Confidence intervals for prevalence estimates from complex surveys with imperfect assays

There are established methods for estimating disease prevalence with associated confidence intervals for complex surveys with perfect assays, or simple random sample surveys with imperfect assays. We develop and study methods for the complicated case of complex surveys with imperfect assays. The new methods use the melding method to combine gamma intervals for directly standardized rates and established adjustments for imperfect assays by estimating sensitivity and specificity. One of the new methods appears to have at least nominal coverage in all simulated scenarios. We compare our new methods to established methods in special cases (complex surveys with perfect assays or simple surveys with imperfect assays). In some simulations, our methods appear to guarantee coverage, while competing methods have much lower than nominal coverage, especially when overall prevalence is very low. In other settings, our methods are shown to have higher 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.