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A Mixed Model Approach for Geoadditive Hazard Regression

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  • THOMAS KNEIB
  • LUDWIG FAHRMEIR
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    Abstract

    Mixed model based approaches for semiparametric regression have gained much interest in recent years, both in theory and application. They provide a unified and modular framework for penalized likelihood and closely related empirical Bayes inference. In this article, we develop mixed model methodology for a broad class of Cox-type hazard regression models where the usual linear predictor is generalized to a geoadditive predictor incorporating non-parametric terms for the (log-)baseline hazard rate, time-varying coefficients and non-linear effects of continuous covariates, a spatial component, and additional cluster-specific frailties. Non-linear and time-varying effects are modelled through penalized splines, while spatial components are treated as correlated random effects following either a Markov random field or a stationary Gaussian random field prior. Generalizing existing mixed model methodology, inference is derived using penalized likelihood for regression coefficients and (approximate) marginal likelihood for smoothing parameters. In a simulation we study the performance of the proposed method, in particular comparing it with its fully Bayesian counterpart using Markov chain Monte Carlo methodology, and complement the results by some asymptotic considerations. As an application, we analyse leukaemia survival data from northwest England. Copyright 2007 Board of the Foundation of the Scandinavian Journal of Statistics..

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    Bibliographic Info

    Article provided by Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association in its journal Scandinavian Journal of Statistics.

    Volume (Year): 34 (2007)
    Issue (Month): 1 ()
    Pages: 207-228

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    Handle: RePEc:bla:scjsta:v:34:y:2007:i:1:p:207-228

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    Cited by:
    1. Thomas Kneib & Bernhard Baumgartner & Winfried Steiner, 2007. "Semiparametric multinomial logit models for analysing consumer choice behaviour," AStA Advances in Statistical Analysis, Springer, Springer, vol. 91(3), pages 225-244, October.
    2. Benjamin Hofner & Torsten Hothorn & Thomas Kneib, 2013. "Variable selection and model choice in structured survival models," Computational Statistics, Springer, Springer, vol. 28(3), pages 1079-1101, June.
    3. Costa, M.J. & Shaw, J.E.H., 2009. "Parametrization and penalties in spline models with an application to survival analysis," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 53(3), pages 657-670, January.
    4. Ezra Gayawan & Samson B. Adebayo, 2013. "A Bayesian semiparametric multilevel survival modelling of age at first birth in Nigeria," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 28(45), pages 1339-1372, June.

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