Regression models for relative survival

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.

Sex Differences in Treatments, Relative Survival, and Excess Mortality Following Acute Myocardial Infarction: National Cohort Study Using the SWEDEHEART Registry

“…Using the relative survival approach, we found that women with STEMI and NSTEMI had higher excess mortality rates compared with their male counterparts. Unlike standard survival, relative survival accounts for differences in background mortality across groups, allowing for the distinction between death due to the index AMI and deaths due to other causes, and avoids the risk of classification errors in cause‐of‐death records 27. Our results and the findings of a recent study by Baart et al13 illustrate that measuring relative survival and excess mortality may have important implications for acute coronary care.…”

Relative survival of childhood and adult medulloblastomas and primitive neuroectodermal tumors (PNETs)

“…This model, which was presented by Dickman et al in 2004, allows the calculation of excess hazard ratios through maximum likelihood estimation methods. 21 Different age categorizations were explored, and the regression models fit best when patients ages birth to 1 year and patients who did not receive radiation or surgery were excluded from the regression modeling.…”

Prognostic value of morphology and hormone receptor status in breast cancer – a population-based study

“…Differences in 5-year relative survival by tumour morphology and hormone receptor status were modelled with a recently developed multiple regression approach based on generalised linear models and adopting the Poisson assumption for the observed number of deaths (Dickman et al, 2004). The relative excess risks (RERs) derived from these models quantify the extent to which the hazard of death in a given group differs from that in the reference category, after taking into account the background risk of death in the general population of each country or region.…”