论文标题
单调危险比顺序下的非参数推断
Nonparametric inference under a monotone hazard ratio order
论文作者
论文摘要
两个人群的危险功能或两个人口层的危险功能比在事实分析中起重要作用。 COX回归通常用于估计危险比在及时恒定的假设下，这被称为比例危害假设。但是，在实践中通常会违反该假设，并且在违反该假设时，Cox回归估计的参数很难解释。危险比可以使用平滑方式以非参数方式估算，但是基于平滑的估计器对选择调谐参数的选择敏感，并且通常很难对此类估计器执行有效的推断。在某些情况下，众所周知，危险比函数是单调的。在本文中，我们证明了危险比函数的单调性定义了不变的随机顺序，并且我们研究了该顺序的特性。此外，我们在单调性约束下引入了危险比函数的估计器。我们证明我们的估计器将分布收敛到平均零极限，我们使用此结果来构建渐近有效的置信区间。最后，我们进行数值研究以评估估计量的有限样本行为，并使用我们的方法估计肺腺癌患者接受吉非替尼或甲状腺素磷脂蛋白 - 帕克列赛治疗的肺腺癌患者中无进展生存率的危害比。
The ratio of the hazard functions of two populations or two strata of a single population plays an important role in time-to-event analysis. Cox regression is commonly used to estimate the hazard ratio under the assumption that it is constant in time, which is known as the proportional hazards assumption. However, this assumption is often violated in practice, and when it is violated, the parameter estimated by Cox regression is difficult to interpret. The hazard ratio can be estimated in a nonparametric manner using smoothing, but smoothing-based estimators are sensitive to the selection of tuning parameters, and it is often difficult to perform valid inference with such estimators. In some cases, it is known that the hazard ratio function is monotone. In this article, we demonstrate that monotonicity of the hazard ratio function defines an invariant stochastic order, and we study the properties of this order. Furthermore, we introduce an estimator of the hazard ratio function under a monotonicity constraint. We demonstrate that our estimator converges in distribution to a mean-zero limit, and we use this result to construct asymptotically valid confidence intervals. Finally, we conduct numerical studies to assess the finite-sample behavior of our estimator, and we use our methods to estimate the hazard ratio of progression-free survival in pulmonary adenocarcinoma patients treated with Gefitinib or carboplatin-paclitaxel.
