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Randomized trials balance all covariates on average and provide the goldstandard for estimating treatment effects. Chance imbalances nevertheless existmore or less in realized treatment allocations and intrigue an importantquestion: what should we do in case the treatment groups differ with respect tosome important baseline characteristics? A common strategy is to conduct a {\itpreliminary test} of the balance of baseline covariates after randomization,and invoke covariate adjustment for subsequent inference if and only if therealized allocation fails some prespecified criterion. Although such practiceis intuitive and popular among practitioners, the existing literature has sofar only evaluated its properties under strong parametric model assumptions intheory and simulation, yielding results of limited generality. To fill thisgap, we examine two strategies for conducting preliminary test-based covariateadjustment by regression, and evaluate the validity and efficiency of theresulting inferences from the randomization-based perspective. As it turns out,the preliminary-test estimator based on the analysis of covariance can be evenless efficient than the unadjusted difference in means, and risksanticonservative confidence intervals based on normal approximation even withthe robust standard error. The preliminary-test estimator based on the fullyinteracted specification is on the other hand less efficient than itscounterpart under the {\it always-adjust} strategy, and yields overconservativeconfidence intervals based on normal approximation. Based on theory andsimulation, we echo the existing literature and do not recommend thepreliminary-test procedure for covariate adjustment in randomized trials.

A randomization-based theory for preliminary testing of covariate balance in controlled trials