Bayesian Power-Based Sample Size Determination for Diagnostic Accuracy Studies

In diagnostic accuracy studies, it is crucial to estimate the required sample size beforehand for the appropriate evaluation of diagnostic measures (e.g., sensitivity and/or specificity). In the development of pharmaceuticals and medical devices, although frequentist approaches have been used for sample size determination, Bayesian approaches have gained attention recently. We propose a Bayesian method for sample size determination using two kinds of priors (i.e., analysis prior and design prior) based on "Bayesian power." In the proposed method, an analysis prior and a design prior were introduced for the sensitivity and/or specificity parameters and a design prior for the prevalence parameter. For each possible future dataset at a given sample size, the analysis prior was updated to calculate the posterior probability of satisfying a prespecified success criterion. The design priors were used to obtain the prior predictive distribution of the future data, and Bayesian power was calculated as the prior predictive probability of satisfying the success criterion. Sample size determination was performed by evaluating Bayesian power over a range of candidate sample sizes according to a prespecified criterion. Numerical results showed that, under the parameter settings considered, the required sample size generally decreased as uncertainty in the design priors decreased when their means were above the corresponding target values. With the effective sample size of the analysis prior fixed, a more optimistic analysis prior reduced the required sample size. We also evaluated the method for joint sensitivity and specificity criteria and performed comparisons with commonly used frequentist methods. These results demonstrate how uncertainty represented by the design priors and information represented by the analysis prior affect Bayesian power and the required sample size.