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

In terms of competing risks Mixture Long-term Survival Models are widely used for the analysis of individuals may never suffer the considered cause of failure. Under condition of a cured fraction, some individuals will be treated as immune to a specific cause of failure or be defined as long-term survivors. In case of multi- or bivariate cause-specific survival data different dependence structures between variables can be suited with different copula functions. There are two main methodical aspects for the marginal distributions need to account for: first the maximum of flexibility and second the application in case of masked causes. We proposed a bivariate mixture long-term model based on the Farlie-Gumbel-Morgenstern (FGM)copula. Data simulations will be provided with SEER Breast Cancer Data, and comparing the model with different types of copulas e.g. FGM, Positive Stable, Frank and Clayton Copula. Otherwise we will discuss optional ideas for this approach in a semi-competing risk setting.