Statistical Modelling 11 (2011), 3–24
Building Cox-type structured hazard regression models with time-varying effects
Benjamin Hofner
Institut für Medizininformatik, Biometrie und Epidemiologie,
Friedrich-Alexander-Universität Erlangen-Nürnberg
Germany
eMail: benjamin.hofner@imbe.med.uni-erlangen.de
Thomas Kneib
Institut für Mathematik,
Carl von Ossietzky Universität,
Oldenburg
Germany
Wolfgang Hartl
Department of Surgery,
Campus Großhadern,
Ludwig-Maximilians-Universität München
Germany
Helmut Küchenhoff
Institut für Statistik,
Ludwig-Maximilians-Universität München
Germany
Abstract:
In recent years, flexible hazard regression models based on penalized splines
have been developed that allow us to extend the classical Cox model via the
inclusion of time-varying and nonparametric effects. Despite their immediate
appeal in terms of flexibility, these models introduce additional difficulties
when a subset of covariates and the corresponding modelling alternatives have
to be chosen. We present an analysis of data from a specific patient population
with 90-day survival as the response variable. The aim is to determine a
sensible prognostic model where some variables have to be included due to
subject-matter knowledge while other variables are subject to model selection.
Motivated by this application, we propose a two-stage stepwise model building
strategy to choose both the relevant covariates and the corresponding modelling
alternatives within the choice set of possible covariates simultaneously. For
categorical covariates, competing modelling approaches are linear effects and
time-varying effects, whereas nonparametric modelling provides a further
alternative in case of continuous covariates. In our data analysis, we
identified a prognostic model containing both smooth and time-varying effects.
Keywords:
hazard regression; mixed models; model building; prognostic model;
P-splines; time-varying effects
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