Goodness of fit of relative survival models

Additive regression models are preferred over multiplicative models in the analysis of relative survival data. Such preferences are mainly grounded in practical experience with mostly cancer registries data, where the basic assumption of the additivity of hazards is more likely to be met. Also, the interpretation of coefficients is more meaningful in additive than in multiplicative models. Nonetheless, the question of goodness of fit of the assumed model must still be addressed, and while there is an abundance of methods to check the goodness of fit of multiplicative models, the respective arsenal for additive models is almost empty. We propose here a variety of procedures for testing the null hypothesis of a good fit. These are based on partial residuals defined similarly to Schoenfeld residuals familiar for Cox model diagnostics. The tests have appropriate sizes under the null hypothesis, and good power under different alternatives. We investigate their performance through simulations and apply the methods to data from a study into survival of colon cancer patients.