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High-dimensional variable selection accounting for heterogeneity in regression coefficients across multiple data

Tingting Yu1, Shangyuan Ye2, Rui Wang1,3

  • 1Department of Population Medicine, Harvard Pilgrim Health Care Institute and Harvard Medical School, Boston, Massachusetts, U.S.A.

The Canadian Journal of Statistics = Revue Canadienne De Statistique
|September 25, 2024
PubMed
Summary

This study introduces an adaptive clustering penalty (ACP) method for analyzing multi-source data, effectively handling heterogeneity by clustering regression coefficients. The ACP method demonstrates a strong oracle property and identifies sub-homogeneity in treatment effects.

Keywords:
ADMMMSC 2020Primary 62J07coefficient clusteringdata heterogeneityk-meanssecondary 62J05variable selection

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Area of Science:

  • Statistics
  • Biostatistics
  • Data Science

Background:

  • Analyzing data from multiple sources requires accounting for heterogeneity.
  • High-dimensional linear regression is crucial for integrative data analysis.

Purpose of the Study:

  • To propose a novel adaptive clustering penalty (ACP) method for simultaneous variable selection and clustering of source-specific regression coefficients.
  • To address sub-homogeneity in regression coefficients across diverse data sources.
  • To develop an efficient algorithm for parameter estimation in integrative data analysis.

Main Methods:

  • Proposed adaptive clustering penalty (ACP) for high-dimensional linear models.
  • Utilized alternating direction method of multipliers (ADMM) for efficient parameter estimation.
  • Evaluated performance against fused LASSO and multi-directional shrinkage penalty methods via simulations.

Main Results:

  • The ACP method demonstrated a strong oracle property under regularity conditions.
  • Simulation studies confirmed the effectiveness of the ACP method.
  • The method successfully identified sub-homogeneity in treatment effects in a real-world clinical trial.

Conclusions:

  • The proposed ACP method offers a robust approach for integrative data analysis with high-dimensional data.
  • ACP effectively handles data heterogeneity by clustering source-specific coefficients.
  • The method has practical applications in identifying variations in treatment effects across different study sites.