Statistical Efficiency of Model-Robust Direct Regression Adjustment in Randomized Clinical Trials with Binary Outcomes

Covariate adjustment in randomized clinical trials improves statistical precision and power compared to unadjusted analyses. A simple covariate adjustment method is direct regression adjustment, which uses the estimated treatment coefficient in a regression model as the effect estimate (e.g., analysis of covariance for continuous outcomes). Although maximum likelihood estimation does not yield model-robust direct regression adjustment for binary outcomes, such adjustment can be obtained via working normal linear regression for risk difference and working Poisson regression for risk ratio. This article examines the theoretical and empirical efficiency of these methods under misspecified regression models. We show that, asymptotically, they are as efficient as or more efficient than unadjusted analyses, strictly for working normal linear regression and typically for working Poisson regression. Efficiency gain is explained by reduced residual variation due to covariate adjustment. A simulation study showed that, even under model misspecification, these methods achieve efficiency comparable to logistic regression standardization with correctly specified models in a usual range of the outcome–covariate associations. Analysis of a randomized anti-HIV drug trial corroborated these findings. Direct regression adjustment using working normal linear and working Poisson regression provides simple, robust, and efficient methods for covariate adjustment in randomized trials with binary outcomes.