Covariate‐adaptive randomization (CAR) procedures have been developed in clinical trials to mitigate the imbalance of treatments among covariates. In recent years, an increasing number of trials have started to use CAR for the advantages in statistical efficiency and enhancing credibility. At the same time, sample size re‐estimation (SSR) has become a common technique in industry to reduce time and cost while maintaining a good probability of success. Despite the widespread popularity of combining CAR designs with SSR, few researchers have investigated this combination theoretically. More importantly, the existing statistical inference must be adjusted to protect the desired type I error rate when a model that omits some covariates is used. In this article, we give a framework for the application of SSR in CAR trials and study the underlying theoretical properties. We give the adjusted test statistic and derive the sample size calculation formula under the CAR setting. We can tackle the difficulties caused by the adaptive features in CAR and prove the asymptotic independence between stages. Numerical studies are conducted under multiple parameter settings and scenarios that are commonly encountered in practice. The results show that all advantages of CAR and SSR can be preserved and further improved in terms of power and sample size.

中文翻译：

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协变量自适应随机临床试验的样本量重新估计

为了缓解协变量之间的治疗失衡，临床试验中已经开发出了协变量自适应随机（CAR）程序。近年来，越来越多的试验开始使用CAR来提高统计效率和增强可信度。同时，样本量重估（SSR）已成为行业中一种常见的技术，可以减少时间和成本，同时又保持成功的可能性。尽管将CAR设计与SSR结合起来非常流行，但是很少有研究人员从理论上研究这种结合。更重要的是，当使用忽略某些协变量的模型时，必须调整现有的统计推断，以保护所需的I型错误率。在本文中，我们提供了SSR在CAR试验中的应用框架，并研究了潜在的理论特性。我们给出调整后的测试统计量，并在CAR设置下得出样本量计算公式。我们可以解决由CAR的自适应特征引起的困难，并证明各阶段之间的渐近独立性。数值研究是在实际中经常遇到的多个参数设置和场景下进行的。结果表明，就功效和样本量而言，CAR和SSR的所有优势都可以保留并得到进一步改善。数值研究是在实际中经常遇到的多个参数设置和场景下进行的。结果表明，就功效和样本量而言，CAR和SSR的所有优势都可以保留并得到进一步改善。数值研究是在实际中经常遇到的多个参数设置和场景下进行的。结果表明，就功效和样本量而言，CAR和SSR的所有优势都可以保留并得到进一步改善。