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Application of Shrinkage Techniques in Logistic Regression Analysis: A Case Study

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  • E. W. Steyerberg
  • M. J. C. Eijkemans
  • J. D. F. Habbema

Abstract

Logistic regression analysis may well be used to develop a predictive model for a dichotomous medical outcome, such as short‐term mortality. When the data set is small compared to the number of covariables studied, shrinkage techniques may improve predictions. We compared the performance of three variants of shrinkage techniques: 1) a linear shrinkage factor, which shrinks all coefficients with the same factor; 2) penalized maximum likelihood (or ridge regression), where a penalty factor is added to the likelihood function such that coefficients are shrunk individually according to the variance of each covariable; 3) the Lasso, which shrinks some coefficients to zero by setting a constraint on the sum of the absolute values of the coefficients of standardized covariables. Logistic regression models were constructed to predict 30‐day mortality after acute myocardial infarction. Small data sets were created from a large randomized controlled trial, half of which provided independent validation data. We found that all three shrinkage techniques improved the calibration of predictions compared to the standard maximum likelihood estimates. This study illustrates that shrinkage is a valuable tool to overcome some of the problems of overfitting in medical data.

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  • E. W. Steyerberg & M. J. C. Eijkemans & J. D. F. Habbema, 2001. "Application of Shrinkage Techniques in Logistic Regression Analysis: A Case Study," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 55(1), pages 76-88, March.
    • Handle: RePEc:bla:stanee:v:55:y:2001:i:1:p:76-88
    DOI: 10.1111/1467-9574.00157
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    1. Campbell Foubister & Esther M F van Sluijs & Anna Vignoles & Paul Wilkinson & Edward C F Wilson & Caroline H D Croxson & Helen Elizabeth Brown & Kirsten Corder, 2021. "The school policy, social, and physical environment and change in adolescent physical activity: An exploratory analysis using the LASSO," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-14, April.
    2. Steffen CE Schmidt & Jennifer Schneider & Anne Kerstin Reimers & Claudia Niessner & Alexander Woll, 2019. "Exploratory Determined Correlates of Physical Activity in Children and Adolescents: The MoMo Study," IJERPH, MDPI, vol. 16(3), pages 1-16, January.
    3. 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).
    4. Muhammad Amin & Lixin Song & Milton Abdul Thorlie & Xiaoguang Wang, 2015. "SCAD-penalized quantile regression for high-dimensional data analysis and variable selection," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 212-235, August.

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