Inference on the average treatment effect under minimization and other covariate-adaptive randomization methods

Abstract

Covariate-adaptive randomization schemes such as minimization and stratified permuted blocks are often applied in clinical trials to balance treatment assignments across prognostic factors. The existing theory for inference after covariate-adaptive randomization is mostly limited to situations where a correct model between the response and covariates can be specified or the randomization method has well-understood properties. Based on stratification with covariate levels utilized in randomization and a further adjustment for covariates not used in randomization, we propose several estimators for model free inference of the average treatment effect, the difference between response means under two treatments. We establish asymptotic normality of the proposed estimators under all popular covariate-adaptive randomization schemes including the minimization method, and we show that the asymptotic distributions are invariant with respect to covariate-adaptive randomization methods. Consistent variance estimators are constructed for asymptotic inference. Asymptotic relative efficiencies and finite sample properties of estimators are also studied. We recommend using one of our proposed estimators for valid and model free inference after covariate-adaptive randomization.

Regression analysis for covariate‐adaptive randomization: A robust and efficient inference perspective

“…We leave to future work the investigation of semi‐parametric efficiency under covariate‐adaptive randomization. Second, to further improve efficiency, one can use the stratum‐specific adjusted vectors $$$ {\hat{\beta}}_{\left[k\right]}(1) $$$ and $$$ {\hat{\beta}}_{\left[k\right]}(0) $$$ within stratum $$$ k $$$ instead of the common adjusted vectors $$$ \hat{\beta}(1) $$$ and $$$ \hat{\beta}(0) $$$ for all strata, 33,34 which is equivalent to adding higher‐order interactions, such as $$$ {A}_i{I}_{i\in \left[k\right]}{\boldsymbol{X}}_i $$$, to the regression models. We do not explore this approach further in this work because such models, in our experience, are seldom specified as primary analyses in statistical analysis plans for clinical trials.…”

Randomizing a clinical trial in neuro-degenerative disease

“…There is some recent theoretical work on the properties of designs when , that is “what is the effect of the randomization on the non-randomized covariates?”. Unfortunately, this work does not cover our situation as Liu and Hu [40] only consider discretized covariates and Ye et al [41] develop a model-free approach. Both papers usefully present details of recent work on covariate-adaptive randomization.…”

Regression-Based Multiple Treatment Effect Estimation under Covariate-Adaptive Randomization

“…This approach produces a valid inference by using a working model between responses and covariates, regardless of whether the working model is correct or not. To consider the regression adjustment for baseline covariates in addition to stratification covariates, stratum-common estimators and stratum-specific estimators have been developed, mainly for the case in which the allocation ratios are the same across strata (Liu et al, 2023;Ma et al, 2022;Ye et al, 2022aYe et al, , 2022b. However, little attention has been paid to the case in which the allocation ratios are different across strata, especially when additional baseline covariates are included, although different allocation ratios are commonly used in practice and are more flexible (Angrist et al, 2014;Chong et al, 2016).…”