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The Use of Resampling Methods to Simplify Regression Models in Medical Statistics

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  • Willi Sauerbrei

Abstract

The number of variables in a regression model is often too large and a more parsimonious model may be preferred. Selection strategies (e.g. all‐subset selection with various penalties for model complexity, or stepwise procedures) are widely used, but there are few analytical results about their properties. The problems of replication stability, model complexity, selection bias and an over‐optimistic estimate of the predictive value of a model are discussed together with several proposals based on resampling methods. The methods are applied to data from a case–control study on atopic dermatitis and a clinical trial to compare two chemotherapy regimes by using a logistic regression and a Cox model. A recent proposal to use shrinkage factors to reduce the bias of parameter estimates caused by model building is extended to parameterwise shrinkage factors and is discussed as a further possibility to illustrate problems of models which are too complex. The results from the resampling approaches favour greater simplicity of the final regression model.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssc:v:48:y:1999:i:3:p:313-329
    DOI: 10.1111/1467-9876.00155
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    Cited by:

    1. Patrick Royston & Willi Sauerbrei, 2007. "Multivariable modeling with cubic regression splines: A principled approach," Stata Journal, StataCorp LP, vol. 7(1), pages 45-70, February.
    2. Dunkler, Daniela & Sauerbrei, Willi & Heinze, Georg, 2016. "Global, Parameterwise and Joint Shrinkage Factor Estimation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i08).
    3. Hapfelmeier Alexander & Hothorn Torsten & Riediger Carina & Ulm Kurt, 2014. "Estimation of a Predictor’s Importance by Random Forests When There Is Missing Data: RISK Prediction in Liver Surgery using Laboratory Data," The International Journal of Biostatistics, De Gruyter, vol. 10(2), pages 165-183, November.
    4. Sauerbrei, W. & Meier-Hirmer, C. & Benner, A. & Royston, P., 2006. "Multivariable regression model building by using fractional polynomials: Description of SAS, STATA and R programs," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3464-3485, August.
    5. Simone P Rauh & Martijn W Heymans & Anitra D M Koopman & Giel Nijpels & Coen D Stehouwer & Barbara Thorand & Wolfgang Rathmann & Christa Meisinger & Annette Peters & Tonia de las Heras Gala & Charlott, 2017. "Predicting glycated hemoglobin levels in the non-diabetic general population: Development and validation of the DIRECT-DETECT prediction model - a DIRECT study," PLOS ONE, Public Library of Science, vol. 12(2), pages 1-13, February.
    6. Hapfelmeier, A. & Ulm, K., 2013. "A new variable selection approach using Random Forests," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 50-69.
    7. Patrick Royston & Willi Sauerbrei, 2009. "Bootstrap assessment of the stability of multivariable models," Stata Journal, StataCorp LP, vol. 9(4), pages 547-570, December.
    8. Toshiki Doi & Suguru Yamamoto & Takatoshi Morinaga & Ken-ei Sada & Noriaki Kurita & Yoshihiro Onishi, 2015. "Risk Score to Predict 1-Year Mortality after Haemodialysis Initiation in Patients with Stage 5 Chronic Kidney Disease under Predialysis Nephrology Care," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-14, June.
    9. 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.

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