Modified power prior with multiple historical trials for binary endpoints

Including historical data may increase the power of the analysis of a current clinical trial and reduce the sample size of the study. Recently, several Bayesian methods for incorporating historical data have been proposed. One of the methods consists of specifying a so-called power prior whereby the historical likelihood is downweighted with a weight parameter. When the weight parameter is also estimated from the data, the modified power prior (MPP) is needed. This method has been used primarily when a single historical trial is available. We have adapted the MPP for incorporating multiple historical control arms into a current clinical trial, each with a separate weight parameter. Three priors for the weights are considered: (1) independent, (2) dependent, and (3) robustified dependent. The latter is developed to account for the possibility of a conflict between the historical data and the current data. We analyze two real-life data sets and perform simulation studies to compare the performance of competing Bayesian methods that allow to incorporate historical control patients in the analysis of a current trial. The dependent power prior borrows more information from comparable historical studies and thereby can improve the statistical power. Robustifying the dependent power prior seems to protect against prior-data conflict.