-test, SAM(0.3) and Fold change. E: SWang(2,4), T-test, F-test, SAM(0.3) and Fold change. F: SWang(3, 4), T-test, F-test, SAM(0.3) and Fold change. (Note: the Size is equal to the product of (Total-2)*m+n-3*Total+4, the total is the largest sample size is simulation.)\n(9.06 MB TIF)\nFigure S16\nStatistical power of T-test, F-test, Fold change, SWang (1, 4), SAM(0.3) under complex distribution and Normal distribution. The statistical power of T-test (black spotline), F-test(gray spotline), Fold change(green spotline), SWang(blue spotline), and SAM(0.3)(red spotline) under simulation. A: SWang(1,2), T-test, F-test, SAM(0.3) and Fold change. B: SWang(1,3), T-test, F-test, SAM(0.3) and Fold change. C: SWang(1,4), T-test, F-test, SAM(0.3) and Fold change; D: SWang(2,3), T-test, F-test, SAM(0.3) and Fold change. E: SWang(2,4), T-test, F-test, SAM(0.3) and Fold change. F: SWang(3, 4), T-test, F-test, SAM(0.3) and Fold change. (Note: the Size is equal to the product of (Total-2)*m+n-3*Total+4, the total is the largest sample size is simulation.)\n(9.06 MB TIF)\nFigure S17\nWNT Signal Pathway. The genes detected by SWang test but not by T-test, F-test, Fold-change, and SAM in Wnt signaling pathway based on KEGG. The genes in pink are the genes selected with our method.\n(6.98 MB TIF)\nFigure S18\n5-venn diagram in dataset1. The cut-off of p-value of T-test, F-test, SAM(0.3), and SWang is 0.05, the cut-off of Fold-change is 2.\n(8.71 MB TIF)\nFigure S19\n5-venn diagram in dataset2. The cut-off of p-value of T-test, F-test, SAM (0.3), and SWang is 0.05, while the cut-off of Fold-change is 2.\n(8.75 MB TIF)\nFigure S20\nSemiquantative RT-PCR comparision. The genes which could not be detected by Swang test but were by the others are randomly selected. MCF-10A cells were cultured in DMEM/F12 with 10%FBS, 20ng/ml EGF, 0.5ug/ml Hydrocortisone, 0.01ug/ml Insulin and 0.1ug/ml Cholera toxin. MCF-7, SK-BR-3, MDA-MB-453 and MDA-MB-231 were maintained in DMEM with 10%FBS. PCR products were run on 2% agarose gel and then stained with ethidium bromide. Stained bands were visualized under UV light and photographed. The beta-actin used as an internal control.\n(1.90 MB TIF)\n"]}, { "id":"10.1371/journal.pone.0134578/results_and_discussion", "doc_partial_parent_id":"10.1371/journal.pone.0134578", "doc_type":"partial", "journal_eissn":"1932-6203", "publisher":"Public Library of Science", "journal":"PLOS ONE", "journal_id_pmc":"plosone", "journal_id_publisher":"plos", "journal_id_nlm_ta":"PLoS ONE", "eissn":"1932-6203", "publication_date":"2015-07-30T00:00:00Z", "received_date":"2015-06-01T00:00:00Z", "accepted_date":"2015-07-13T00:00:00Z", "article_type":"Research Article", "article_type_facet":"Research Article", "author":["Lee F Schroeder", "Ali Elbireer", "J Brooks Jackson", "Timothy K Amukele"], "author_facet":["Lee F Schroeder", "Ali Elbireer", "J Brooks Jackson", "Timothy K Amukele"], "editor":["Madhukar Pai"], "editor_facet":["Madhukar Pai"], "pagecount":14, "volume":10, "issue":7, "elocation_id":"e0134578", "journal_name":"PLOS ONE", "journal_key":"PLoSONE", "subject":["/Biology and life sciences/Microbiology/Medical microbiology/Microbial pathogens/Viral pathogens/Immunodeficiency viruses/HIV", "/Biology and life sciences/Microbiology/Medical microbiology/Microbial pathogens/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Biology and life sciences/Organisms/Viruses/Immunodeficiency viruses/HIV", "/Biology and life sciences/Organisms/Viruses/RNA viruses/Retroviruses/Lentivirus/HIV", "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Immunodeficiency viruses/HIV", "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Medicine and health sciences/Diagnostic medicine/Clinical laboratory sciences/Clinical laboratories", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Health care/Health economics", "/Medicine and health sciences/Medical conditions/Infectious diseases/Bacterial diseases/Tuberculosis", "/Medicine and health sciences/Medical conditions/Parasitic 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and life sciences/Organisms/Viruses/RNA viruses/Retroviruses/Lentivirus/HIV", "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Immunodeficiency viruses/HIV", "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Medicine and health sciences/Diagnostic medicine/Clinical laboratory sciences/Clinical laboratories", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Health care/Health economics", "/Medicine and health sciences/Medical conditions/Infectious