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Exact Tests for Disease Prevalence Studies With Partially Validated Data

Abstract To estimate the disease prevalence, a gold standard test is the best choice for accurate estimation. The gold standard could be very expensive or time consuming for use in practice. For this reason, a screening test may be used together with the gold standard to improve the test results, although the new test may not be as accurate as the gold standard. When some subjects in the study are tested by both tests and the remaining subjects are only tested by the screening test, this is a so-called double-sampling scheme. Data from such studies are partially validated. The prevalence of disease is often the parameter of interest from such studies. The traditionally used asymptotic approach based on limiting distributions of test statistics generally has unacceptable Type I error control. The approximate unconditional approach based on estimation was applied to this problem and shown to have a better performance than the asymptotic approach with regard to Type I error control. These approaches do not guarantee the Type I error rate. For this reason, we consider two exact approaches for testing the prevalence of disease for data from a double-sampling scheme. One is the exact approach based on maximization, and the other is the approach based on estimation and maximization. The approach based on estimation and maximization needs more computational cost than the approach based on maximization. The former approach is generally more powerful than the maximization approach, although the gain is negligible to small. We found that exact approaches based on the Wald-type test statistic with variance estimate using the restricted parameter estimates have a satisfactory performance as compared to exact approaches based on other test statistics.