Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL, 32224, USA.
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC, 28223, USA.
Lifetime Data Anal. 2020 Oct;26(4):731-760. doi: 10.1007/s10985-020-09497-y. Epub 2020 Apr 9.
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.
本文研究了失效原因存在缺失时，针对特定原因风险函数的时变系数 Cox 模型。研究了逆概率加权和增强逆概率加权估计量。后者被视为一种两阶段估计量，通过直接利用逆概率加权估计量，并通过对可用辅助变量进行建模来提高效率。研究了这两种估计量的渐近性质。提出了假设检验程序，以检验协变量效应为零和协变量效应为常数的零假设。我们进行了模拟研究，以在辅助变量的各种设置以及缺失的失效原因百分比下，检查拟议的估计和假设检验程序的有限样本性质。这些模拟结果表明，增强逆概率加权估计量比逆概率加权估计量更有效，并且提出的检验程序在大小和功效方面具有预期的满意结果。使用 Mashi 临床试验数据说明了所提出的方法，以研究博茨瓦纳将随机分配给配方喂养与母乳喂养加婴儿齐多夫定扩展预防对母婴 HIV 传播导致的死亡的效果。
