This paper studies the Cox model with time-varying coefficients for cause-specific hazard functions when the causes of failure are subject to missingness. Inverse probability weighted and augmented inverse probability weighted estimators are investigated. The latter is considered as a two-stage estimator by directly utilizing the inverse probability weighted estimator and through modeling available auxiliary variables to improve efficiency. The asymptotic properties of the two estimators are investigated. Hypothesis testing procedures are developed to test the null hypotheses that the covariate effects are zero and that the covariate effects are constant. We conduct simulation studies to examine the finite sample properties of the proposed estimation and hypothesis testing procedures under various settings of the auxiliary variables and the percentages of the failure causes that are missing. These simulation results demonstrate that the augmented inverse probability weighted estimators are more efficient than the inverse probability weighted estimators and that the proposed testing procedures have the expected satisfactory results in sizes and powers. The proposed methods are illustrated using the Mashi clinical trial data for investigating the effect of randomization to formula-feeding versus breastfeeding plus extended infant zidovudine prophylaxis on death due to mother-to-child HIV transmission in Botswana.

中文翻译：

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具有缺失原因的特定原因危害函数的时变 Cox 模型分析。

本文研究了当故障原因缺失时具有特定原因危险函数的时变系数的 Cox 模型。研究了逆概率加权和增广逆概率加权估计量。后者被认为是通过直接利用逆概率加权估计量并通过对可用辅助变量建​​模来提高效率的两阶段估计量。研究了两个估计量的渐近性质。开发假设检验程序以检验协变量效应为零且协变量效应恒定的零假设。我们进行模拟研究，以检查在各种辅助变量设置和缺失的故障原因百分比下所提出的估计和假设检验程序的有限样本特性。这些模拟结果表明，增强的逆概率加权估计量比逆概率加权估计量更有效，并且建议的测试程序在大小和功效方面具有预期的令人满意的结果。建议的方法使用 Mashi 临床试验数据来说明，用于调查随机分配到配方奶喂养与母乳喂养加上延长婴儿齐多夫定预防对博茨瓦纳母婴 HIV 传播导致的死亡的影响。这些模拟结果表明，增强的逆概率加权估计量比逆概率加权估计量更有效，并且建议的测试程序在大小和功效方面具有预期的令人满意的结果。建议的方法使用 Mashi 临床试验数据来说明，用于调查随机分配到配方奶喂养与母乳喂养加上延长婴儿齐多夫定预防对博茨瓦纳母婴 HIV 传播导致的死亡的影响。这些模拟结果表明，增强的逆概率加权估计量比逆概率加权估计量更有效，并且建议的测试程序在大小和功效方面具有预期的令人满意的结果。建议的方法使用 Mashi 临床试验数据来说明，用于调查随机分配到配方奶喂养与母乳喂养加上延长婴儿齐多夫定预防对博茨瓦纳母婴 HIV 传播导致的死亡的影响。