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Stability analysis of an additive spline model for respiratory health data by using knot removal

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  • Harald Binder
  • Willi Sauerbrei

Abstract

Summary. In many settings with possibly non‐linear influence of covariates, such as in the present application with children's respiratory health data, generalized additive models are an attractive choice. Although techniques for fitting these have been extensively investigated, there are fewer results on stability of replication, i.e. stability of fitted model components with respect to perturbations in the data. Nevertheless, this aspect is essential for judging how useful the present model is for understanding predictors of lung function. We therefore investigate existing tools for stability analysis based on bootstrap samples, such as quantities for variability and bias, for our application. Furthermore, as the focus is on models based on B‐splines, knot removal techniques are available. These can help to provide more insight into the stability of local features that are fitted in bootstrap samples. We analyse the bootstrap result matrix via log‐linear models. Specifically, the relationship with respect to local features between the influence functions of potential lung function predictors is investigated.

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  • Harald Binder & Willi Sauerbrei, 2009. "Stability analysis of an additive spline model for respiratory health data by using knot removal," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(5), pages 577-600, December.
    • Handle: RePEc:bla:jorssc:v:58:y:2009:i:5:p:577-600
    DOI: 10.1111/j.1467-9876.2009.00668.x
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    References listed on IDEAS

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    1. Willi Sauerbrei, 1999. "The Use of Resampling Methods to Simplify Regression Models in Medical Statistics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 313-329.
    2. Simon N. Wood, 2004. "Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 673-686, January.
    3. W. Sauerbrei & P. Royston, 1999. "Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(1), pages 71-94.
    4. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, September.
    5. Breiman, Leo, 1993. "Fitting additive models to regression data : Diagnostics and alternative views," Computational Statistics & Data Analysis, Elsevier, vol. 15(1), pages 13-46, January.
    6. Binder, Harald & Sauerbrei, Willi, 2008. "Increasing the usefulness of additive spline models by knot removal," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5305-5318, August.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, September.
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    1. Patrick Royston & Willi Sauerbrei, 2009. "Bootstrap assessment of the stability of multivariable models," Stata Journal, StataCorp LP, vol. 9(4), pages 547-570, December.

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