A Latent Gaussian Copula Model for Mixed Data Analysis in Brain Imaging Genetics.

Recent advances in imaging genetics make it possible to combine different types of data including medical images like functional magnetic resonance imaging (fMRI) and genetic data like single nucleotide polymorphisms (SNPs) for comprehensive diagnosis of mental disorders. Understanding complex interactions among these heterogeneous data may give rise to a new perspective, while call for statistical models for their integration. Various graphical models have been proposed for the study of association networks with continuous, binary, and count data as well as the mixture of them. However, limited efforts have been made for the multinomial case, like SNP data. Our goal is therefore to fill the void by developing a graphical model for the integration of fMRI image and SNP data, which can provide deeper understanding of the neurogenetic mechanism. We propose a latent Gaussian copula model for mixed data containing multinomial components. The simulation results demonstrate that the proposed latent correlation has more steady and accurate performance in detecting graph structure. When applying to a real schizophrenia data consisting of SNP array and fMRI image, the proposed method reveals a set of distinct SNP-brain associations, which are biologically significant. To promote reproducible research, the R code is available at https://github.com/Aiying0512/LGCM.