Weighted estimators for proportional hazards regression with missing covariates
Weighted estimators for proportional hazards regression with missing covariates
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DOI：
10.1198/016214505000000295
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发表时间：
2005-12-01
影响因子：
3.7
通讯作者：
Prentice, RL
中科院分区：
文献类型：
--
作者：
Qi, LH;Wang, CY;Prentice, RL
缺失协变量数据在流行病学研究和疾病预防试验中很常见。在这篇文章中，回归参数估计的考克斯比例风险模型被认为是当某些协变量观察到所有的研究对象和其他协变量的数据只收集了一个子集。本文提出了简单的加权和核辅助完全增广加权估计，使用部分不完全数据非参数。我们使用非参数方法来估计简单加权估计函数中的选择概率。我们还使用非参数核平滑技术来估计完全增强加权估计函数中的某些条件期望。所提出的方法是非参数的意义上说，他们既不需要一个模型的缺失数据的机制，也不指定的条件分布的缺失协变量的观察到的协变量。这些估计量允许缺失数据机制依赖于结果变量和观察到的协变量，并且它们适用于各种队列抽样程序，包括病例队列和嵌套病例对照设计。我们证明了简单的和核辅助的完全增广加权估计是典型的一致和渐近正态的。此外，所提出的估计是更有效的比简单的加权估计与真实的选择概率的倒数作为权重。当缺失数据机制依赖于结果变量时，它们还纠正了仅对完整数据进行分析的估计偏差。此外，当协变量是时间无关的，某些简单的加权估计被证明是渐近等价的核辅助完全增广加权估计。中等样本量的估计性能通过模拟和两个真实的数据集的应用程序进行检查。
Missing covariate data are common in epidemiologic studies and disease prevention trials. In this article regression parameter estimation in the Cox proportional hazards model is considered when certain covariates are observed for all study subjects and other covariate data are collected only for a subset. The article presents both simple weighted and kernel-assisted fully augmented weighted estimators that use the partially incomplete data nonparametrically. We use nonparametric methods to estimate selection probabilities in the simple weighted estimating functions. We also use nonparametric kernel smoothing techniques to estimate certain conditional expectations in fully augmented weighted estimating functions. The proposed methods are nonparametric in the sense that they require neither a model for the missing-data mechanism nor specification of the conditional distribution of missing covariates given observed covariates. These estimators allow the missing-data mechanism to depend on outcome variables and observed covariates, and they are applicable to various cohort Sampling procedures, including case-cohort and nested case-control designs. We show that the simple and the kernel-assisted fully augmented weighted estimators are typically consistent and asymptotically normal. Moreover, the proposed estimators are more efficient than the simple weighted estimator with the inverse of true selection probability as weight. They also correct the bias of estimates from analysis of the complete data alone when the missing-data mechanism depends on outcome variables. In addition, when covariates are time-independent, certain simple weighted estimators are shown to be asymptotically equivalent to the kernel-assisted fully augmented weighted estimators. Moderate sample size performance of the estimators is examined via simulation and by application to two real datasets.