Bayesian sample size for diagnostic test studies in the absence of a gold standard: Comparing identifiable with non-identifiable models.

Diagnostic tests rarely provide perfect results. The misclassification induced by imperfect sensitivities and specificities of diagnostic tests must be accounted for when planning prevalence studies or investigations into properties of new tests. The previous work has shown that applying a single imperfect test to estimate prevalence can often result in very large sample size requirements, and that sometimes even an infinite sample size is insufficient for precise estimation because the problem is non-identifiable. Adding a second test can sometimes reduce the sample size substantially, but infinite sample sizes can still occur as the problem remains non-identifiable. We investigate the further improvement possible when three diagnostic tests are to be applied. We first develop methods required for studies when three conditionally independent tests are available, using different Bayesian criteria. We then apply these criteria to prototypic scenarios, showing that large sample size reductions can occur compared to when only one or two tests are used. As the problem is now identifiable, infinite sample sizes cannot occur except in pathological situations. Finally, we relax the conditional independence assumption, demonstrating in this once again non-identifiable situation that sample sizes may substantially grow and possibly be infinite. We apply our methods to the planning of two infectious disease studies, the first designed to estimate the prevalence of Strongyloides infection, and the second relating to estimating the sensitivity of a new test for tuberculosis transmission. The much smaller sample sizes that are typically required when three as compared to one or two tests are used should encourage researchers to plan their studies using more than two diagnostic tests whenever possible. User-friendly software is available for both design and analysis stages greatly facilitating the use of these methods.