Confidence Intervals for Seroprevalence

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. To conclude, we outline the application of the methods that we consider to several related problems, and we provide a set of practical recommendations.

Operational analysis for COVID-19 testing: Determining the risk from asymptomatic infections

“…Third, an objection may be made that we have assumed the values for test errors rather than estimating them. DiCiccio et al [54] show that estimating test errors at the same time as incidence rate is a much more complex problem, and is likely one whose solution is not easily transferred to recommendations for practice. An alternative is to stratify test results by both symptomatic or not and time since putative exposure, have approximate values for the test errors for each time since exposure, and conduct sensitivity analysis by varying the values of the test errors.…”

Confidence Intervals for Prevalence Estimates from Complex Surveys with Imperfect Assays

“…For simple random sample surveys with imperfect sensitivity and specificity, Lang and Reiczigel 4 proposed an approximate method that performed well in simulations. Recent work by DiCiccio, et al 5 and Cai et al 6 study both valid (i.e., exact) and approximate methods. Their valid methods use test inversion and the adjustment of Berger and Boos 7 , while their approximation methods use the bootstrap with the test inversion approach.…”

“…Kalish et al 8 developed one such method that is closely related to one of the methods presented here, but that method's properties were not studied. Cai et al 6 (see also discussion in DiCiccio et al 5 ) modify their approximation approach to allow sample weights, but it assumes that the number of counts of events within the strata are large (see their Remark 4). Thus, it would not apply to a weighted survey method where each individual their own weight.…”

“…and show through simulations that it beats the best of those in each of the three stages with respect to guaranteeing coverage. We did not include in our simulations the new methods that have been developed in response to the COVID-19 pandemic and are not yet in print in peer reviewed journals 6,5,9 . The exact method of DiCiccio, et al 5 would guarantee coverage, although applying it to a survey with a large number of strata would be "computationally expensive", and it has not been applied to surveys using post-stratification weighting.…”