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Biostatistics Advance Access originally published online on July 3, 2008
Biostatistics 2009 10(1):136-146; doi:10.1093/biostatistics/kxn021
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

An approach to estimation in relative survival regression

Maja Pohar Perme*

Department of Biomedical Informatics, University of Ljubljana, Vrazov trg 2, SI-1000 Ljubljana, Slovenia, maja.pohar{at}mf.uni-lj.si

Robin Henderson

Mathematics & Statistics, University of Newcastle, UK

Janez Stare

Department of Biomedical Informatics, University of Ljubljana, Slovenia

* To whom correspondence should be addressed.

The goal of relative survival methodology is to compare the survival experience of a cohort with that of the background population. Most often an additive excess hazard model is employed, which assumes that each person's hazard is a sum of 2 components—the population hazard obtained from life tables and an excess hazard attributable to the specific condition. Usually covariate effects on the excess hazard are assumed to have a proportional hazards structure with parametrically modelled baseline. In this paper, we introduce a new fitting procedure using the expectation–maximization algorithm, treating the cause of death as missing data. The method requires no assumptions about the baseline excess hazard thus reducing the risk of bias through misspecification. It accommodates the possibility of knowledge of cause of death for some patients, and as a side effect, the method yields an estimate of the ratio between the excess and the population hazard for each subject. More importantly, it estimates the baseline excess hazard flexibly with no additional degrees of freedom spent. Finally, it is a generalization of the Cox model, meaning that all the wealth of options in existing software for the Cox model can be used in relative survival. The method is applied to a data set on survival after myocardial infarction, where it shows how a particular form of the hazard function could be missed using the existing methods.

Keywords: Additive model; EM algorithm; Relative survival

Received February 9, 2007; revised October 23, 2007; revised February 22, 2008; revised March 26, 2008; accepted for publication June 3, 2008.


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