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

Lea Kats, Malka Gorfine

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Early online date17 May 2023
StateE-pub ahead of print - 17 May 2023
Externally publishedYes

Bibliographical note

Funding Information:
The work was supported by the Israel Science Foundation grant number 767/21 and by a grant from the Tel Aviv University Center for AI and Data Science (TAD).

Publisher Copyright:
© 2023 The Authors. Biometrics published by Wiley Periodicals LLC on behalf of International Biometric Society.


  • goodness of fit
  • illness–death model
  • kernel method
  • semicompeting risks
  • shared frailty


Dive into the research topics of 'An accelerated failure time regression model for illness–death data: A frailty approach'. Together they form a unique fingerprint.

Cite this