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Estimation of Population Prevalence of COVID-19 Using Imperfect Tests

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  • Leonid Hanin

    (Department of Mathematics and Statistics, Idaho State University, 921 S. 8th Avenue, Stop 8085, Pocatello, ID 83209-8085, USA)

Abstract

I formulate three basic biomedical/statistical assumptions that should ideally guide well-designed population prevalence studies of the present or past disease including COVID-19. On the basis of these assumptions alone, I compute several probability distributions required for statistical analysis of testing data collected from a sample of individuals drawn from a heterogeneous population. I also construct a consistent asymptotically unbiased estimator of the population prevalence of the disease or infection from the collected data and derive a simple upper bound for its variance. All the results are rigorously proved and valid for any test for COVID-19 or other disease provided that the sum of the test’s sensitivity and specificity is larger than 1. A few recommendations for the design of COVID-19 prevalence studies informed by the results of this work are formulated. The methodology developed in this article may prove applicable to diseases and conditions other than COVID-19 as well as in some non-epidemiological settings.

Suggested Citation

  • Leonid Hanin, 2020. "Estimation of Population Prevalence of COVID-19 Using Imperfect Tests," Mathematics, MDPI, vol. 8(11), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1900-:d:438091
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    References listed on IDEAS

    as
    1. Andrew Gelman & Bob Carpenter, 2020. "Bayesian analysis of tests with unknown specificity and sensitivity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1269-1283, November.
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