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EVIDENCE BASEDÌýINSIGHT

Simulation of Pool Testing to Identify Patients with Coronavirus Disease 2019 under Conditions of Limited Test Availability

ÌýSeptember 21, 2020 Ä¢¹½´«Ã½¢ 4 min read

ALHAJI CHERIF, PhDÌýÄ¢¹½´«Ã½¢ÌýNADJA GROBE, PhDÌýÄ¢¹½´«Ã½¢ÌýXIAOLING WANG, PhDÌýÄ¢¹½´«Ã½¢ÌýPETER KOTANKO, MD, FASN

Specimens from patients with suspected coronavirus disease 2019Ìý() undergo real-time reverse transcriptaseÄ¢¹½´«Ã½“polymeraseÌýchain reaction (RT-PCR) testing for severe acute respiratoryÌýsyndrome coronavirus 2 (SARS-CoV-2) RNA detection. The highÌýdemand for SARS-CoV-2 RT-PCR tests during the COVID-19Ìýpandemic has resulted in local shortages, prompting researchersÌýto consider pool testing strategies.¹ÌýCOVID-19 pool testing is usedÌýin several countries. On July 18th, 2020 the U.S. Food and DrugÌýAdministration (FDA) issued the first emergency use authorizationÌýfor COVID-19 pool testing.

Pool testing strategies build on testing a pooled sample fromÌýseveral patients: If the results from the pool test are negative,Ìýall patients in the pooled sample are declared not to haveÌýCOVID-19; if the results of the pool are positive, each patientÌýsample is tested individually. The pooled testing strategyÌýis appealing, particularly when test availability is limited.ÌýHowever, any test sensitivity less than 100 percent bears theÌýrisk of a false-negative result for the entire pool. To supportÌýinformed decision making regarding the implementation ofÌýpool testing for COVID-19, we have developed a probabilisticÌýmodel to estimate the risk of false negatives considering threeÌýdetermining factors: COVID-19 prevalence, test sensitivity, andÌýpatient pool size (Figure 1).

FIGURE 1Ìý|ÌýOptimal pool size and corresponding efficiency, probability of false negative, savings, and expected number of false negatives with respect to prevalence and test errors for a pool of 94 patients

FIGURE 1Ìý| cont.

METHODS

This decision analytical model study did not require institutionalÌýreview board review because it used simulation-based research,Ìýper Common Rule 45 CFR §102 (e). This study followed theÌýStrengthening the Reporting of Empirical Simulation StudiesÌý(STRESS) reporting guideline.Ìý

We considered a two-stage pool testing^2,3Ìýin the presence ofÌýimperfect testing, in whichÌý±èÌýis prevalence,Ìý³§±ðÌýis test sensitivity, andÌýS±èÌýis specificity. We assumed that the probability of a true-positiveÌýresult pool test equalsÌýSe, the probability of a false-positive resultÌýequals 1 −ÌýS_p, testsÌýS_eÌýandÌýS_pÌýwould be unaffected by the number ofÌýpatients in a pool (k), and all tests are identically distributed. LetÌýZÌýbe a random variable denoting the number of tests needed toÌýcomplete the pooling strategy. LetÌýNÌýbe the total number of patients,Ìýthen there areÌýN/kÌýsubgroups, each withÌýkÌýmembers. AssumingÌýindependent Bernoulli trials, letÌýP_kÌýbe the probability of having atÌýleast 1 positive test inÌýkÌýpatients. If 1 patient of the subgroup hasÌýRT-PCR results positive for SARS-CoV-2, then there will beÌý(kÌý+ 1) tests necessary; otherwise, only one test will be needed. TheÌýexpected number of tests for each subgroup withÌýkÌýpatients isÌý(kÌý+ 1)P_kÌý+ (1 −ÌýP_k). Then, forÌýN/kÌýsubgroups, the expected numberÌýof tests needed isÌýE(Z) = (N/k)[(kÌý+ 1)P_kÌý+ (1 −ÌýP_k)] = (N/k)[kP_kÌý+ 1], inÌýwhichÌýP_kÌý= (1 −ÌýS_p)(1 −Ìýp)^kÌý+ÌýS_e(1 − (1 −Ìýp)^k), which incorporates theÌýeffects of test sensitivity and specificity. The optimal pool size isÌýachieved forÌýkÌýthat minimizesÌýE(Z). To characterize the pooled testÌýstrategy, we define efficiency of the pool asÌýEfÌý=ÌýE(Z)/NÌý= [kP_kÌý+ 1]/kÌýand expected number of false negatives (ENFN) asÌýkp(1 −ÌýS²_e). This method does not include a dilution effect on the pooling strategyÌýsensitivity,ÌýPSÌý=ÌýS²_e, as a function of pool size, whereÌýS²_eÌýprovides the upperÌýbound of the pooling sensitivity.

