An Accelerated Failure Time Regression Model for Illness-Death Data: A Frailty Approach

TL;DR

This paper introduces a novel frailty-based accelerated failure time model for illness-death data, employing a semi-parametric EM algorithm and bootstrap for estimation, demonstrated through breast cancer data analysis.

Contribution

The work develops a new shared frailty AFT model with a semi-parametric estimation method, enhancing modeling of dependent failure times in illness-death data.

Findings

Model effectively captures dependence between failure times.

Simulation studies validate the estimation procedure.

Application to breast cancer data demonstrates practical utility.

Abstract

This work presents a new model and estimation procedure for the illness-death survival data where the hazard functions follow accelerated failure time (AFT) models. A shared frailty variate induces positive dependence among failure times of a subject for handling the unobserved dependency between the non-terminal and the terminal failure times given the observed covariates. Semi-parametric maximum likelihood estimation procedure is developed via a kernel smoothed-aided EM algorithm, and variances are estimated by weighted bootstrap. The model is presented in the context of existing frailty-based illness-death models, emphasizing the contribution of the current work. The breast cancer data of the Rotterdam tumor bank are analyzed using the proposed and existing illness-death models. The results are contrasted and evaluated based on a new graphical goodness-of-fit procedure. Simulation results and data analysis nicely demonstrate the practical utility of the shared frailty variate with the AFT regression model under the illness-death framework.