Covariate adjustment using linear models for continuous outcomes in randomized trials has been shown to increase efficiency and power over the unadjusted method in estimating the marginal effect of treatment. However, for binary outcomes, investigators generally rely on the unadjusted estimate as the literature indicates that covariate-adjusted estimates based on logistic regression models are less efficient. The crucial step that has been missing when adjusting for covariates is that one must integrate/average the adjusted estimate over those covariates in order to obtain the marginal effect. We apply the method of targeted maximum likelihood estimation (MLE), as presented in van der Laan and Rubin (2006), to obtain estimators for the marginal effect using covariate adjustment for binary outcomes. We show that the covariate adjustment in randomized trials using logistic regression models can be mapped, by averaging over the covariate(s), to obtain a fully robust and efficient estimator of the marginal effect, which equals the targeted maximum likelihood estimator (MLE). We present simulation studies that show the targeted MLE increases efficiency and power over the unadjusted method, particularly for smaller sample sizes, even when the regression model is mis-specified.
Statistical Methodology | Statistical Theory
Moore, Kelly L. and van der Laan, Mark J., "Covariate Adjustment in Randomized Trials with Binary Outcomes: Targeted Maximum Likelihood Estimation" (April 2007). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 215.