Adjusting for prognostic baseline covariates can improve precision in analyzing randomized trials, leading to greater power to detect a treatment effect. For binary outcomes, a logistic regression estimator is commonly used for such adjustment. This has led to substantial efficiency gains in practice; for example, gains equivalent to reducing the required sample size by 20-28% were observed in a recent survey of traumatic brain injury trials. Robinson and Jewell (1991) proved that the logistic regression estimator is guaranteed to have equal or better asymptotic efficiency compared to the unadjusted estimator (which ignores baseline variables). Unfortunately, the logistic regression estimator has the following dangerous vulnerabilities: it is only interpretable when the treatment effect is identical within every stratum of baseline covariates; also, it is inconsistent under model misspecification, which is virtually guaranteed whenever the baseline covariates are continuous or categorical with more than a few levels. An open problem was whether there exists an equally powerful, covariate-adjusted estimator with no such vulnerabilities, i.e., one that (i) is interpretable and consistent without requiring any model assumptions, and (ii) matches the efficiency gains of the logistic regression estimator whenever the logistic model is correct. Such an estimator would provide the best of both worlds: interpretability and consistency under no model assumptions (like the unadjusted estimator) and power gains from covariate adjustment (that match the logistic regression estimator). We prove a new asymptotic result showing that, surprisingly, there are simple estimators satisfying the above properties. These estimators are easy to implement and perform well in simulations. We argue that these rarely used estimators have substantial advantages over the more commonly used logistic regression estimator for covariate adjustment in randomized trials with binary outcomes.
Biostatistics | Statistical Methodology
Rosenblum, Michael and Steingrimsson, Jon Arni, "MATCHING THE EFFICIENCY GAINS OF THE LOGISTIC REGRESSION ESTIMATOR WHILE AVOIDING ITS INTERPRETABILITY PROBLEMS, IN RANDOMIZED TRIALS WITH BINARY OUTCOMES" (August 2016). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 281.