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A Mixed Model Approach for Geoadditive Hazard Regression

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  • THOMAS KNEIB
  • LUDWIG FAHRMEIR

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..

Suggested Citation

  • Thomas Kneib & Ludwig Fahrmeir, 2007. "A Mixed Model Approach for Geoadditive Hazard Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(1), pages 207-228.
  • Handle: RePEc:bla:scjsta:v:34:y:2007:i:1:p:207-228
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9469.2006.00524.x
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    Cited by:

    1. 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, vol. 53(3), pages 657-670, January.
    2. HÃ¥vard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392.
    3. Benjamin Hofner & Torsten Hothorn & Thomas Kneib, 2013. "Variable selection and model choice in structured survival models," Computational Statistics, Springer, vol. 28(3), pages 1079-1101, June.
    4. Westerheide Nina & Kauermann Goeran, 2012. "Flexible Modelling of Duration of Unemployment Using Functional Hazard Models and Penalized Splines: A Case Study Comparing Germany and the UK," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(1), pages 1-27, January.
    5. Thomas Kneib & Bernhard Baumgartner & Winfried Steiner, 2007. "Semiparametric multinomial logit models for analysing consumer choice behaviour," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 91(3), pages 225-244, October.
    6. 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.
    7. Li Li & Timothy Hanson & Jiajia Zhang, 2015. "Spatial extended hazard model with application to prostate cancer survival," Biometrics, The International Biometric Society, vol. 71(2), pages 313-322, June.
    8. Nikolaus Umlauf & Nadja Klein & Achim Zeileis, 2017. "BAMLSS: Bayesian Additive Models for Location, Scale and Shape (and Beyond)," Working Papers 2017-05, Faculty of Economics and Statistics, University of Innsbruck.
    9. Susanne Konrath & Ludwig Fahrmeir & Thomas Kneib, 2015. "Bayesian accelerated failure time models based on penalized mixtures of Gaussians: regularization and variable selection," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 259-280, July.

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