Efficient Subgroup Analysis via Optimal Trees with Global Parameter Fusion

TL;DR

This paper introduces a fused optimal causal tree method using mixed integer optimization to improve subgroup analysis accuracy and efficiency in clinical research, addressing limitations of traditional tree-based methods.

Contribution

It proposes a globally optimal tree-based approach with parameter fusion for better subgroup identification and statistical efficiency, backed by theoretical guarantees and empirical validation.

Findings

Outperforms baseline methods in simulations

Provides tighter risk bounds than classical trees

Yields meaningful clinical insights in case study

Abstract

Identifying and making statistical inferences on differential treatment effects (commonly known as subgroup analysis in clinical research) is central to precision health. Subgroup analysis allows practitioners to pinpoint populations for whom a treatment is especially beneficial or protective, thereby advancing targeted interventions. Tree based recursive partitioning methods are widely used for subgroup analysis due to their interpretability. Nevertheless, these approaches encounter significant limitations, including suboptimal partitions induced by greedy heuristics and overfitting from locally estimated splits, especially under limited sample sizes. To address these limitations, we propose a fused optimal causal tree method that leverages mixed integer optimization (MIO) to facilitate precise subgroup identification. Our approach ensures globally optimal partitions and introduces a parameter fusion constraint to facilitate information sharing across related subgroups. This design substantially improves subgroup discovery accuracy and enhances statistical efficiency. We provide theoretical guarantees by rigorously establishing out of sample risk bounds and comparing them with those of classical tree based methods. Empirically, our method consistently outperforms popular baselines in simulations. Finally, we demonstrate its practical utility through a case study on the Health and Aging Brain Study Health Disparities (HABS-HD) dataset, where our approach yields clinically meaningful insights.