Statistical Modelling 10 (2010), 315–332
Robust frailty modelling using non-proportional hazards models
Il Do Ha
Department of Asset Management,
Daegu Haany University
South Korea
Gilbert MacKenzie
Centre of Biostatistics,
Department of Mathematics & Statistics,
University of Limerick
Ireland
and
ENSAI,
Rennes
France
eMail: gilbert.mackenzie@ul.ie
Abstract:
Correlated survival times can be modelled by introducing a random effect, or
frailty component, into the hazard function. For multivariate survival data,
we extend a non-proportional hazards (PH) model, the generalized
time-dependent logistic survival model, to include random effects. The
hierarchical likelihood procedure, which obviates the need for marginalization
over the random effect distribution, is derived for this extended model and
its properties are discussed. The extended model leads to a robust estimation
result for the regression parameters against the misspecification of the form
of the basic hazard function or frailty distribution compared to PH-based
alternatives. The proposed method is illustrated by two practical examples
and a simulation study which demonstrate the advantages of the new model.
Keywords:
frailty models; generalized time-dependent logistic; hierarchical likelihood;
non-PH model; random effect
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