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 paper, 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.