A closer look at combining data among a small number of binomial experiments

In a regulatory environment, the regulators and the regulated may not be able to agree on the use of subjective prior information for a clinical trial. The use of a data-based prior offers a greater possibility for agreement, however, the degree of importance given to the prior data may still be contentious. The use of a hierarchical model to link the prior data and the current trial is shown to provide a relatively objective method for assigning weight to the prior data. Using a series of examples combining two binomial experiments, the effect of a hierarchical model on estimating rates, on the degree to which data is combined and on hypothesis testing is illustrated. In addition, the phenomenon in which combining data reduces the precision is explained. Simpler models based on finite mixtures of beta distributions are shown to work as well as the more computationally intensive, continuous mixtures. Lastly, an example combining three concurrent studies is illustrated.