Joint Frailty Model of Recurrent and Terminal Events in the Presence of Cure Fraction using a Bayesian Approach

Zahra  Arab Borzu; Ahmad Reza Baghestani; Elaheh Talebi Ghane; Ali Akbar  Khadem Maboudi; Ali Akhavan; Anahita Saeedi

doi:10.18502/jbe.v8i3.12306

Zahra Arab Borzu Department of Biostatistics, School of Health, Zahedan University of Medical Sciences, Zahedan, Iran.
Ahmad Reza Baghestani Department of Biostatistics, Physiotherapy Research Center, Faculty of Paramedical Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran.
Elaheh Talebi Ghane Department of Biostatistics, Modeling of Noncommunicable Diseases Research Center, Hamadan University of Medical Sciences, Hamadan, Iran.
Ali Akbar Khadem Maboudi Department of Biostatistics, Physiotherapy Research Center, Faculty of Paramedical Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran.
Ali Akhavan Assistant Professor of Radiation Oncology, Isfahan University of Medical Sciences, Isfahan, Iran.
Anahita Saeedi Department of Biostatistics, School of Public Health & Health Sciences, University of Massachusetts, Amherst, MA, USA.Department of Biostatistics, School of Public Health & Health Sciences, University of Massachusetts, Amherst, MA, USA.

DOI: https://doi.org/10.18502/jbe.v8i3.12306

Keywords: Bayesian approach; Breast cancer; Cure fraction; Joint frailty model; Recurrent event.

Abstract

Introduction: Recurrent event data are common in many longitudinal studies. Often, a terminating event such as death can be correlated with the recurrent event process. A shared frailty model applied to account for the association between recurrent and terminal events. In some situations, a fraction of subjects experience neither recurrent events nor death; these subjects are cured.

Methods: In this paper, we discussed the Bayesian approach of a joint frailty model for recurrent and terminal events in the presence of cure fraction. We compared estimates of parameters in the Frequentist and Bayesian approaches via simulation studies in various sample sizes; we applied the joint frailty model in the presence of cure fraction with Frequentist and Bayesian approaches for breast cancer.

Results: In small sample size Bayesian approach compared to Frequentist approach had a smaller standard error and mean square error, and the coverage probabilities close to nominal level of 95%. Also, in Bayesian approach, the sampling means of the estimated standard errors were close to the empirical standard error.

Conclusion: The simulation results suggested that when sample size was small, the use of Bayesian joint frailty model in the presence of cure fraction led to more efficiency in parameter estimation and statistical inference.