Modelling relative survival using transformation methods

Patient survival is often assessed as a measure of effectiveness of treatment in cancer clinical trials. The relative survival rate is a measure of patient survival corrected for the effect of other causes of death. We incorporate an additive hazards model for the overall force of mortality focusing attention on the form of the underlying disease process. Transformation models for the cause-specific hazard rate describing the disease process are considered. We demonstrate a method for estimating the transformation parameter providing insight into the appropriate choice of model structure. The models include the additive and multiplicative structures as special cases. We write the models in the generalized linear model framework and demonstrate ease of fitting via existing statistical software. The methodology is applied to a Hodgkin's disease data set to assess the effect of clinical trial results on population survival. Our analysis concludes that the multiplicative structure provides a more appropriate description of the data as compared to the additive structure.