diseases/Bacterial diseases/Tuberculosis", "/Medicine and health sciences/Medical conditions/Parasitic diseases/Malaria", "/Medicine and health sciences/Medical conditions/Tropical diseases/Malaria", "/Medicine and health sciences/Medical conditions/Tropical diseases/Tuberculosis", "/Medicine and health sciences/Pathology and laboratory medicine/Pathogens/Microbial pathogens/Viral pathogens/Immunodeficiency viruses/HIV", "/Medicine and health sciences/Pathology and laboratory medicine/Pathogens/Microbial pathogens/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Medicine and health sciences/Public and occupational health", "/People and places/Geographical locations/Africa/Uganda", "/Social sciences/Economics/Health economics"], "subject_facet":["/Biology and life sciences/Microbiology/Medical microbiology/Microbial pathogens/Viral pathogens/Immunodeficiency viruses/HIV", "/Biology and life sciences/Microbiology/Medical microbiology/Microbial pathogens/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Biology and life sciences/Organisms/Viruses/Immunodeficiency viruses/HIV", "/Biology and life sciences/Organisms/Viruses/RNA viruses/Retroviruses/Lentivirus/HIV", "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Immunodeficiency viruses/HIV", "/Biology and life sciences/Organisms/Viruses/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Medicine and health sciences/Diagnostic medicine/Clinical laboratory sciences/Clinical laboratories", "/Medicine and health sciences/Diagnostic medicine/Virus testing", "/Medicine and health sciences/Health care/Health economics", "/Medicine and health sciences/Medical conditions/Infectious diseases/Bacterial diseases/Tuberculosis", "/Medicine and health sciences/Medical conditions/Parasitic diseases/Malaria", "/Medicine and health sciences/Medical conditions/Tropical diseases/Malaria", "/Medicine and health sciences/Medical conditions/Tropical diseases/Tuberculosis", "/Medicine and health sciences/Pathology and laboratory medicine/Pathogens/Microbial pathogens/Viral pathogens/Immunodeficiency viruses/HIV", "/Medicine and health sciences/Pathology and laboratory medicine/Pathogens/Microbial pathogens/Viral pathogens/Retroviruses/Lentivirus/HIV", "/Medicine and health sciences/Public and occupational health", "/People and places/Geographical locations/Africa/Uganda", "/Social sciences/Economics/Health economics"], "subject_level_1":["Biology and life sciences", "Medicine and health sciences", "People and places", "Social sciences"], "striking_image":"10.1371/journal.pone.0134578.g003", "timestamp":"2026-03-14T03:36:13.279Z", "doc_partial_body":["Test menus and daily laboratory-wide test volumes were obtained from 95% (907/954) of the laboratories identified in Kampala city. Based on these 907 laboratories, 100 different types of tests were offered in the city (Fig 1).\n10.1371/journal.pone.0134578.g001\nFig 1\n\nFull list of tests offered in Kampala, grouped by Availability Index.\nThe numbers in parentheses refer to position of the test in Figs 2 and 3. The Availability Index takes into account the size of the laboratories offering the test. See methods for the calculation.\n\n\n\nCommon Test Types and their Prices\nTable 1 shows the 10 most commonly offered tests in Kampala. It also shows the average price of these tests in Kampala in Ugandan shillings and U.S. dollars, and the price of similar tests in the United States as determined by Center for Medicare and Medicaid Services clinical laboratory fee schedule.[18] In decreasing order, the most commonly offered test types in Kampala were Malaria, Human Chorionic Gonadotropin (HCG), HIV serology, Syphilis, Typhoid, Urinalysis, Brucellosis, Stool Analysis, Glucose, and ABO/Rh typing. The average price of these tests in Kampala, Uganda was $2.62, ranging from $1.83 to $3.46. In the U.S., the average price of similar tests was $10.21, ranging from $3.62 to $17.97.\n\n10.1371/journal.pone.0134578.t001\nTable 1 Ten most commonly offered tests in Kampala: Names, Number of laboratories, and Prices.\n\n\n\n\n\n\n\n\n\n\n\n\n\nTest\nNumber of Labs\nPercent of Labs\nPrice per test in Kampala (Uganda Shilling)*\nPrice per test in Kampala (US$)**\nPrice per test in US (US$)***\n\n\n\n\nMalaria****\n822\n91%\n5,321\n1.83\n7.95\n\n\nHCG\n743\n82%\n6,375\n2.20\n11.24\n\n\nHIV\n736\n81%\n8,887\n3.06\n17.97\n\n\nSyphilis\n619\n68%\n7,940\n2.74\n7.00\n\n\nTyphoid\n560\n62%\n9,838\n3.39\n17.27\n\n\nUrinalysis\n496\n55%\n7,561\n2.61\n3.62\n\n\nBrucellosis\n353\n39%\n10,041\n3.46\n11.70\n\n\nStoolAnalysis\n350\n39%\n6,965\n2.40\n17.22\n\n\nGlucose\n293\n32%\n5,937\n2.05\n4.19\n\n\nABORh\n228\n25%\n7,298\n2.52\n3.90\n\n\n\n\n\n* Prices adjusted by the Ugandan consumer price index to 2011 prices\n** Prices converted at an exchange rate of 2,900 Ugandan Shillings to 1 US dollar\n***Prices derived from CMS fee schedule (see methods) and converted to 2011 prices\n****Price is for malaria smear microscopy.