A General Approach to Sample Size Determination for Prevalence Surveys that Use Dual Test Protocols Dunlei Cheng 1 , James D. Stamey *,2 , and Adam J. Branscum 3 1 Institute for Health Care Research and Improvement, Baylor Health Care System, 8080 North Central Expressway, #500, Dallas, TX 75206, USA 2 Department of Statistical Science, 97140 One Bear Place, Baylor University, Waco, TX 76798, USA 3 Departments of Biostatistics, Statistics, and Epidemiology, University of Kentucky, Suite 205, 121 Washington Ave., Lexington, KY 40536, USA Received 26 January 2007, revised 17 April 2007, accepted 25 May 2007 Summary We develop a Bayesian simulation based approach for determining the sample size required for estimat- ing 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 out- comes 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. Key words: Bayesian inference; Sample size determination; Sensitivity; Specificity. 1 Introduction Estimating disease prevalence in one or more populations based on results of multiple diagnostic tests applied to sampled individuals is a common inferential goal in both human and animal disease stu- dies. In the single population setting, the source population has unknown infection prevalence, p, and the study is designed to accurately estimate p with a certain level of precision. In comparative studies the goal is to estimate the difference between two population prevalences, p 1  p 2 . We focus on dual testing protocols, which are commonly used in prevalence surveys. Here, a joint testing scheme is employed in which sampled individuals are subjected to two imperfect diagnostic procedures. Exam- ples include evaluation of the prevalence of tuberculosis (Mycobacterium tuberculosis) infection in two populations using two skin tests (Hui and Walter, 1980; Su, Johnson, and Gardner, 2002), or estimating the prevalence of Strongyloides infection in Cambodian refugees in Canada using a stool examination and a serologic test (Joseph, Gyorkos, and Coupal, 1995; Dendukuri and Joseph 2001), among many others. The statistical analysis of data from dual test prevalence surveys is complicated by several factors. First, a perfect, definitive diagnostic procedure (“gold-standard”) is often too expensive or invasive to * Corresponding author: e-mail: James_Stamey@baylor.edu, Phone: +1 254 710 7405, Fax: +1 254 710 1669 694 Biometrical Journal 49 (2007) 5, 694–706 DOI: 10.1002/bimj.200710365 # 2007 WILEY-VCH Verlag GmbH &Co. KGaA, Weinheim