RESULTS

For demonstration purposes, we reported the results for aÌýtypical number of RT-PCR tests for 94 patients, a specificityÌýof 100 percent, a prevalence from 0.001 percent to 40 percent,Ìýand sensitivities from 60 percent to 100 percent (Figure 1).ÌýMathematical simulations showed that a pool testing strategy wasÌýan improvement over individual testing for a prevalence less thanÌý30 percent and that the optimal pool size,Ìýk0, was approximatelyÌý1 + 1/√(pS_e),±èÌý∈ (0.1 percent, 30 percent). For a realistic scenario,Ìýsuch as a sensitivity of 70 percent and prevalence of 1 percent,Ìýthe optimal strategy required 13 patients per subgroup. With thisÌýoptimal pool size, only 16 percent as many tests would be requiredÌýby subgroup tests than by individual tests. Figure 2 shows testÌýefficiency, cost savings, probability of false negatives, and theÌýexpected number of false negatives forÌýkÌýandÌýp.

FIGURE 2Ìý|ÌýOperating characteristics of pooled testing stratified by prevalence

DISCUSSION

This decision analytical model study found that pool testingÌýefficiency varied with prevalence, test sensitivity, and patient poolÌýsize. Therefore, pool testing may be considered as an alternative,Ìýespecially in circumstances of limited SARS-CoV-2 test availabilityÌýand a COVID-19 prevalence less 30 percent. One potentialÌýlimitation of pool testing is that the false-negative rate mayÌýincrease owing to dilution of positive samples. The mean viralÌýload of more than 1.5 × 10⁴ÌýRNA copies per mL in nasal swabs⁴Ìýspikes within the first week after clinical onset and reachesÌý1.5×10⁷ÌýRNA copies per mL.⁵ÌýIn our example with an optimalÌýpool size of 13 patients, high-sensitivity RT-PCR assays with aÌýlower detection limit of more than 1,100 RNA copies per mLÌýwill detect SARS-CoV-2 in pooled samples. If sensitivity of theÌýtest at hand is a concern, test swabs can be collected and elutedÌýinto one virus transportation medium container, therebyÌýincreasing reliability. However, this requires re-collectingÌýindividual samples if a pool tests positive. The mathematicalÌýunderpinning of the proposed method is generic and can beÌýapplied to other infectious diseases.^6,7

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References

1. Yelin I, Aharony N, Shaer Tamar E, et al. Evaluation of COVID-19 RT-qPCR test in multi-sample pools.ÌýClin Infect Dis.ÌýPublished online May 2, 2020;ciaa531. doi:10.1093/cid/ciaa531.
2. Dorfman R. The detection of defective numbers of large populations.ÌýAnn Math Stat.Ìý1943;14:436-440. doi:10.1214/aoms/1177731363.
3. Johnson NL, Kotz S, Wu X.ÌýInspection errors for attributes in quality control.ÌýLondon, New York: Chapman & Hall, 1991.
4. Wang W, Xu Y, Gao R, et al. Detection of SARS-CoV-2 in different types of clinical specimens. JAMA. 2020;323(18):1843-1844. doi:10.1001/jama.2020.3786.
5. Zou L, Ruan F, Huang M, et al. SARS-CoV-2 viral load in upper respiratory specimens of infected patients.ÌýN Engl J Med.Ìý2020;382(12):1177-1179. doi:10.1056/NEJMc2001737.
6. Zenios SA, Wein LM. Pooled testing for HIV prevalence estimation: exploiting the dilution effect.ÌýStat MedÌý1998;17(13):1447-67. doi:10.1002/(SICI)1097- 0258(19980715)17:13<1447::AID-SIM862>3.0.CO;2-K.
7. Cherif A, Grobe N, Wang X, Kotanko, P. Simulation of pool testing to identify patients with coronavirus disease 2019 under conditions of limited test availability.ÌýJAMA Network OpenÌý2020 May;3(6):e2013075. doi: 10.1001/jamanetworkopen.2020.13075.