  We present several related methods for creating confidence intervals to
assess disease prevalence in variety of survey sampling settings. These include
simple random samples with imperfect tests, weighted sampling with perfect
tests, and weighted sampling with imperfect tests, with the first two settings
considered special cases of the third. Our methods use survey results and
measurements of test sensitivity and specificity to construct melded confidence
intervals. We demonstrate that our methods appear to guarantee coverage in
simulated settings, while competing methods are shown to achieve much lower
than nominal coverage. We apply our method to a seroprevalence survey of
SARS-CoV-2 in undiagnosed adults in the United States between May and July
2020.