\n\n\n\nTest Availability\nTests varied widely in their availability. The 10 most commonly offered tests were offered in a median of 528 laboratories each, while the bottom 80 tests were offered in a median of 6 laboratories each. The 100 tests offered in Kampala clustered into 3 groups based on their Availability Indices (S1 Fig). The full bars in Figs 2 and 3 represent the raw data points used in clustering. The boundaries (dashed lines) describing high, moderate, and minimal availability represent results of clustering. The three test clusters had average Availability Indices of 64%, 26%, and 4%, which we describe as high, moderate, and minimal availability (Fig 1). The high availability group consisted of 12 types of tests, the moderate availability group consisted of 33 types of tests, and the minimally available group consisted of 55 types of tests.\n\n10.1371/journal.pone.0134578.g002\nFig 2\n\nBar graph of tests offered in Kampala, ranked by Availability Index* and sub-categorized by laboratory affiliation.\nBar graph depicting the contribution of different sectors in the laboratory market to availability of tests in Kampala, Uganda. Each number on the Y axis corresponds to a different test (see Fig 1 or S2 Table for identification of tests).\n\n\n\n\n10.1371/journal.pone.0134578.g003\nFig 3\n\nBar graph of tests offered in Kampala, ranked by Availability Index* and sub-categorized by laboratory complexity.\nBar graph depicting the contribution of complex versus POC laboratories to availability of tests in Kampala, Uganda. Each number on the Y axis corresponds to a different test (see Fig 1 or S2 Table for identification of tests).\n\n\n\n\nLaboratory Affiliation\nPrivate laboratories offered 99 different types of tests, public laboratories offered 56 types of tests, religious/NGO laboratories offered 66 types of tests, and academic laboratories offered 19 types of tests.\nAs the vast majority of laboratories in Kampala are private laboratories,[15] the availability of a given test as measured solely by the number of laboratories offering the test, is dominated by the private sector (Table 1). However, when using the Availability Index, which adjusts for the size of laboratories offering the test, both private and public laboratories contributed substantially (Fig 2). Private laboratories contributed 65% and public laboratories contributed 26% to the availability of highly available tests. Public laboratories contributed 52% and private laboratories contributed 35% to the availability of moderately available tests. Private laboratories contributed 59% and NGO/religious laboratories contributed 34% to the availability of minimally available tests. Overall, test availability was provided primarily through private laboratories (50%) and public laboratories (36%). Tests in which availability was provided largely by private laboratories included tests that are available in POC formats (e.g. HIV serology) as well as those not available in POC formats (e.g. HIV PCR). Conversely, tests with availability largely deriving from public laboratories tended to be tests that are not typically available in POC formats (e.g. thyroid function, bilirubin). Finally, private laboratories offered 18 tests in excess of 15% Availability Index, while public laboratories offered 37 such tests.\n\nLaboratory Complexity\nLaboratories in the survey were also categorized based on whether they performed only simple POC tests, or also high complexity tests (Fig 3). POC laboratories contributed significantly only to a handful of tests, but these ranked among the most available in Kampala. The high availability group of tests had significant contribution from both POC and high complexity laboratories. The moderate and minimal availability groups of tests had significant contribution only from high complexity laboratories.