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Parametrization and penalties in spline models with an application to survival analysis

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  • Costa, M.J.
  • Shaw, J.E.H.

Abstract

A simple parametrization, built from the definition of cubic splines, is shown to facilitate the implementation and interpretation of penalized spline models, whatever configuration of knots is used. The parametrization is termed value-first derivative parametrization. Inference is Bayesian and explores the natural link between quadratic penalties and Gaussian priors. However, a full Bayesian analysis seems feasible only for some penalty functionals. Alternatives include empirical Bayes inference methods involving model selection type criteria. The proposed methodology is illustrated by an application to survival analysis where the usual Cox model is extended to allow for time-varying regression coefficients.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:3:p:657-670
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    References listed on IDEAS

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    1. 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, March.
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    5. Kauermann, Goran, 2005. "Penalized spline smoothing in multivariable survival models with varying coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 169-186, April.
    6. Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian inference for generalized additive mixed models based on Markov random field priors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(2), pages 201-220.
    7. Lu Tian & David Zucker & L.J. Wei, 2005. "On the Cox Model With Time-Varying Regression Coefficients," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 172-183, March.
    8. Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.
    9. Aldrin, Magne, 2006. "Improved predictions penalizing both slope and curvature in additive models," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 267-284, January.
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    Cited by:

    1. Rui Martins, 2022. "A flexible link for joint modelling longitudinal and survival data accounting for individual longitudinal heterogeneity," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(1), pages 41-61, March.

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