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On the true number of COVID-19 infections: Effect of Sensitivity, Specificity and Number of Tests on Prevalence Ratio Estimation

Abstract : In this report, a formula for estimating the prevalence ratio of a disease in a population that is tested with imperfect tests is given. The formula is in terms of the fraction of positive test results and test parameters, i.e., probability of true positives (sensitivity) and the probability of true negatives (specificity). The motivation of this work arises in the context of the COVID-19 pandemic in which estimating the number of infected individuals depends on the sensitivity and specificity of the tests. In this context, it is shown that approximating the prevalence ratio by the ratio between the number of positive tests and the total number of tested individuals leads to dramatically high estimation errors, and thus, unadapted public health policies. The relevance of estimating the prevalence ratio using the formula presented in this work is that precision increases with the number of tests. Two conclusions are drawn from this work. First, in order to ensure that a reliable estimation is achieved with a finite number of tests, testing campaigns must be implemented with tests for which the sum of the sensitivity and the specificity is sufficiently different from one. Second, the key parameter for reducing the estimation error is the number of tests. For large number of tests, as long as the sum of the sensitivity and specificity is different from one, the exact values of these parameters have very little impact on the estimation error.
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https://hal.inria.fr/hal-02633844
Contributor : Samir M. Perlaza <>
Submitted on : Tuesday, August 4, 2020 - 10:42:03 AM
Last modification on : Tuesday, September 15, 2020 - 9:42:31 AM

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Eitan Altman, Izza Mounir, Fatim-Zahra Najid, Samir Perlaza. On the true number of COVID-19 infections: Effect of Sensitivity, Specificity and Number of Tests on Prevalence Ratio Estimation. [Research Report] RR-9344, INRIA Sophia Antipolis - Méditerranée. 2020. ⟨hal-02633844v3⟩

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