\n\nSpending on Laboratory Testing\nThe average price of a test in Kampala was $2.62 (Table 2) and the aggregate daily testing volume of all laboratories in Kampala, Uganda was 13,189. Assuming 250 active days per year for laboratories, this equates to 3.3 million tests annually. The population of Kampala is estimated at 1.72 million,[19] and thus 1.9 tests per person per year were performed on average, and at $2.62 per test, $5.02 was spent on testing per person per year. The World Bank estimates the amount spent on health expenditures per person per year in Uganda was $54 in 2011.[17] Because Kampalans likely spend more on healthcare per person than Ugandans, this $54 was multiplied by an estimate of the ratio of consumption expenditure in Kampala vs Uganda. According to the Ugandan Board Of Statistics in 2012, this ratio was 2.0 when considering the monthly household consumption expenditure per month and was 2.8 when considering the average per capita consumption expenditure.[19] Depending on which estimate is used, the annual spent on health per person in Kampala ranges from $110 to $152. If $5.02 is spent on testing per person per year in Kampala, this estimate of medical laboratory expenditures represents 3.3% to 4.6% of total health spending.\n\n10.1371/journal.pone.0134578.t002\nTable 2 Per capita spending on Laboratory Testing in Kampala, Uganda.\n\n\n\n\n\n\n\n\n\n\n\n\nHealth Spending on Laboratory Testing in Kampala, Uganda\n\n\nAverage price of a test\nAnnual tests per person*\nAnnual $ spent on tests per person\nAnnual $ spent on health per person**\nHealth spending on laboratory\n\n\n\n\n$2.6\n1.9\n$5.0\n$110–$152\n3.3%–4.6%\n\n\n\n\n\n* Assumed population of Kampala of 1.72 million[19]\n**Annual total health spending per person for Uganda taken from The World Bank, adjusted by the ratio of consumption expenditures in Kampala vs Uganda (see methods)[19].\n\n\nThis report, based on a comprehensive survey of laboratories in Kampala, Uganda (population ~ 1.72 million), presents data on test availability and price in this sub-Saharan African city. It also describes the relationship of test availability to laboratory affiliation, such as private, public, NGO/religious, or academic, as well as laboratory complexity. There were 100 distinct test types offered in Kampala. These tests fell into three groups in terms of their relative Availability Index (high, moderate, minimal) and the average prices of the 10 most commonly offered tests ranged from $1.83-$3.46.\nNumber of Test Types in Kampala\nThis survey included all tests from both public and non-public laboratories. Compared to prior studies, this more comprehensive approach helped unearth unique information. For example we found 100 different types of tests in use in Kampala city, where the DHS Program Service Provision Assessment (SPA) typically surveys for roughly 25 tests.[12] Clearly, 100 is a larger number than 25, but it begs a deeper question: is this variety broad enough to address the basic clinical queries of Kampala’s citizens’? This question cannot be answered directly because local disease burdens in Kampala are not well-described, and furthermore, refined test utilization algorithms do not exist for most tests. However an indirect comparison, based on patterns of laboratory testing use in the USA, suggests that 100 tests are sufficiently varied to meet the basic clinical needs of a community. To illustrate, there are 1250 Healthcare Common Procedure Coding System (HCPCS) codes listed in the CMS clinical laboratory fee schedule.[18] However, the CMS Physician Supplier Procedure Summary 2012 data base, which lists tests and volumes reimbursed by CMS programs, shows that 100 HCPCS codes account for 86% of test volume, and 200 codes account for 95% of test volume. Furthermore, a particular type of test may be represented in more than one code. For example, there is an HCPCS code for manual urinalysis, and another for automated urinalysis. Seen in this context, the 100 types of tests available in laboratories in Kampala appear to provide a level of test variety that is on par with the basic level of test variety in Western countries.\nHowever, this conclusion assumes that all 100 tests are available at a level needed for clinical care. Although disease burdens do vary between Kampalan and U.S. populations, overall testing per person in Kampala is 2 tests per person per year, contrasted with 20 to 30 tests per person per year in the United States.[20,21] Furthermore, the availability of roughly half of the 100 tests found in Kampala—those in the minimal availability cluster—was very restricted. To illustrate, at the time of the survey we found only 2 laboratories in Kampala providing D-dimer testing. Further studies investigating disease burdens and optimal test utilization could help address if test availability is adequate.