Regression models for relative survival

Four approaches to estimating a regression model for relative survival using the method of maximum likelihood are described and compared. The underlying model is an additive hazards model where the total hazard is written as the sum of the known baseline hazard and the excess hazard associated with a diagnosis of cancer. The excess hazards are assumed to be constant within pre-specified bands of follow-up. The likelihood can be maximized directly or in the framework of generalized linear models. Minor differences exist due to, for example, the way the data are presented (individual, aggregated or grouped), and in some assumptions (e.g. distributional assumptions). The four approaches are applied to two real…