  Randomized trials balance all covariates on average and provide the gold
standard for estimating treatment effects. Chance imbalances nevertheless exist
more or less in realized treatment allocations and intrigue an important
question: what should we do in case the treatment groups differ with respect to
some important baseline characteristics? A common strategy is to conduct a {\it
preliminary test} of the balance of baseline covariates after randomization,
and invoke covariate adjustment for subsequent inference if and only if the
realized allocation fails some prespecified criterion. Although such practice
is intuitive and popular among practitioners, the existing literature has so
far only evaluated its properties under strong parametric model assumptions in
theory and simulation, yielding results of limited generality. To fill this
gap, we examine two strategies for conducting preliminary test-based covariate
adjustment by regression, and evaluate the validity and efficiency of the
resulting inferences from the randomization-based perspective. As it turns out,
the preliminary-test estimator based on the analysis of covariance can be even
less efficient than the unadjusted difference in means, and risks
anticonservative confidence intervals based on normal approximation even with
the robust standard error. The preliminary-test estimator based on the fully
interacted specification is on the other hand less efficient than its
counterpart under the {\it always-adjust} strategy, and yields overconservative
confidence intervals based on normal approximation. Based on theory and
simulation, we echo the existing literature and do not recommend the
preliminary-test procedure for covariate adjustment in randomized trials.
