Identifying Heterogeneous Effect Using Latent Supervised Clustering With Adaptive Fusion

Precision medicine is an important area of research with the goal of identifying the optimal treatment for each individual patient. In the literature, various methods are proposed to divide the population into subgroups according to the heterogeneous effects of individuals. In this article, a new exploratory machine learning tool, named latent supervised clustering, is proposed to identify the heterogeneous subpopulations. In particular, we formulate the problem as a regression problem with subject specific coefficients, and use adaptive fusion to cluster the coefficients into subpopulations. This method has two main advantages. First, it relies on little prior knowledge and weak parametric assumptions on the underlying subpopulation structure. Second, it makes use of the outcome-predictor relationship, and hence can have competitive estimation and prediction accuracy. To estimate the parameters, we design a highly efficient accelerated proximal gradient algorithm which guarantees convergence at a competitive rate. Numerical studies show that the proposed method has competitive estimation and prediction accuracy, and can also produce interpretable clustering results for the underlying heterogeneous effect. Supplementary materials for this article are available online.

精准医学（precision medicine）是重要的研究领域，其核心目标为针对每位患者确定最优治疗方案。现有研究已提出多种方法，可依据个体间的异质性效应将人群划分为不同亚组。本文提出一种全新的探索性机器学习工具——潜监督聚类（latent supervised clustering），用于识别异质性亚人群。具体而言，我们将该问题建模为带有个体特异性系数的回归问题，并通过自适应融合将系数聚类至不同亚群。该方法具备两大核心优势：其一，对底层亚群结构所需的先验知识极少，且参数假设极为宽松；其二，充分利用了结局-预测变量间的关联关系，因此可获得具有竞争力的估计与预测精度。为估计模型参数，我们设计了一种高效的加速近端梯度算法（accelerated proximal gradient algorithm），该算法可保证以具有竞争力的收敛速率完成收敛。数值研究结果表明，所提方法不仅具备优异的估计与预测精度，还可针对底层异质性效应生成可解释的聚类结果。本文配套补充材料可在线获取。