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Dynamic regression hazards models for relative survival
Author(s) -
Cortese Giuliana,
Scheike Thomas H.
Publication year - 2008
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.3242
Subject(s) - covariate , econometrics , semiparametric regression , proportional hazards model , parametric statistics , semiparametric model , estimator , statistics , additive model , resampling , inference , population , context (archaeology) , regression analysis , statistical inference , mathematics , computer science , paleontology , demography , artificial intelligence , sociology , biology
A natural way of modelling relative survival through regression analysis is to assume an additive form between the expected population hazard and the excess hazard due to the presence of an additional cause of mortality. Within this context, the existing approaches in the parametric, semiparametric and non‐parametric setting are compared and discussed. We study the additive excess hazards models, where the excess hazard is on additive form. This makes it possible to assess the importance of time‐varying effects for regression models in the relative survival framework. We show how recent developments can be used to make inferential statements about the non‐parametric version of the model. This makes it possible to test the key hypothesis that an excess risk effect is time varying in contrast to being constant over time. In case some covariate effects are constant, we show how the semiparametric additive risk model can be considered in the excess risk setting, providing a better and more useful summary of the data. Estimators have explicit form and inference based on a resampling scheme is presented for both the non‐parametric and semiparametric models. We also describe a new suggestion for goodness of fit of relative survival models, which consists on statistical and graphical tests based on cumulative martingale residuals. This is illustrated on the semiparametric model with proportional excess hazards. We analyze data from the TRACE study using different approaches and show the need for more flexible models in relative survival. Copyright © 2008 John Wiley & Sons, Ltd.