\n\nTest Availability versus Disease Burden\nTest availability appears to follow burden of disease. For example, HIV and malaria rapid testing are highly available, while testing for prostate-specific antigen and testosterone are minimally available. Still, there are some peculiarities that deserve discussion.\nFirst, although tuberculosis represents a major burden of disease, tuberculosis testing does not appear in the high availability group. There are likely explanations for this. For example tuberculin skin testing (TST), an inexpensive screen for TB, is minimally available. While this may not seem rational at first, Uganda recommends use of BCG vaccination; thus reducing the utility of TST. Likewise, tuberculosis serological testing is in the minimal availability group, but this test has not proven to be useful for tuberculosis testing and as discussed below, the World Health Organization has recommended against its use. Acid fast bacilli staining and microscopy is an appropriate testing strategy for Kampala, but is only found in the moderate availability group. This is likely because it is a complex test while the high availability testing group consists nearly exclusively of tests that are available in easy to use, point of care formats (see Fig 3). This gap supports the global effort that has been underway to develop and employ inexpensive point of care devices for tuberculosis testing.[22]\nSecond, tests for non-communicable diseases, with the exception of glucose, were found in the moderately available group. This is likely because all these tests (except glucose) are offered nearly exclusively in complex laboratories while glucose testing is offered in POC labs as well as complex labs (Fig 3).\nFinally, some tests addressing relatively low burdens of disease are much more available than many tests addressing high burdens of disease. This can be understood in part by realizing that the ideal availability of a test depends on many factors beyond the burden of disease it addresses: cost of the test, accuracy of the test, clinical impact of the test (e.g., does it change management and outcome), and use of the test in diseases that mimic more common diseases with higher burdens. For example, several accurate, inexpensive, and easy to use tests are available for syphilis testing (Treponema pallidum particle agglutination assay, rapid plasma reagin, and multiple lateral flow diagnostic immunoassays), which may explain why syphilis testing is the 2nd most available test although it addresses a relatively low burden of disease. Likewise, brucellosis testing is relatively highly available while addressing a relatively low burden of disease. This could be due to availability of inexpensive lateral flow testing formats, high prevalence of brucellosis in Uganda with occasional outbreaks, and the fact that brucellosis is on the differential with more common non-specific febrile disease like malaria.[23]\n\nTest Availability versus Laboratory Affiliation\nOnly public and private laboratories contributed significantly to the availability of high and moderate availability tests. Private and NGO/religious sectors were the primary contributors of the minimal availability tests, thus providing low volume, niche tests like Hb A1c, C-reactive protein, and HIV PCR. For example, contributions to the HIV PCR Availability Index were 58% from private laboratories, 26% from NGO/religious laboratories, and 16% from public laboratories. This pattern is consistent with recent literature demonstrating the significant impact the private sector has on health care in resource limited settings. For instance, The World Bank estimates that 74% of health care dollars spent in Uganda are spent in the private sector, and 50.5% of health care dollars spent in sub-Saharan Africa are spent in the private sector.[13]\nHowever, the impact of private sector health care delivery is not always positive. The World Bank reported that the private health sector was regulated as intended in only 6 of 45 countries.[13] To illustrate the impact that an unregulated laboratory testing market can have, we present the example of tuberculosis serology testing in India.[24] TB serology testing has never enjoyed a robust evidence base for diagnosis of TB. For this reason the WHO had never included these tests in guidelines. However, the private sector in India primarily offered serological TB tests because they were very popular among patients and physicians.