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Alternatives to default shrinkage methods can improve prediction accuracy, calibration, and coverage: A methods

Mark A van de Wiel1, Gwenaël Gr Leday2, Martijn W Heymans1

  • 1Department of Epidemiology and Data Science, Amsterdam Public Health Research Institute, Amsterdam University Medical Centers, Amsterdam, the Netherlands.

Statistical Methods in Medical Research
|May 29, 2025
PubMed
Summary

Alternative shrinkage methods improve regression prediction accuracy, calibration, and confidence interval coverage in low-dimensional settings. These methods offer better performance than standard techniques like lasso and ridge regression.

Keywords:
Shrinkagecalibrationcoveragepredictionregression

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Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiology

Background:

  • Shrinkage methods reduce variance in high-dimensional settings, potentially improving prediction accuracy.
  • However, shrinkage can introduce bias, negatively impacting calibration and confidence interval coverage in low-dimensional regression.
  • Standard shrinkage methods (e.g., lasso, ridge) with single penalties are often criticized for these limitations.

Purpose of the Study:

  • To investigate alternative shrinkage methods for low-dimensional regression.
  • To demonstrate improvements in prediction accuracy, calibration, and confidence interval coverage.
  • To provide accessible R implementations for these advanced techniques.

Main Methods:

  • Studied linear and logistic regression models.
  • Utilized small sample splits from a large epidemiological dataset for linear regression.
  • Employed Bayesian hierarchical modeling for enhanced shrinkage in linear regression.
  • Used external simulations for logistic regression analysis.

Main Results:

  • Differential ridge penalties enhanced prediction accuracy in linear regression.
  • Additional shrinkage improved calibration and coverage for linear models.
  • Local shrinkage outperformed global shrinkage in logistic regression, improving calibration and accuracy.
  • Alternative methods showed better performance than Firth's correction in logistic regression.

Conclusions:

  • Alternative shrinkage methods offer significant benefits over standard techniques for regression-based prediction.
  • These methods enhance accuracy, calibration, and coverage, addressing limitations of traditional approaches.
  • Accessible R implementations facilitate the adoption of these advanced statistical techniques.