  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.
