  Covariate adjustment and methods of incorporating historical data in
randomized clinical trials (RCTs) each provide opportunities to increase trial
power. We unite these approaches for the analysis of RCTs with binary outcomes
based on the Cochran-Mantel-Haenszel (CMH) test for marginal risk ratio (RR).
In PROCOVA-CMH, subjects are stratified on a single prognostic covariate
reflective of their predicted outcome on the control treatment (e.g. placebo).
This prognostic score is generated based on baseline covariates through a model
trained on historical data. We propose two closed-form prospective estimators
for the asymptotic sampling variance of the log RR that rely only on values
obtainable from observed historical outcomes and the prognostic model.
Importantly, these estimators can be used to inform sample size during trial
planning. PROCOVA-CMH demonstrates type I error control and appropriate
asymptotic coverage for valid inference. Like other covariate adjustment
methods, PROCOVA-CMH can reduce the variance of the treatment effect estimate
when compared to an unadjusted (unstratified) CMH analysis. In addition to
statistical methods, simulations and a case study in Alzheimer's Disease are
given to demonstrate performance. Results show that PROCOVA-CMH can provide a
gain in power, which can be used to conduct smaller trials.
