August 2022 Confidence Intervals for Seroprevalence
Thomas J. DiCiccio, David M. Ritzwoller, Joseph P. Romano, Azeem M. Shaikh
Author Affiliations +
Statist. Sci. 37(3): 306-321 (August 2022). DOI: 10.1214/21-STS844


This paper concerns the construction of confidence intervals in standard seroprevalence surveys. In particular, we discuss methods for constructing confidence intervals for the proportion of individuals in a population infected with a disease using a sample of antibody test results and measurements of the test’s false positive and false negative rates. We begin by documenting erratic behavior in the coverage probabilities of standard Wald and percentile bootstrap intervals when applied to this problem. We then consider two alternative sets of intervals constructed with test inversion. The first set of intervals are approximate, using either asymptotic or bootstrap approximation to the finite-sample distribution of a chosen test statistic. We consider several choices of test statistic, including maximum likelihood estimators and generalized likelihood ratio statistics. We show with simulation that, at empirically relevant parameter values and sample sizes, the coverage probabilities for these intervals are close to their nominal level and are approximately equi-tailed. The second set of intervals are shown to contain the true parameter value with probability at least equal to the nominal level, but can be conservative in finite samples.

Funding Statement

We acknowledge funding from the National Science Foundation under the Graduate Research Fellowship Program and under the grants MMS-1949845 and SES-1530661.


The authors would like to thank the anonymous referees, an Associate Editor, and the Editor for their constructive comments that improved the quality of this paper.


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Thomas J. DiCiccio. David M. Ritzwoller. Joseph P. Romano. Azeem M. Shaikh. "Confidence Intervals for Seroprevalence." Statist. Sci. 37 (3) 306 - 321, August 2022.


Published: August 2022
First available in Project Euclid: 21 June 2022

MathSciNet: MR4444369
zbMATH: 07569963
Digital Object Identifier: 10.1214/21-STS844

Keywords: confidence intervals , novel coronavirus , serology testing , seroprevalence , test inversion

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.37 • No. 3 • August 2022
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