Bayesian approaches for the design and analysis of prevalence and diagnostic accuracy studies

Diagnostic tests are widely used in disease prevalence and diagnostic accuracy studies. For many diseases or conditions there is no perfect diagnostic test available, and researchers instead rely on one or more imperfect tests instead to detect the presence of the disease. The analysis of the resulting data requires the use of latent class models, a family of statistical models that is able to adjust for the imperfect nature of the tests. Latent class models suitable for diagnostic research have appeared in the literature since the 1980s, but many methodological challenges remain. This thesis proposes novel Bayesian methods to address three such challenges that arise in the design and analysis of diagnostic studies in the absence of a perfect test. The first part of the thesis deals with possible correlation between multiple imperfect dichotomous diagnostic tests. When such tests are applied to an individual, it is possible that their results remain dependent even after conditioning on true disease status, resulting in biased estimates if ignored. While methods exist to handle pair-wise correlations between tests, there has been no general method for dealing with higher-order conditional dependence terms. We extend a Bayesian fixed effects model for two diagnostic tests with pair-wise correlation to the case with three or more diagnostic tests with higher-order correlations. Simulation results show that the proposed fixed effects model works well both in the case when the tests are highly correlated and in the case when the tests are truly conditionally independent, provided adequate external information is available in the form of fixed constraints or prior distributions. A data set on the diagnosis of childhood pulmonary tuberculosis is used to illustrate a practical application of the proposed model.In the latter part of the thesis we address the issue of sample size determination, an essential component of study design. This is an area where methods for diagnostic research studies lag behind analytic developments for intervention studies. We address two gaps in this literature. First, we develop Bayesian sample size methods for planning studies involving two correlated diagnostic tests whose results will be analyzed using latent class models that adjust for conditional dependence using either fixed or random effects models. An illustrative example based on diagnosing Strongyloides infection shows that when conditional dependence exists but is ignored in the sample size calculations, the sample size is often quite different compared to that calculated assuming independent tests. Our results suggest that taking conditional dependence into account is important in the design of prevalence and diagnostic accuracy studies. Secondly, in a separate manuscript, we consider optimal design for prevalence and other diagnostic testing studies in terms of minimizing total testing costs. This is particularly challenging in the absence of a perfect reference test for the disease because different combinations of imperfect tests need to be considered. We develop Bayesian methods to address this problem, illustrated through designing a study with minimum cost to accurately estimate the prevalence of childhood tuberculosis in a hospital setting. The results show how total testing costs can be minimized when designing a prevalence study without losing estimation accuracy. For example, one strategy is to use a larger number of diagnostic tests when imperfect diagnostic tests are used.

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