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

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.