A class of transformation covariate regression models for estimating the excess hazard in relative survival analysis

Relative survival is the standard measure of excess mortality due to cancer in population-based cancer survival studies. In relative survival analysis, the observed hazard for cancer patients is the sum of the expected hazard for the general cancer-free population and the excess hazard associated with a cancer diagnosis. Previous models for relative survival analysis have assumed that the excess hazard rate is related to covariates by additive or multiplicative regression models. In this paper, a transformation covariate regression model is developed for estimation of the excess hazard rate, which includes both the additive and the multiplicative regression models as special cases. The baseline excess hazard rate and time-dependent hazard ratios can be approximated by means of regression splines, and the parameter estimates can be obtained using a standard statistical package. As is demonstrated through simulation, the proposed transformation hazards model provides a reasonably good fit to typical relative survival data. For illustration purposes, the sex difference in relative survival for lung and bronchus cancer patients is examined using data from population-based cancer registries (1973-2003).