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A crucial task for a randomized controlled trial (RCT) is to specify astatistical method that can yield an efficient estimator and powerful test forthe treatment effect. A novel and effective strategy to obtain efficient andpowerful treatment effect inferences is to incorporate predictions fromgenerative artificial intelligence (AI) algorithms into covariate adjustmentfor the regression analysis of a RCT. Training a generative AI algorithm onhistorical control data enables one to construct a digital twin generator (DTG)for RCT participants, which utilizes a participant's baseline covariates togenerate a probability distribution for their potential control outcome.Summaries of the probability distribution from the DTG are highly predictive ofthe trial outcome, and adjusting for these features via regression can thusimprove the quality of treatment effect inferences, while satisfying regulatoryguidelines on statistical analyses, for a RCT. However, a critical assumptionin this strategy is homoskedasticity, or constant variance of the outcomeconditional on the covariates. In the case of heteroskedasticity, existingcovariate adjustment methods yield inefficient estimators and underpoweredtests. We propose to address heteroskedasticity via a weighted prognosticcovariate adjustment methodology (Weighted PROCOVA) that adjusts for both themean and variance of the regression model using information obtained from theDTG. We prove that our method yields unbiased treatment effect estimators, anddemonstrate via comprehensive simulation studies and case studies fromAlzheimer's disease that it can reduce the variance of the treatment effectestimator, maintain the Type I error rate, and increase the power of the testfor the treatment effect from 80% to 85%~90% when the variances from the DTGcan explain 5%~10% of the variation in the RCT participants' outcomes.

A Weighted Prognostic Covariate Adjustment Method for Efficient and Powerful Treatment Effect Inferences in Randomized Controlled Trials