Background: Renal cell carcinoma (RCC) remains a global health concern due to its poor survival rate. This study aimed to investigate the influence of medical determinants and socioeconomic status on survival outcomes of RCC patients. We analyzed the survival data of 41,563 RCC patients recorded under the Surveillance, Epidemiology, and End Results (SEER) program from 2012 to 2020. Methods: We employed a competing risk model, assuming lifetime of RCC patients under various risks follows Chen distribution. This model accounts for uncertainty related to survival time as well as causes of death, including missing cause of death. For model analysis, we utilized Bayesian inference and obtained the estimate of various key parameters such as cumulative incidence function (CIF) and cause-specific hazard. Additionally, we performed Bayesian hypothesis testing to assess the impact of multiple factors on the survival time of RCC patients. Results: Our findings revealed that the survival time of RCC patients is significantly influenced by gender, income, marital status, chemotherapy, tumor size, and laterality. However, we observed no significant effect of race and origin on patient's survival time. The CIF plots indicated a number of important distinctions in incidence of causes of death corresponding to factors income, marital status, race, chemotherapy, and tumor size. Conclusions: The study highlights the impact of various medical and socioeconomic factors on survival time of RCC patients. Moreover, it also demonstrates the utility of competing risk model for survival analysis of RCC patients under Bayesian paradigm. This model provides a robust and flexible framework to deal with missing data, which can be particularly useful in real-life situations where patients information might be incomplete.