Analysis of Bladder Tumor Recurrence Data with the Terminal Event and Cure Fraction

Complete observation of the recurrent events may not be available, since some subjects might drop out or fail before the endpoint of observation. However, the assumption of independency of the recurrent events and the censoring is not realistic in many situations. In this paper, we develop an innovative model based on the Clayton-Oakes copula function to fit the correlation of these variables. The joint survival function of the recurrent event times can be obtained through the marginal hazard functions with copula parameters which measure the degree of dependence and control the association between these variables. The cure fraction can be concluded into the proposed model as well. An example of application on bladder tumor recurrence data is re-analyzed to assess the proposed models and methodologies.