A Novel Criterion for Selecting Covariates

Through a combination of bad luck and possibly selection bias, imbalances in prognostic baseline variables across treatment groups have plagued many randomized clinical trials. It is common, in practice, to test for imbalances and adjust for variables observed to be sufficiently unbalanced at baseline. Yet, the literature condemns these practices on the grounds that imbalances are necessarily random when observed in the context of a randomized trial (hence, testing is illogical), and suggests that all prognostic covariates, unbalanced or not, should be included in the model used for analysis. When there are a large number of covariates relative to the sample size, decisions need to be made regarding which covariates to actually include in a suitably parsimonious model. Proponents of the approach to model-building by testing for baseline imbalances might suggest reaching these decisions by considering the degree of imbalance of each covariate; those that criticize this approach might instead consider the ability of the covariate to predict the outcome of interest. Some hybrid approaches have been explored as well. We introduce a criterion that allows for the specification of an optimal hybrid approach.