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On the True Number of COVID-19 Infections: Effect of Sensitivity, Specificity and Number of Tests on Prevalence Ratio Estimation

Author

Listed:
  • Eitan Altman

    (INRIA, Centre de Recherche de Sophia Antipolis-Mediterranee, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis CEDEX, France
    Laboratoire Informatique d’Avignon, Campus Jean-Henri Fabre, Avignon Universite, 84 911 Avignon, France
    Laboratory of Information, Network and Communication Sciences, Avignon Universite, 75013 Paris, France)

  • Izza Mounir

    (Centre Hospitalier Universitaire de Nice, School of Medicine, Université Côte D’Azur, 30 Voie Romaine, 06000 Nice, France)

  • Fatim-Zahra Najid

    (Centre Hospitalier Universitaire Amiens Picardie, School of Medicine, Université de Picardie Jules Verne, 1 Rue du Professeur Christian Cabrol, 80054 Amiens, France)

  • Samir M. Perlaza

    (INRIA, Centre de Recherche de Sophia Antipolis-Mediterranee, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis CEDEX, France)

Abstract

In this paper, 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 than one. Second, the key parameter for reducing the estimation error is the number of tests. For a large number of tests, as long as the sum of the sensitivity and specificity is different than one, the exact values of these parameters have very little impact on the estimation error.

Suggested Citation

  • Eitan Altman & Izza Mounir & Fatim-Zahra Najid & Samir M. Perlaza, 2020. "On the True Number of COVID-19 Infections: Effect of Sensitivity, Specificity and Number of Tests on Prevalence Ratio Estimation," IJERPH, MDPI, vol. 17(15), pages 1-21, July.
    • Handle: RePEc:gam:jijerp:v:17:y:2020:i:15:p:5328-:d:389075
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