Robust meta‐analytic‐predictive priors in clinical trials with historical control information

Historical information is always relevant for clinical trial design. Additionally, if incorporated in the analysis of a new trial, historical data allow to reduce the number of subjects. This decreases costs and trial duration, facilitates recruitment, and may be more ethical. Yet, under prior‐data conflict, a too optimistic use of historical data may be inappropriate. We address this challenge by deriving a Bayesian meta‐analytic‐predictive prior from historical data, which is then combined with the new data. This prospective approach is equivalent to a meta‐analytic‐combined analysis of historical and new data if parameters are exchangeable across trials. The prospective Bayesian version requires a good approximation of the meta‐analytic‐predictive prior, which is not available analytically. We propose two‐ or three‐component mixtures of standard priors, which allow for good approximations and, for the one‐parameter exponential family, straightforward posterior calculations. Moreover, since one of the mixture components is usually vague, mixture priors will often be heavy‐tailed and therefore robust. Further robustness and a more rapid reaction to prior‐data conflicts can be achieved by adding an extra weakly‐informative mixture component. Use of historical prior information is particularly attractive for adaptive trials, as the randomization ratio can then be changed in case of prior‐data conflict. Both frequentist operating characteristics and posterior summaries for various data scenarios show that these designs have desirable properties. We illustrate the methodology for a phase II proof‐of‐concept trial with historical controls from four studies. Robust meta‐analytic‐predictive priors alleviate prior‐data conflicts ' they should encourage better and more frequent use of historical data in clinical trials.