  In randomized clinical trials, adjustments for baseline covariates at both
design and analysis stages are highly encouraged by regulatory agencies. A
recent trend is to use a model-assisted approach for covariate adjustment to
gain credibility and efficiency while producing asymptotically valid inference
even when the model is incorrect. In this article we present three
considerations for better practice when model-assisted inference is applied to
adjust for covariates under simple or covariate-adaptive randomized trials: (1)
guaranteed efficiency gain: a model-assisted method should often gain but never
hurt efficiency; (2) wide applicability: a valid procedure should be
applicable, and preferably universally applicable, to all commonly used
randomization schemes; (3) robust standard error: variance estimation should be
robust to model misspecification and heteroscedasticity. To achieve these, we
recommend a model-assisted estimator under an analysis of heterogeneous
covariance working model including all covariates utilized in randomization.
Our conclusions are based on an asymptotic theory that provides a clear picture
of how covariate-adaptive randomization and regression adjustment alter
statistical efficiency. Our theory is more general than the existing ones in
terms of studying arbitrary functions of response means (including linear
contrasts, ratios, and odds ratios), multiple arms, guaranteed efficiency gain,
optimality, and universal applicability.
