Variable selection for covariate-adjusted semiparametric inference in randomized clinical trials.

Extensive baseline covariate information is routinely collected on participants in randomized clinical trials, and it is well recognized that a proper covariate-adjusted analysis can improve the efficiency of inference on the treatment effect. However, such covariate adjustment has engendered considerable controversy, as post hoc selection of covariates may involve subjectivity and may lead to biased inference, whereas prior specification of the adjustment may exclude important variables from consideration. Accordingly, how to select covariates objectively to gain maximal efficiency is of broad interest. We propose and study the use of modern variable selection methods for this purpose in the context of a semiparametric framework, under which variable selection in modeling the relationship between outcome and covariates is separated from estimation of the treatment effect, circumventing the potential for selection bias associated with standard analysis of covariance methods. We demonstrate that such objective variable selection techniques combined with this framework can identify key variables and lead to unbiased and efficient inference on the treatment effect. A critical issue in finite samples is validity of estimators of uncertainty, such as standard errors and confidence intervals for the treatment effect. We propose an approach to estimation of sampling variation of estimated treatment effect and show its superior performance relative to that of existing methods.