An accelerated failure time regression model for illness–death data: A frailty approach

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 nonterminal and the terminal failure times given the observed covariates. The motivation behind the proposed modeling approach is to leverage the well‐known interpretability advantage of AFT models with respect to the observed covariates, while also benefiting from the simple and intuitive interpretation of the hazard functions. A semiparametric maximum likelihood estimation procedure is developed via a kernel smoothed‐aided expectation‐maximization algorithm, and variances are estimated by weighted bootstrap. We consider existing frailty‐based illness–death models and place particular emphasis on highlighting the contribution of our current research. The breast cancer data of the Rotterdam tumor bank are analyzed using the proposed as well as 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.