Comment: inference after covariate-adaptive randomisation: aspects of methodology and theory

We first want to commend (Shao, 2021) for a timely paper that reviews the methodological and theoretical advances in statistical inference after covariateadaptive randomisation in the last decade. The paper clearly presents the important considerations and pragmatic recommendations when analysing data obtained from covariate-adaptive randomisation, which provides principled guidelines for the practice. The aim of our remaining comments is to extend the discussion on the invariance property in Shao (2021). That is, the asymptotic distribution of an estimator remains the same under different covariate-adaptive randomisation schemes. For ease of reading, we follow the notation in Shao (2021) whenever possible and focus on the case of two treatment arms (i.e., k = 2). The ideas can be extended to the case of multiple treatment arms. For continuous or binary outcomes, Shao (2021) describes three post-stratified estimators for the population mean difference θ0 = E(Y(2) − Y(1)):