Consistent Covariance estimation for stratum imbalances under minimization method for covariate-adaptive randomization

TL;DR

This paper introduces a bootstrap-based estimator for the covariance matrix of covariate imbalances in minimization-based covariate-adaptive randomization, improving statistical inference in clinical trials.

Contribution

It proposes a consistent bootstrap estimator for the limiting covariance matrix of within-stratum imbalances under minimization, with theoretical validation and practical application.

Findings

The estimator is consistent and validated by Le Cam's third lemma.

Adjusted robust tests maintain nominal size in simulations.

Unadjusted tests exhibit size inflation under minimization.

Abstract

Pocock and Simon's minimization method is a popular approach for covariate-adaptive randomization in clinical trials. Valid statistical inference with data collected under the minimization method requires the knowledge of the limiting covariance matrix of within-stratum imbalances, whose existence is only recently established. In this work, we propose a bootstrap-based estimator for this limit and establish its consistency, in particular, by Le Cam's third lemma. As an application, we consider in simulation studies adjustments to existing robust tests for treatment effects with survival data by the proposed estimator. It shows that the adjusted tests achieve a size close to the nominal level, and unlike other designs, the robust tests without adjustment may have an asymptotic size inflation issue under the minimization method.