Copulas and Competing Risks: Applications for Long-Term Mixture Survival Models

Ronny Westerman, University of Marburg
Andrea Werdecker, University of Marburg
Ulrich O. Mueller, University of Marburg

In terms of competing risks Long-term Mixture Survival Models are widely used for the analysis of individuals who may never experience the considered type of failure. If we add the possibility of a lasting therapy success. some individuals have to be treated as immune to a specific cause of failure or to be defined as long-term survivors. In case of multi- or bivariate cause-specific survival data different dependence structures can be modeled with different copula functions. There are two main methodical goals for modeling marginal distributions to be considered: First flexibility and second masked causes. We propose a Bivariate Mixture Long-term Survival model based on the Farlie-Gumbel-Morgenstern (FGM) copula. Data simulations will be provided with SEER Breast Cancer Data. The major gains of this approach yield on the high flexibility for the copulas to account for different dependence structures.