RESUMEN
Integrating and analyzing multiple omics data sets, including genomics, proteomics and radiomics, can significantly advance researchers' comprehensive understanding of Alzheimer's disease (AD). However, current methodologies primarily focus on the main effects of genetic variation and protein, overlooking non-additive effects such as genotype-protein interaction (GPI) and correlation patterns in brain imaging genetics studies. Importantly, these non-additive effects could contribute to intermediate imaging phenotypes, finally leading to disease occurrence. In general, the interaction between genetic variations and proteins, and their correlations are two distinct biological effects, and thus disentangling the two effects for heritable imaging phenotypes is of great interest and need. Unfortunately, this issue has been largely unexploited. In this paper, to fill this gap, we propose $\textbf{M}$ulti-$\textbf{T}$ask $\textbf{G}$enotype-$\textbf{P}$rotein $\textbf{I}$nteraction and $\textbf{C}$orrelation disentangling method ($\textbf{MT-GPIC}$) to identify GPI and extract correlation patterns between them. To ensure stability and interpretability, we use novel and off-the-shelf penalties to identify meaningful genetic risk factors, as well as exploit the interconnectedness of different brain regions. Additionally, since computing GPI poses a high computational burden, we develop a fast optimization strategy for solving MT-GPIC, which is guaranteed to converge. Experimental results on the Alzheimer's Disease Neuroimaging Initiative data set show that MT-GPIC achieves higher correlation coefficients and classification accuracy than state-of-the-art methods. Moreover, our approach could effectively identify interpretable phenotype-related GPI and correlation patterns in high-dimensional omics data sets. These findings not only enhance the diagnostic accuracy but also contribute valuable insights into the underlying pathogenic mechanisms of AD.