Effects-Nested Multi-Level Supervised Heterogeneity Analysis

Under supervised heterogeneity analysis, samples within a population form groups, and different groups have different regression models.In most of the existing analyses, a single level of heterogeneity structure is considered.Partly motivated by multi-level unsupervised analysis such as hierarchical clustering, we consider multi-level supervised heterogeneity analysis.Consider for example a two-level analysis.At the higher level, "coarse" information is used, and samples form a smaller number of groups.At the lower level, "more subtle" information is used, and samples form a larger number of subgroups.To achieve more lucid interpretations, we further consider the scenario where only some variables are relevant at each level, different groups (subgroups) have the same set of relevant variables, and the important variables at the higher level are nested in those at the lower level.A penalized estimation and selection approach is developed, and its theoretical and computational properties are established.Simulation demonstrates competitive performance of the proposed approach.In the analysis of TCGA breast cancer data, the proposed approach leads to sensible Statistica Sinica: Newly accepted Paper grouping/subgrouping, identification, and estimation results.Overall, this study expands the scope of heterogeneity analysis and delivers a practically useful tool.