A Bayesian multivariate joint frailty model for disease recurrences and survival

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Motivated by a study for soft tissue sarcoma, this article considers the analysis of diseases recurrence and survival. A multivariate frailty hazard model is established for joint-modeling of three correlated time-to-event outcomes: local disease recurrence, distant disease recurrence (metastasis) and death. The goals are to find out (1) the effects of treatments on local and distant disease recurrences, and death, (2) the effects of local and distant disease recurrences on death, and (3) the correlation between local and distant recurrences. By our approach, all these three important questions, which are commonly asked in similar medical research studies, can be answered by a single model. We put the proposed joint frailty model in a Bayesian framework, and use a hybrid Monte Carlo algorithm for the computation of posterior distributions. This hybrid algorithm relies on the evaluation of the gradient of target log-density and a guided walk progress, and it combines these two strategies to suppress random walk behaviour. A further distinction is that the hybrid algorithm can update all the components of a multivariate state vector simultaneously. Simulation studies are conducted to assess the proposed joint frailty model and the computation algorithm. The motivating soft tissue sarcoma data set is analyzed for illustration purpose.