When analyzing data combined from multiple sources (e.g., hospitals, studies), the heterogeneity across different sources must be accounted for. In this paper, we consider high-dimensional linear regression models for integrative data analysis. We propose a new adaptive clustering penalty (ACP) method to simultaneously select variables and cluster source-specific regression coefficients with sub-homogeneity. We show that the estimator based on the ACP method enjoys a strong oracle property under certain regularity conditions. We also develop an efficient algorithm based on the alternating direction method of multipliers (ADMM) for parameter estimation. We conduct simulation studies to compare the performance of the proposed method to three existing methods (a fused LASSO with adjacent fusion, a pairwise fused LASSO, and a multi-directional shrinkage penalty method). Finally, we apply the proposed method to the multi-center Childhood Adenotonsillectomy Trial to identify sub-homogeneity in the treatment effects across different study sites.
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Keywords: ADMM; MSC 2020; Primary 62J07; coefficient clustering; data heterogeneity; k-means; secondary 62J05; variable selection.