Confidence Intervals for Seroprevalence

TL;DR

This paper evaluates methods for constructing confidence intervals in seroprevalence surveys, highlighting issues with standard approaches and proposing alternative test-inversion techniques that improve coverage accuracy.

Contribution

It introduces and compares test-inversion based confidence intervals for seroprevalence, demonstrating their improved coverage properties over standard methods.

Findings

Standard Wald and bootstrap intervals show erratic coverage.

Test-inversion intervals achieve near-nominal coverage in simulations.

Some intervals are conservative but reliably contain the true parameter.

Abstract

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.