[25] Subsequent studies showing lack of diagnostic utility were performed[26,27] and led the WHO to issue their first ever negative endorsement.[28] Today, TB serology testing is no longer legal in India. This example shows the negative impact the private sector can have, operating largely out of view of policy makers. Because of the significant impact the private sector makes to many health systems, it should not be ignored.\n\nTest Availability versus Test Complexity\nRegarding POC vs high complexity laboratory testing, our data are consistent with the prevailing idea that implementation of POC diagnostics can increase test access in resource-limited settings.[2,29] In our survey, tests that had the greatest Availability Indices were also those that were being offered to a significant extent in POC laboratories, and were thus available in a POC format. Roughly one-third of the availability of the high availability tests were contributed by POC laboratories. Of the moderate and minimal availability tests, only 6% was contributed by POC laboratories.\nBut a key concern of promoting additional POC testing is quality. Although there are very few laboratories of any type in sub-Saharan Africa that are accredited to international standards,[30] smaller laboratories in both high- and low-resourced environments, tend to be more POC-reliant and more quality-challenged than larger laboratories.[31] The smaller laboratories in Kampala, which were largely POC laboratories, tended to be the laboratories with the lowest quality scores. Elbireer et al. survey found that 704 out of 718 POC laboratories did not meet the lowest quality standards defined by the WHO/AFRO-derived laboratory strengthening tool (1–5 stars).[15] Thus the benefits of the POC format must be balanced against the challenge of assuring quality in the laboratories that will likely be using the tests.\n\nTest Prices\nFinally, our data show that the most commonly offered tests are priced between $1.83 and $3.46. We estimate that a similar fraction of the household healthcare budgets in Kampala is spent on laboratory testing compared to levels in the US market. At a population level of 1.72 million and a daily testing volume of 13,189, citizens of Kampala, Uganda consume an average of 1.9 tests per year. In the United States this number is estimated at 20 to 30 tests per person per year,[20,21] which is clearly much higher. However, when considering the health dollars spent in Kampala and the price of testing, total investment in laboratory medicine is substantial. As detailed in Table 2, our estimates of the percentage of health spending in Kampala that is devoted to laboratory testing ranges from 3.3% to 4.6%. This rough estimate is similar to that for the United States where 3% of Medicare part B payments in 2010 were laboratory expenditures.[32] Furthermore, estimates of U.S. laboratory testing expenditures as a percent of total health expenditures have been very stable, varying between 2–3% from 1998 to 2007.[20]\nThis analysis had several limitations. First, the survey was conducted in 2011 and there may have been significant changes in the laboratory landscape since that time. For example, if more automated analyzers are being employed in Kampala, it would be likely that testing for non-communicable diseases—which are more commonly performed on automated analyzers—has increased. Second, the original survey only collected up to 18 tests per laboratory. Although this was sufficient for the majority of laboratories[14] some did offer more than 18 tests and in the attempt to gather these additional data we were successful for only a subset of laboratories. Third, price data were collected in 2015, and although adjusted by the consumer price index, may have introduced a bias when comparing to the original 2011 test volume data. Furthermore, price data was collected from a small subset of the laboratory landscape (20 laboratories). Although they were chosen to represent the complexity distribution of the overall laboratories, they may not represent the full variation of prices in Kampala. Additionally, test menus and volumes were self-reported as opposed to employing more active surveillance methods such as review of monthly testing workloads. Still, this study is important because it represents the first comprehensive description of the utilization of laboratory testing in a large sub-Saharan Africa city. It provides unique actionable data to guide interventions that are locally relevant.\n"]}] }}