Regression models for relative survival

TLDR

The study builds on an additive hazards model where total hazard equals baseline plus excess cancer‑related hazard, noting that minor differences arise from data presentation and distributional assumptions. The paper describes and compares four maximum‑likelihood approaches to estimating a regression model for relative survival. The authors assume excess hazards constant within follow‑up bands, maximize the likelihood directly or via generalized linear models, and implement the model in any GLM‑capable software (SAS, Stata, S‑plus, R) using GLM theory for fit assessment and diagnostics. Applied to two real data sets, the four approaches yield very similar estimates even when proportional excess hazards are violated, and the authors recommend a generalized linear model with a Poisson error structure on collapsed data for its ease of use and software availability. © 2004 John Wiley & Sons, Ltd.

Abstract

Abstract 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 data sets and produce very similar estimates even when the assumption of proportional excess hazards is violated. The choice of approach to use in practice can, therefore, be guided by ease of use and availability of software. We recommend using a generalized linear model with a Poisson error structure based on collapsed data using exact survival times. The model can be estimated in any software package that estimates GLMs with user‐defined link functions (including SAS, Stata, S‐plus, and R) and utilizes the theory of generalized linear models for assessing goodness‐of‐fit and studying regression diagnostics. Copyright © 2004 John Wiley & Sons, Ltd.