Linked shrinkage to improve estimation of interaction effects in regression models

Area of Science:

• Statistics
• Computational Biology
• Bioinformatics

Background:

• High-dimensional data presents challenges for statistical modeling, particularly when incorporating two-way interactions.
• Existing methods often simplify interactions by focusing only on relevant main effects, potentially limiting model scope.

Purpose of the Study:

• To develop an estimation method capable of managing the quadratic increase in dimensionality caused by interactions.
• To create computational tools for quantifying variable importance and improving model interpretability.

Main Methods:

• A local shrinkage model is proposed, linking the shrinkage of interaction effects to their corresponding main effects.
• A novel analytical formula for Shapley values is derived for rapid, individual-specific variable importance assessment.

Main Results:

• The developed approach demonstrates accurate parameter estimation and competitive predictive accuracy.
• The Bayesian framework facilitates inherent inference and variable selection.
• Empirical evaluations on large-scale cohort data validate the method's performance.

Conclusions:

• The linked local shrinkage model offers an effective alternative for handling interactions in epidemiological and clinical studies.
• The method enhances parameter accuracy, prediction, and variable selection while providing robust inference and interpretation.
• It presents a competitive option against less interpretable machine learning algorithms for predictive tasks.