Prognostic Covariate Adjustment for Binary Outcomes Using Stratification

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.