High dimensional latent Gaussian copula model for mixed data in imaging genetics

Recent advances in imaging genetics combine different types of data including medical images like functional MRI images and genetic data like single nucleotide polymorphisms (SNPs). Many studies have proved that several mental diseases such as autism, ADHD, schizophrenia are affected by gene mutations. Understanding the complex interactions among these heterogeneous datasets may give rise to a new perspective for diseases diagnosis and prevention. In statistics, various graphical models have been proposed for the study of association networks with continuous data, binary data, and count data as well as the mixture of them. However, limited efforts have been made for the multinomial case, which has a direct application for SNP data. Therefore, in this paper, we propose a latent Gaussian copula model for mixed data containing multinomial components, which fills a vacancy of graphical models in imaging genetics. The performance of the proposed methods is first numerically assessed through simulation studies. Then it is validated with fMRI and SNP data collected by the Mind Clinical Imaging Consortium (MCIC) for a schizophrenia study.