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 ab le 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 con tentious. The use of a hierarchical model to link the prior data and the cu rrent trial is shown to provide a relatively objective method for assigning weight to the prior data. Using a series of examples combining two binomia l experiments, the effect of a hierarchical model on estimating rates, on t he degree to which data is combined and on hypothesis testing is illustrate d. In addition, the phenomenon in which combining data reduces the precisio n is explained. Simpler models based on finite mixtures of beta distributio ns are shown to work as well as the more computationally intensive, continu ous mixtures. Lastly, an example combining three concurrent studies is illu strated.