Bayesian Frailty for Competing Risks Survival Analysis in the Iranian Metastatic Colorectal Patients

Objective: In the competing risks problem, wherein only the event due one cause is observed, the cause-specific hazard rates are usually estimated by considering the independence assumption on the competing causes. However, this assumption is too rigorous in the practical situations. This paper aimed to extend the results of Finkelstein and Esaulova (2008), in order to relax the problem of independence assumption in the competing risks survival analysis with counting process approach by exerting frailty term and in the Bayesian framework. Material and Methods: The results were applied on Iranian metastatic colorectal cancer patients data set. Several frailty distributions were tried. The survival probability and their 95 percent confidence interval were calculated based on the best model and using 10000 MCMC samples after burning 1000 samples. Results: The results showed better survival for the patients with rectal cancer than with colon cancer. Conclusion: These findings may be useful for many situations at which there is uncertainty about or the independence assumption of failure times is not hold, such as competing risks, recurrent events and clustered data including modeling clustered survival data from multicenter clinical trials, especially in the case of moderate to small sample size.