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

Eitan Altman, Izza Mounir, Fatim-Zahra Najid and Samir M. Perlaza
Additional contact information
Eitan Altman: INRIA, Centre de Recherche de Sophia Antipolis-Mediterranee, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis CEDEX, 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

IJERPH, 2020, vol. 17, issue 15, 1-21

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.

Keywords: SARS-CoV-2; Covid-19; cross-sectional studies; prevalence ratio; sensitivity and specificity; molecular, serological and medical imaging diagnostics; number of infections; false positive and false negative probabilities; policy-making and testing campaigns (search for similar items in EconPapers)
JEL-codes: I I1 I3 Q Q5 (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/1660-4601/17/15/5328/pdf (application/pdf)
https://www.mdpi.com/1660-4601/17/15/5328/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jijerp:v:17:y:2020:i:15:p:5328-:d:389075

Access Statistics for this article

IJERPH is currently edited by Ms. Jenna Liu

More articles in IJERPH from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().