  Historical data about disease outcomes can be integrated into the analysis of
clinical trials in many ways. We build on existing literature that uses
prognostic scores from a predictive model to increase the efficiency of
treatment effect estimates via covariate adjustment. Here we go further,
utilizing a Bayesian framework that combines prognostic covariate adjustment
with an empirical prior distribution learned from the predictive performances
of the prognostic model on past trials. The Bayesian approach interpolates
between prognostic covariate adjustment with strict type I error control when
the prior is diffuse, and a single-arm trial when the prior is sharply peaked.
This method is shown theoretically to offer a substantial increase in
statistical power, while limiting the type I error rate under reasonable
conditions. We demonstrate the utility of our method in simulations and with an
analysis of a past Alzheimer's disease clinical trial.
