Comment on ‘Inference after covariate-adaptive randomisation: aspects of methodology and theory’

We congratulate Professor Shao on his exciting and thought-provoking paper and appreciate the Editor’s invitation to discuss it. This paper provided a comprehensive review of the methodology and theory for statistical inference under covariate-adaptive randomisation. Covariate-adaptive randomisation is widely used in the design stage of clinical trials to balance baseline covariates that are most relevant to the outcomes. Researchers often use linear regression or analysis of covariance (ANCOVA) to analyse the experimental results in the analysis stage. However, the validity of the resulting inferences is not crystal clear because the usual modelling assumptions might not be justified by covariate-adaptive randomisation. It is essential to develop a model-assisted methodology and theory for statistical inference under covariate-adaptive randomisation, allowing the working model to be arbitrarily misspecified. Professor Shao’s paper discussed recent developments in this aspect and made recommendations on using valid and efficient inference procedures under covariate-adaptive randomisation. As pointed out by Professor Shao, Ye, Yi, et al. (2020) proposed a model-assisted regression approach and showed that the resulting regression-adjusted average treatment effect estimator is more efficient than (as least as efficient as) the difference-in-means estimator, without any modelling assumptions on the potential outcomes and covariates. In other words, the modelassisted inference is efficient and robust to model misspecification. The efficiency gain and robustness of regression adjustment have been widely investigated under simple randomisation. When there are two treatment arms (treatment and control), Yang and Tsiatis (2001) examined three commonly used regression models for estimating the average treatment effect: