Estimation of Population Prevalence of COVID-19 Using Imperfect Tests

Leonid Hanin
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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

Mathematics, 2020, vol. 8, issue 11, 1-16

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.

Keywords: COVID-19; disease prevalence; false positive test result; false negative test result; sensitivity; specificity; study design (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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