We study inference for censored survival data where some covariates are distorted by some unknown functions of an observable confounding variable in a multiplicative form. An example of this kind of data in medical studies is normalizing some important observed exposure variables by patients' body mass index , weight, or age. Such a phenomenon also appears frequently in environmental studies where an ambient measure is used for normalization and in genomic studies where the library size needs to be normalized for the next generation sequencing of data. We propose a new covariate-adjusted Cox proportional hazards regression model and utilize the kernel smoothing method to estimate the distorting function, then employ an estimated maximum likelihood method to derive the estimator for the regression parameters. We establish the large sample properties of the proposed estimator. Extensive simulation studies demonstrate that the proposed estimator performs well in correcting the bias arising from distortion. A real dataset from the National Wilms' Tumor Study is used to illustrate the proposed approach.

中文翻译：

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具有未知失真函数的失真协变量的 Cox 回归分析

我们研究了截尾生存数据的推理，其中一些协变量被可观察混杂变量的一些未知函数以乘法形式扭曲。医学研究中此类数据的一个示例是根据患者的体重指数、体重或年龄对一些重要的观察到的暴露变量进行标准化。这种现象也经常出现在环境研究中，其中环境测量用于标准化，在基因组研究中，文库大小需要为下一代数据测序进行标准化。我们提出了一种新的协变量调整 Cox 比例风险回归模型，并利用核平滑方法来估计失真函数，然后采用估计的最大似然方法来推导出回归参数的估计量。我们建立了建议的估计器的大样本属性。广泛的模拟研究表明，所提出的估计器在校正由失真引起的偏差方面表现良好。来自 National Wilms 肿瘤研究的真实数据集用于说明所提出的方法。