Covariate‐adaptive randomization is popular in clinical trials with sequentially arrived patients for balancing treatment assignments across prognostic factors that may have influence on the response. However, existing theory on tests for the treatment effect under covariate‐adaptive randomization is limited to tests under linear or generalized linear models, although the covariate‐adaptive randomization method has been used in survival analysis for a long time. Often, practitioners will simply adopt a conventional test to compare two treatments, which is controversial since tests derived under simple randomization may not be valid in terms of type I error under other randomization schemes. We derive the asymptotic distribution of the partial likelihood score function under covariate‐adaptive randomization and a working model that is subject to possible model misspecification. Using this general result, we prove that the partial likelihood score test that is robust against model misspecification under simple randomization is no longer robust but conservative under covariate‐adaptive randomization. We also show that the unstratified log‐rank test is conservative and the stratified log‐rank test remains valid under covariate‐adaptive randomization. We propose a modification to variance estimation in the partial likelihood score test, which leads to a score test that is valid and robust against arbitrary model misspecification under a large family of covariate‐adaptive randomization schemes including simple randomization. Furthermore, we show that the modified partial likelihood score test derived under a correctly specified model is more powerful than log‐rank‐type tests in terms of Pitman's asymptotic relative efficiency. Simulation studies about the type I error and power of various tests are presented under several popular randomization schemes.

中文翻译：

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协变量适应随机化下生存分析中治疗效果的稳健检验

在连续到达的患者中，协变量自适应随机方法在临床试验中很普遍，可以平衡可能影响疗效的预后因素之间的治疗分配。然而，尽管协变量自适应随机方法已在生存分析中使用了很长时间，但现有的关于协变量自适应随机方法的治疗效果测试的理论仅限于线性或广义线性模型下的测试。通常，从业人员会简单地采用常规测试来比较两种治疗方法，这是有争议的，因为在其他随机方案下，根据简单随机分配得出的测试对于I型错误可能无效。我们推导了在协变量自适应随机化和可能存在模型错误指定的工作模型下部分似然评分函数的渐近分布。使用这一一般结果，我们证明了在简单随机化下对模型错误指定具有鲁棒性的部分似然评分测试在稳健的协变量自适应随机化下不再具有鲁棒性，而是保守的。我们还表明，未分层的对数秩检验是保守的，并且分层的对数秩检验在协变量自适应随机化下仍然有效。我们提出了对部分似然评分测试中方差估计的一种修改，这导致了分数测试在包括简单随机在内的大量协变量自适应随机方案下对任意模型的错误指定是有效且健壮的。此外，我们证明，在Pitman的渐近相对效率方面，在正确指定的模型下得出的改进的部分似然评分检验比对数秩检验更强大。在几种流行的随机方案下，对I型错误和各种测试的功效进行了仿真研究。