Regression and subgroup detection for heterogeneous samples

Regression analysis of heterogeneous samples with subgroup structure is essential to the development of precision medicine. In practice, this task is often challenging owing to the lack of prior knowledge of subgroup labels. Therefore, detecting the subgroups with similar characteristics becomes critical, which often controls the accuracy of regression analysis. In this article, we investigate a new framework for detecting the subgroups that have similar characters in feature space and similar treatment effects. The key idea is that we incorporate K-means clustering into the regression framework of concave pairwise fusion, so that the regression and subgroup detection tasks can be performed simultaneously. Our method is specifically tailored for handling the situations where the sample is not homogeneous in the sense that the response variables in different domains of feature space are generated through different mechanisms.