Sample size calculation for a historically controlled clinical trial with adjustment for covariates

We present a Bayesian approach to determining the optimal sample size for a historically controlled clinical trial. This work is motivated by a trial of a new coronary stent that uses a retrospective control group formed from seven trials of coronary stents currently marketed in the United States. In studies involving nonrandomized control groups, hierarchical regression, propensity score methods, or other sophisticated models are typically required to account for heterogeneity among groups which, if ignored could bias the results. Sample size calculations for historically controlled trials of medical devices are often based on formulae derived for randomized trials and fail to account for estimation of model parameters, correlation of observations, and uncertainty in the distribution of covariates of the patients recruited in the new trial. We propose methodology based on stochastic optimization that overcomes these deficiencies. The methodology is demonstrated using an objective function based on the power of the trial from a Bayesian approach. Analytic approximations based on a covariate-free analysis that convey features of the power function are developed. Our principle conclusions are that exact sample size calculations can be substantially different from current approximations, and stochastic optimization provides a convenient method of computation.