Integrative sparse reduced-rank regression via orthogonal rotation for analysis of high-dimensional multi-source data.

Recent advancements in technology have allowed for the collection of large amounts of data from multiple sources for individuals, leading to an increase in interest in developing statistical methods for analyzing the multi-source data. One of the main interests is to identify the structural association of multiple sources on multiple correlated responses, including individual, joint, and partially-joint structures. In this work, we propose a novel integrative sparse reduced-rank regression (iSRRR) model for identifying the structural associations between multi-source data and multiple responses. The model is based on the assumption of a structured decomposition of the coefficient matrix, and utilizes a new constraint based on orthogonal rotation to ensure model identifiability. The constraint imposes a specific structure, quartimax-simple, on the loading matrix, which enhances interpretability when identifying the multi-source structures relevant to specific responses. An iterative algorithm for estimating the iSRRR model parameters is also proposed. Simulation studies have demonstrated the ability of the proposed method to identify the underlying structured associations between multi-source data and multiple responses. The method has been applied to multi-omics dataset with multiple drug responses, and has been shown to be capable of detecting structured association patterns.