Analysis of survival data of patients with breast cancer with Cox proportional hazards model for dependent censoring based on copula function

In the common Cox proportional hazards model one of the basic assumptions is independence between censoring time and event time. In clinical studies, when censoring is caused by competing risks or patient withdrawal, there is always a concern about the validity of treatment effect estimates that are obtained under the assumption of independent censoring. Introduction a solution for checking the assumption of independent and extending the Cox model for dependent censoring is useful. To achieve this goal, we use copula function and extend the Cox model. This model can also perform a sensitivity analysis for checking the assumption of independent. We generalize the likelihood function in R software and estimate the parameters by using a iteration algorithm. We apply the proposed method to the data of breast cancer patients at Ghaem and Omid hospitals and check the independence assumption. We show by Simulation that this algorithm works well and show the effect of dependent censoring on estimated parameters. We apply the proposed method to the data of breast cancer patients at Ghaem and Omid hospitals and show that the independence assumption is true. Not assumption of independence causes bias in estimation in Cox model and the bias is dependent on the degree of association between event and censoring times. In dataset of breast cancer patients the primary diagnosis is an important role in Success in the treatment.