Bayesian hypothesis testing with frequentist characteristics in clinical trials

Through the use of an informative prior, Bayesian methodologies could potentially borrow the strength of historical information and become more and more popular for their applications to clinical trials. Nonetheless, even with tremendous effort, the reconciliation of the formulation of the hypotheses and the calculation of type I error between a Bayesian analysis and traditional frequentist analysis is still not very clear. In this research, we apply an inferential prior, null prior and design prior to the Bayesian data analysis, type I error control and sample size calculation. As demonstrated theoretically, the type I error control denies any borrowing of favorable prior information. Thus, the use of the calibrated critical value obtained through simulation for the commensurate or power prior for a Bayesian analysis has the effect of eliminating the borrowing of historical information. The validity of a Bayesian analysis with the borrowing of historical data should rest on the a priori assumption of consistency of data from the historical and current studies. Just in case the consistency assumption is not totally true, dynamic borrowing through the commensurate or power prior can regulate the level of borrowing based on the degree of consistency in the data. An example along with simulations are used to illustrate the applications and compare the characteristics of the methods.