Multivariate Frailty Modeling in Joint Analyzing of Recurrent Events with Terminal Event and its Application in Medical Data

Background and Objectives: In many medical situations, people can experience recurrent events with a terminal event. If the terminal event is considered a censor in this type of data, the assumption of independence in the analysis of survival data may be violated. This study was conducted to investigate joint modeling of frequent events and a final event (death) in breast cancer patients using a frailty model.   Methods: In this retrospective cohort study, 443 patients with breast cancer registered at the Hospital of Shohadaye Tajrish Cancer Research Center were studied. The model of Liu (2004) was applied for joint modeling of recurrent events and a terminal event in which a shared frailty with gamma-distribution was used. Data modeling and data analysis were done using the R software.   Results: Four hundred and forty three women with breast cancer were studied. Univariate and multivariate analysis were performed in these patients. Of these, 338 cases (76.3%) had recurrence events, and 105 (23.7%) were censored. The obtained results of joint frailty model indicated that the relative risk of relapse in patients with a positive first-degree family history was 36% higher than that of other people (P<0.05). The relative risk of relapse in patients with stage 3 disease was 19% more than other stages and also the relative risk of relapse in patients with chemotherapy was 2.5 times higher than those without chemotherapy.   Conclusion: In this study, the presented model, in addition to simultaneous modeling capability of the event, could help prevent a higher prevalence of the terminal event (death) and thus reduce the adverse effects of reversible diseases.