Bayesian Prognostic Covariate Adjustment With Additive Mixture Priors

Effective and rapid decision-making from randomized controlled trials (RCTs) requires unbiased and precise treatment effect inferences. Two strategies to address this requirement are to adjust for covariates that are highly correlated with the outcome, and to leverage historical control information via Bayes' theorem. We propose a new Bayesian prognostic covariate adjustment methodology, referred to as Bayesian PROCOVA, that combines these two strategies. Covariate adjustment is based on generative artificial intelligence (AI) algorithms that construct a digital twin generator (DTG) for RCT participants. The DTG is trained on historical control data and yields a digital twin (DT) probability distribution for each participant's control outcome. The expectation of the DT distribution defines the single covariate for adjustment. Historical control information are leveraged via an additive mixture prior with two components: an informative prior probability distribution specified based on historical control data, and a non-informative prior distribution. The weight parameter in the mixture has a prior distribution as well, so that the entire additive mixture prior distribution is completely pre-specifiable and does not involve any information from the RCT. We establish an efficient Gibbs algorithm for sampling from the posterior distribution, and derive closed-form expressions for the posterior mean and variance of the treatment effect conditional on the weight parameter, of Bayesian PROCOVA. We evaluate the bias control and variance reduction of Bayesian PROCOVA compared to frequentist prognostic covariate adjustment (PROCOVA) via simulation studies that encompass different types of discrepancies between the historical control and RCT data. Ultimately, Bayesian PROCOVA can yield informative treatment effect inferences with fewer control participants, accelerating effective decision-making.