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A Partial Likelihood Approach to Smooth Estimation of Dynamic Covariate Effects using Penalised Splines
Author(s) -
Brown Denise,
Kauermann Göran,
Ford Ian
Publication year - 2007
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200510325
Subject(s) - covariate , akaike information criterion , smoothing , spline (mechanical) , mathematics , smoothing spline , proportional hazards model , econometrics , statistics , mixed model , engineering , spline interpolation , structural engineering , bilinear interpolation
Survival data are often modelled by the Cox proportional hazards model, which assumes that covariate effects are constant over time. In recent years however, several new approaches have been suggested which allow covariate effects to vary with time. Non‐proportional hazard functions, with covariate effects changing dynamically, can be fitted using penalised spline ( P ‐spline) smoothing. By utilising the link between P ‐spline smoothing and generalised linear mixed models, the smoothing parameters steering the amount of smoothing can be selected. A hybrid routine, combining the mixed model approach with a classical Akaike criterion, is suggested. This approach is evaluated with simulations and applied to data from the West of Scotland Coronary Prevention Study. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)