[Investigation of influential factors affecting survival rate of patients with colorectal cancer using copula function]

Competing risk data is one of the multivarite survival data. Competing risk data can be modelled using copula function. In this study we propose a bayesian modelling approach of competing risk data using the copula function. We used the data from colorectal cancer registyrarty in Tehran. After constructing likelihood function using Clayton copula by choosing appropriate prior distribution for parameters, we obtained the posterior distribution of parameters using the Metropolis-Hastings algorithms and Slice sampling. The results of univariate analysis showed that sex, histology of tumor, extent of wall penetration, lymph node metastasis, distant metastasis and pathological stage of tumor were significantly associated with colon cancer and sex, histology of tumor, lymph node metastasis, distant metastasis and pathological stage of tumor were were significantly related to rectal cancer. In the multivariate analysis, age at diagnosis, tumor grade and distant metastasis were significant prognostic factors for colon cancer and tumor grade and size of the tumor were significant prognostic factors of rectal cancerAs we showed some variables may have different impacts on colon and rectum cancers, consequently, further studies are needed to be conducted considering risk factors of these cancers separately