  Randomized controlled trials (RCTs) with binary primary endpoints introduce
novel challenges for inferring the causal effects of treatments. The most
significant challenge is non-collapsibility, in which the conditional odds
ratio estimand under covariate adjustment differs from the unconditional
estimand in the logistic regression analysis of RCT data. This issue gives rise
to apparent paradoxes, such as the variance of the estimator for the
conditional odds ratio from a covariate-adjusted model being greater than the
variance of the estimator from the unadjusted model. We address this challenge
in the context of adjustment based on predictions of control outcomes from
generative artificial intelligence (AI) algorithms, which are referred to as
prognostic scores. We demonstrate that prognostic score adjustment in logistic
regression increases the power of the Wald test for the conditional odds ratio
under a fixed sample size, or alternatively reduces the necessary sample size
to achieve a desired power, compared to the unadjusted analysis. We derive
formulae for prospective calculations of the power gain and sample size
reduction that can result from adjustment for the prognostic score.
Furthermore, we utilize g-computation to expand the scope of prognostic score
adjustment to inferences on the marginal risk difference, relative risk, and
odds ratio estimands. We demonstrate the validity of our formulae via extensive
simulation studies that encompass different types of logistic regression model
specifications. Our simulation studies also indicate how prognostic score
adjustment can reduce the variance of g-computation estimators for the marginal
estimands while maintaining frequentist properties such as asymptotic
unbiasedness and Type I error rate control. Our methodology can ultimately
enable more definitive and conclusive analyses for RCTs with binary primary
endpoints.
