Regression models in the presence of semi-competing risks

Evaluation of a therapeutic strategy is complex when the course of a disease is characterized by the occurrence of different kinds of events. Competing risks arise when the occurrence of specific events prevents the observation of other events. A particular case on competing risks arises when only fatal events can prevent the observation of the non fatal ones, but not vice versa (semi-competing risks). If the independence assumption between relapse and death is tenable, Kaplan-Meier method can be used to estimate relapse free survival. Otherwise multivariate distribution of times based on Copulas can be adopted, to estimate the relapse free survival. For example the semi parametric methods proposed by Fine, Jiang and Chappell or the copula graphic estimator can be used. Furthermore when the interest is to evaluate the effect of different therapeutic strategies or covariates on the occurrence of a non terminal event in a semi-competing risks setting, specific regression model have to be adopted. We propose here to adopt the methodology based on pseudo-observations, having the advantage to be implemented by generalized linear models approaches. Simulation studies are performed to compare the performances of regression method for net survival in the presence of semi-competing risks. A case series of breast cancer patients is used to illustrate different methods of estimating relapse free survival in a semi-competing risks framework.