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To make informative public policy decisions in battling the ongoing COVID-19 pandemic, it is important to know the disease prevalence in a population. There are two intertwined difficulties in estimating this prevalence based on testing results from a group of subjects. First, the test is prone to measurement error with unknown sensitivity and specificity. Second, the prevalence tends to be low at the initial stage of the pandemic and we may not be able to determine if a positive test result is a false positive due to the imperfect test specificity. The statistical inference based on a large sample approximation or conventional bootstrap may not be valid in such cases. In this paper, we have proposed a set of confidence intervals, whose validity doesn't depend on the sample size in the unweighted setting. For the weighted setting, the proposed inference is equivalent to hybrid bootstrap methods, whose performance is also more robust than those based on asymptotic approximations. The methods are used to reanalyze data from a study investigating the antibody prevalence in Santa Clara County, California in addition to several other seroprevalence studies. Simulation studies have been conducted to examine the finite-sample performance of the proposed method.

Exact inference for disease prevalence based on a test with unknown specificity and sensitivity