Joint Modeling Recurrent Events and a Terminal Event with Frailty-copula Models

Open Access
Li, Zheng
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
February 28, 2018
Committee Members:
  • Vernon Michael Chinchilli, Dissertation Advisor/Co-Advisor
  • Ming Wang, Committee Chair/Co-Chair
  • Runze Li, Committee Member
  • Nasrollah Ghahramani, Committee Member
  • Feng Yue, Outside Member
  • Joint Frailty-copula Models
  • Bayesian Augmentation
  • Recurrent Events
  • Joint Frailty Model
A terminal event can stop a series of recurrent events, which commonly occurs in biomedical and clinical studies. In this situation, the non-informative censoring assumption could fail because of potential dependency between these two event processes, leading to invalid inference if we analyze recurrent events alone. The joint frailty model is one of the widely used approaches to jointly model these two processes by sharing the same frailty term. One important assumption is that recurrent and terminal event processes are conditionally independent given the subject-level frailty; however, this could be violated when two processes also depends on time-varying covariates across recurrences. For example, time to death and time to stroke might both depend on the age of the patients. And when we do not include age in the survival models, the subject-level frailty cannot capture the change of the age across recurrences and lead to the violation of the conditional independence assumption. Furthermore, marginal correlation between two event processes based on traditional frailty modeling has no closed form solution for estimation. In order to fill these gaps, we propose a novel joint frailty-copula approach to model recurrent events and a terminal event with modest assumptions under Bayesian framework. Metropolis-Hastings within the Gibbs Sampler algorithm is used for parameter estimation. Extensive simulation studies are conducted to evaluate the efficiency, robustness and predictive performance of our proposal. The simulation results show that compared with the joint frailty model, the bias and mean squared error(MSE) of the propose approach is smaller when the conditional independence assumption is violated. We applied our method into a real example extracted from the MarketScan database to identify potential risk factors and study the association between recurrent strokes and all-cause mortality. Another important assumption under the joint frailty model is that the correlation between the terminal event and the recurrent events is constant over time. This is an unrealistic assumption. For example, when we study myocardial infarctions, time to death might be more correlated with the last myocardial infarction compared with the earlier myocardial infarction. We propose a time-varying joint frailty-copula model to further relax this assumption. Under this model, the dynamic correlation between the terminal event and the recurrent event is modeled by a latent Gaussian AR(1) process. The simulation results show that compared with the joint frailty model and the joint frailty-copula model, the bias, SD, MSE and AB of the time-varying frailty copula model are the smallest. Then, we applied our method to analyze the CHS data to identify potential risk factors to myocardial infarction and stroke. In summary, we propose two methods to jointly model recurrent events and a terminal event. Both methods outperform the traditional joint frailty model when the conditional independence assumption is violated. The time-varying joint frailty-copula model is more flexible, which allows the correlation between the recurrent event process and the terminal event process to change over time. One future topic is to jointly modeling biomarker, recurrent events and death time by the frailty-copula models. Other topics include extending the current model to a cure rate model and modeling multiple types of recurrent events.