Summary 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 model-free estimators of the average treatment effect. We establish the 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.

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最小化和其他协变量自适应随机化方法下平均治疗效果的推断

总结 协变量自适应随机化方案，例如最小化和分层置换区组，经常在临床试验中应用，以平衡预后因素的治疗分配。协变量自适应随机化后的现有推理理论主要限于可以指定响应和协变量之间的正确模型或随机化方法具有易于理解的特性的情况。基于随机化中使用的协变量水平的分层以及对随机化中未使用的协变量的进一步调整，我们提出了几种平均治疗效果的无模型估计量。我们在所有流行的协变量自适应随机化方案（包括最小化方法）下建立了提议的估计量的渐近正态性，我们证明了渐近分布对于协变量自适应随机化方法是不变的。为渐近推理构造一致的方差估计量。还研究了估计量的渐近相对效率和有限样本特性。我们建议在协变量自适应随机化后使用我们提出的估计器之一进行有效且无模型的推理。