Two-phase sampling for simultaneous prevalence estimation and case detection

Two-phase designs for estimation of prevalence, where the first-phase classification is fallible and the second is accurate but relatively expensive, are not necessarily justified on efficiency grounds. However, they might be advantageous for dual-purpose studies, for example where prevalence estimation is followed by a clinical trial or case-control study, if they can identify cases of disease for the second study in a cost-effective way. Alternatively, they may be justified on ethical grounds if they can identify more, previously undetected but treatable cases of disease, than a simple random sample design. An approach to sampling is proposed, which formally combines the goals of efficient prevalence estimation and case detection by setting different notional study costs for investigating cases and noncases. Two variants of the method are compared with an "ethical" two-phase scheme proposed by Shrout and Newman (1989, Biometrics 45, 549-555), and with the most efficient scheme for prevalence estimation alone, in terms of the standard error of the prevalence estimate, the expected number of cases, and the fraction of cases among second-phase subjects, given a fixed budget. One variant yields the highest fraction and expected number of cases but also the largest standard errors. The other yields a higher fraction than Shrout and Newman's scheme and a similar number of cases but appears to do so more efficiently.