The statistical efficiency of randomized clinical trials can be improved by incorporating information from baseline covariates (i.e., pre-treatment patient characteristics). This can be done in the design stage using a covariate-adaptive randomization scheme such as stratified (permutated block) randomization, or in the analysis stage through covariate adjustment. This article provides a geometric perspective on covariate adjustment and stratified randomization in a unified framework where all regular, asymptotically linear estimators are identified as augmented estimators. From this perspective, covariate adjustment can be viewed as an effort to approximate the optimal augmentation function, and stratified randomization aims to improve a given approximation by projecting it into an affine subspace containing the optimal augmentation function. The efficiency benefit of stratified randomization is asymptotically equivalent to making full use of stratum information in covariate adjustment, which can be achieved using a simple calibration procedure. Simulation results indicate that stratified randomization is clearly beneficial to unadjusted estimators and much less so to adjusted ones and that calibration is an effective way to recover the efficiency benefit of stratified randomization without actually performing stratified randomization. These insights and observations are illustrated using real clinical trial data.

翻译：随机临床试验的统计效率可通过纳入基线协变量（即治疗前患者特征）信息得到提升。这既可在设计阶段采用协变量自适应随机化方案（如分层（置换区组）随机化）实现，也可在分析阶段通过协变量调整完成。本文在统一框架下提供了协变量调整与分层随机化的几何视角，该框架将所有正则渐近线性估计量识别为增强型估计量。在此视角下，协变量调整可视为逼近最优增强函数的尝试，而分层随机化旨在通过将给定近似投影至包含最优增强函数的仿射子空间来改进该近似。分层随机化的效率增益渐近等价于在协变量调整中充分利用分层信息，这可通过简单校准程序实现。模拟结果表明：分层随机化对未调整估计量具有显著益处，但对调整后估计量的增益微乎其微；校准是恢复分层随机化效率增益的有效替代方案，无需实际实施分层随机化。上述见解与观察通过实际临床试验数据得到验证。