Subgroup Structure Detection and Prediction via Minimal Spanning Tree

Heterogeneity modeling is crucial for developing tailored interventions and policies in medicine, economics, and social sciences. Traditional subgroup analysis methods often impose restrictive distributional or structural assumptions, require high computational costs, or lack direct predictive utility. In this paper, we propose a novel subgroup analysis framework for regression settings that substantially relaxes conventional distributional and pre-specified subgroup assumptions. The proposed method detects subgroup structure of heterogeneous regression coefficients efficiently using a minimum spanning tree (MST)-based regularization approach, estimates the regression coefficients via a post-group estimator based on the estimated subgroup structure, and predicts the subgroup memberships of new subjects via support vector machine (SVM) classifiers. We establish strong consistency of the subgroup membership detection, asymptotic normality of the post-group estimator for regression coefficients, and theoretical properties of the SVM classifier for prediction. We demonstrate the merit of the proposed method through simulation studies and analyses of the National Health and Nutrition Examination Survey.