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.

Objective: Bipolar I disorder is one of the most frequent mental disorders characterized by manic or mixed +/- depressive episodes. Drug treatment has been proved to diminish next episodes, but many other factors are important for exacerbating the conditions. This study aimed to investigate the effective factors on the time and number of episodes in these patients by applying the shared frailty model. Method: In this retrospective longitudinal study, the information of 606 patients with bipolar I disorder, admitted for the first time in Ibn-e-Sina psychiatric hospital in Mashhad from the beginning of 2007 until the end of 2009 were used. These patients were followed up until the end of 2018 for readmission. The Cox model with gamma frailty and Bayesian approach were used to determine the effective factors of frequent recurrences. Results: History of head trauma, substance abuse, and legal conflict had a positive impact on recurrences, while age had a negative effect on recurrences and the risk of recurrence was higher in younger people (P < 0.05). The variance estimation of frailty effect was 0.97 that indicates a correlation between the recurrence intervals of bipolar I patients, owing to a heterogeneity among patients. Conclusion: Based on the results, a higher risk of recurrence of bipolar I disorder was found in younger patients and those with a history of head trauma, substance abuse, and legal conflicts. Further investigations are required to account for the genetic factor and psychosocial exposure during critical periods applying this model.

Background: Hematopoietic stem cell transplantation (HSCT) is the most effective of all hematologic malignancies treatments, resulting in a significant improvement in survival rate. Objectives: This study aimed at determining the survival rate and factors affecting the survival in patients undergoing hematopoietic stem cell transplantation, using the joint model. Methods: This study was a retrospective cohort study, used for collecting data from patients with hematopoietic malignancies who underwent hematopoietic stem cell transplantation in Taleghani Hospital (Shahid Beheshti University of Medical Sciences), Tehran, Iran during the years 2007 and 2015 and were followed up till 2017. A Bayesian joint model of longitudinal and survival was chosen, using Win Bugs software. Results: A total of 395 patients were enrolled. The median overall survival was 6.3 years (95% CI (5.86, 6.76)). Eighty-one patients had died. The obtained results from this study manifested that age (HR: 1.02, 95% CI: (1.002, 1.04)) and pre-transplantation relapse (HR = 1.64, 95% CI: (1.09, 2.4)) have incremental impact on death after transplantation, while malignancy type (NHL (HR: 0.33, 95%CI: (0.152, 0.73)) and AML (HR: 0.62, 95% CI: (0.29, 0.7)) are also effective in reducing death after transplantation. Similarly, the correlation index between longitudinal and survival models proved to be significant (HR: 0.6, 95% CI: (0.0802, 0.37)). Conclusions: This study showed that age, per-transplantation relapse, and malignancy type are the effective factors in the survival rate. Moreover, the link parameter between longitudinal response (WBC) and the survival indicated that an increase in WBC count leads to a decrease in the death risk.

The observations of repeated or recurrent events occur in many longitudinal studies. Furthermore, sometimes there may exist a terminal event such as death, which is strongly correlated with recurrent events. In many situations, a fraction of subjects who will never experience the event of interest during a long follow-up period is considered to be cured. In this article, we proposed a joint frailty model in the presence of cure fraction. The dependency is modeled by shared frailty that is contained in both the recurrent andterminal events hazard functions. It allows to estimate two separate sets of parameters on the recurrent, death, and cure model. We applied the maximum likelihood method under a piecewise constant hazard function for model fitting. The proposed model is evaluated by simulation studies and an application to a breast cancer data is provided.