Estimation of Population Prevalence of COVID-19 Using Imperfect Tests

Leonid Hanin

doi:10.3390/math8111900

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.

Highlights

IntroductionUncovering the true scale of COVID-19 pandemic is critical for shaping public health policy, designing effective medical interventions, and planning economic, social, and educational activities
Uncovering the true scale of COVID-19 pandemic is critical for shaping public health policy, designing effective medical interventions, and planning economic, social, and educational activities.This requires conducting testing studies aimed at the assessment of the unknown prevalence of the ongoing or past infection in a given population
By compounding distributions (1) and (2), we find that random variable X has binomial distribution B( N, αp)

Summary

Introduction

Uncovering the true scale of COVID-19 pandemic is critical for shaping public health policy, designing effective medical interventions, and planning economic, social, and educational activities. This requires conducting testing studies aimed at the assessment of the unknown prevalence of the ongoing or past infection in a given population. Due to the fact that COVID-19 is highly contagious and has a relatively short incubation period, the prevalence of COVID-19 in a population may change on the time scale of weeks. To provide a meaningful estimate of the population prevalence of COVID-19, testing studies should be conducted during a short period of time

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Conclusion