Commensurate Priors for Incorporating Historical Information in Clinical Trials using General and Generalized Linear Models
Bradley P. Carlin, University of Minnesota 
*Brian P. Hobbs, M.D. Anderson Cancer Center 
Daniel J. Sargent, The Mayo Clinic 

Keywords: Adaptive Designs, Bayesian, Correlated Data, Survival Analysis, Clinical Trials

Bayesian clinical trial designs offer the possibility of a substantially reduced sample size, increased statistical power, and reductions in cost and ethical hazard. However when prior and current information conflict, Bayesian methods can lead to higher than expected Type I error, as well as the possibility of a costlier and lengthier trial. The commensurate prior method proposed by Hobbs et al. (2011) offers an adaptive approach for incorporating historical data that is robust to prior information that reveals itself to be inconsistent with the accumulating experimental data. We investigate adaptive randomization schemes rooted in commensurate prior methods that balance the allocation ratio with respect to the amount of incorporated historical information. We refer to our approach as optimal-balance randomization, since we use current patients "optimally", with respect to the amount of information existing on the control therapy. This approach depends upon a reliable measure of the historical data's influence, namely the effective sample size of the historical controls. The method is illustrated using LMs and GLMs in context of two successive clinical trials.