Analysis of the time-varying Cox model for the cause-specific hazard functions with missing causes

Abstract

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.Terms of use and reuse: academic research for non-commercial purposes, see here for full terms. https://www.springer.com/aamterms-v1

Weighting estimation in the cause‐specific Cox regression with partially missing causes of failure

“…In addition, we assumed that the auxiliary variables are independent of the counting processes in the proposed model. As Heng et al 29 suggested, including auxiliary variables in modeling the conditional distribution of the causes of failure may be of interest.…”

“…In scenarios with more than two event types, a Bayesian method was proposed, 27 and an extension of the partial likelihood approach using an estimating equation method was conducted by Chatterjee et al 28 However, Chatterjee et al 28 assumed that the baseline hazard ratio functions for the different disease subtypes were correctly specified to obtain unbiased estimators; therefore, its estimators are not robust to the misspecification of the baseline hazard ratio functions. Recently, other approaches have been proposed based on the cause‐specific proportional hazard models 29,30 . Nevertheless, the partially missing causes of failure have not been addressed.…”