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

TL;DR

This paper investigates the robustness and efficiency of regression models for estimating treatment effects in randomized clinical trials with covariate-adaptive randomization, providing practical recommendations and variance estimation methods.

Contribution

It demonstrates the robustness of various regression estimators under model misspecification and proposes consistent variance estimators, offering clear guidance for their use in clinical trials.

Findings

Regression estimators are robust to model misspecification.

Proposed non-parametric variance estimators outperform model-based ones.

Recommendations vary for equal and unequal allocation scenarios.

Abstract

Linear regression is arguably the most fundamental statistical model; however, the validity of its use in randomized clinical trials, despite being common practice, has never been crystal clear, particularly when stratified or covariate-adaptive randomization is used. In this paper, we investigate several of the most intuitive and commonly used regression models for estimating and inferring the treatment effect in randomized clinical trials. By allowing the regression model to be arbitrarily misspecified, we demonstrate that all these regression-based estimators robustly estimate the treatment effect, albeit with possibly different efficiency. We also propose consistent non-parametric variance estimators and compare their performances to those of the model-based variance estimators that are readily available in standard statistical software. Based on the results and taking into account both theoretical efficiency and practical feasibility, we make recommendations for the effective use of regression under various scenarios. For equal allocation, it suffices to use the regression adjustment for the stratum covariates and additional baseline covariates, if available, with the usual ordinary-least-squares variance estimator. For unequal allocation, regression with treatment-by-covariate interactions should be used, together with our proposed variance estimators. These recommendations apply to simple and stratified randomization, and minimization, among others. We hope this work helps to clarify and promote the usage of regression in randomized clinical trials.