Integrative subgroup analysis for high-dimensional mixed-type multi-response data

Identifying subgroup structures presents an intriguing challenge in data analysis. Various methods have been proposed to divide the population into subgroups based on individual heterogeneity. However, these methods often fail to accommodate mixed multi-responses and high-dimensional covariates. This article considers the problem of high-dimensional mixed multi-response data with heterogeneity and sparsity. We introduce an integrative subgroup analysis approach with general linear models, accounting for heterogeneity through unobserved latent factors across different responses and sparsity due to high-dimensional covariates. Our approach automatically divides observations into subgroups while identifying significant covariates using non-convex penalty functions. We develop an algorithm that combines the alternating direction method of multipliers with the coordinate descent algorithm for implementation. Additionally, we establish the oracle property of the estimator, illustrating consistent identification of latent subgroups and significant covariates. The efficacy of our method is further validated through numerical simulations and a case study on a randomized clinical trial for buprenorphine maintenance treatment in opiate dependence.