A general approach to sample size determination for prevalence surveys that use dual test protocols

We develop a Bayesian simulation based approach for determining the sample size required for estimating a binomial probability and the difference between two binomial probabilities where we allow for dependence between two fallible diagnostic procedures. Examples include estimating the prevalence of disease in a single population based on results from two imperfect diagnostic tests applied to sampled individuals, or surveys designed to compare the prevalences of two populations using diagnostic outcomes that are subject to misclassification. We propose a two stage procedure in which the tests are initially assumed to be independent conditional on true disease status (i.e. conditionally independent). An interval based sample size determination scheme is performed under this assumption and data are collected and used to test the conditional independence assumption. If the data reveal the diagnostic tests to be conditionally dependent, structure is added to the model to account for dependence and the sample size routine is repeated in order to properly satisfy the criterion under the correct model. We also examine the impact on required sample size when adding an extra heterogeneous population to a study.