  A crucial task for a randomized controlled trial (RCT) is to specify a
statistical method that can yield an efficient estimator and powerful test for
the treatment effect. A novel and effective strategy to obtain efficient and
powerful treatment effect inferences is to incorporate predictions from
generative artificial intelligence (AI) algorithms into covariate adjustment
for the regression analysis of a RCT. Training a generative AI algorithm on
historical control data enables one to construct a digital twin generator (DTG)
for RCT participants, which utilizes a participant's baseline covariates to
generate a probability distribution for their potential control outcome.
Summaries of the probability distribution from the DTG are highly predictive of
the trial outcome, and adjusting for these features via regression can thus
improve the quality of treatment effect inferences, while satisfying regulatory
guidelines on statistical analyses, for a RCT. However, a critical assumption
in this strategy is homoskedasticity, or constant variance of the outcome
conditional on the covariates. In the case of heteroskedasticity, existing
covariate adjustment methods yield inefficient estimators and underpowered
tests. We propose to address heteroskedasticity via a weighted prognostic
covariate adjustment methodology (Weighted PROCOVA) that adjusts for both the
mean and variance of the regression model using information obtained from the
DTG. We prove that our method yields unbiased treatment effect estimators, and
demonstrate via comprehensive simulation studies and case studies from
Alzheimer's disease that it can reduce the variance of the treatment effect
estimator, maintain the Type I error rate, and increase the power of the test
for the treatment effect from 80% to 85%~90% when the variances from the DTG
can explain 5%~10% of the variation in the RCT participants' outcomes.
