Correspondence between fMRI and SNP data by group sparse canonical correlation analysis

Highlights

• A group sparse canonical correlation analysis (CCA) model was developed, including several sparse models as special cases.

• The model can overcome the difficulty of conventional CCA in analysing high dimensional data with group structures.

• The model is validated by studying a biologically significant problem on how genetic variations influence brain activities.

Abstract

Both genetic variants and brain region abnormalities are recognized as important factors for complex diseases (e.g., schizophrenia). In this paper, we investigated the correspondence between single nucleotide polymorphism (SNP) and brain activity measured by functional magnetic resonance imaging (fMRI) to understand how genetic variation influences the brain activity. A group sparse canonical correlation analysis method (group sparse CCA) was developed to explore the correlation between these two datasets which are high dimensional-the number of SNPs/voxels is far greater than the number of samples. Different from the existing sparse CCA methods (sCCA), our approach can exploit structural information in the correlation analysis by introducing group constraints. A simulation study demonstrates that it outperforms the existing sCCA. We applied this method to the real data analysis and identified two pairs of significant canonical variates with average correlations of 0.4527 and 0.4292 respectively, which were used to identify genes and voxels associated with schizophrenia. The selected genes are mostly from 5 schizophrenia (SZ)-related signalling pathways. The brain mappings of the selected voxles also indicate the abnormal brain regions susceptible to schizophrenia. A gene and brain region of interest (ROI) correlation analysis was further performed to confirm the significant correlations between genes and ROIs.

Introduction

Schizophrenia is a complex disease and considered to be caused by the interplay of a number of genetic factors (e.g., change of gene regulation, and alteration of mRNA and SNP) and environmental effects. Genetic factors play an important role in causing schizophrenia disease. People born from a family with a history of schizophrenia have higher risks of schizophrenia than those without a family schizophrenia history. In recent years, many studies have focused on exploring critical genes associated with the schizophrenia. Many potential genetic variants have been reported as possible risk factors such as the G72/G30 gene locus on chromosome 13q (Badner and Gershon, 2002; Abecasis et al., 2004) Gene DISC1 variation (Callicott et al., 2005, Porteous et al., 2006) and copy number variations on gene GRIK3, EFNA5, AKAP5 and CACNG2 (Wilson et al., 2006, Sutrala et al., 2007). In addition to genetic studies, fMRI has also been widely used for the study of schizophrenia because of its capability to identify functional abnormalities within brain regions of schizophrenic patients (Jansma et al., 2004, Li et al., 2007, Meda et al., 2008, Szycik et al., 2009).

Genetic variants and brain region abnormalities are both important markers for the study of schizophrenia. Combining both data can not only contribute to a better understanding of biological mechanisms on brain structure and function but also have the potential to improve the diagnosis and treatments of complex diseases. However, current imaging genetics studies either take brain imaging measurements as endophenotypes to study the associated genetic variants or investigate the effects of a small set of candidate genetic variants on the whole brain measurements (Hamid et al., 2009, Le Cao et al., 2009, Wiley, 2011). It is still challenging to explore the relationship between a large amount of genetic variants and a large number of brain imaging measurements. Therefore, correlative analysis approaches for large-scale multimodal data analysis are highly demanded.

In this work, we aim to study the effects of multiple SNPs or genes on functional brain activity in schizophrenia. An effective multivariate statistical method is needed. Canonical Correlation Analysis (CCA (Hotelling, 1936)) or Partial Least Squares regression (PLSR (Le Cao et al., 2008)) have been proposed to analyze multimodal datasets. The CCA aims to maximize the correlation between the linear combinations of variables from two data sets, e.g., a linear combination of SNPs and a linear combination of voxels. However, the method will have the over-fitting issues in analyzing high dimensional data such as SNP and brain imaging data as shown in Fig. 1. Thousands of SNPs with linkage disequilibrium (LD) are detected to reflect the genetic variant at different locus. The number of voxels included in the whole brain fMRI image is also very large (e.g., 53 × 63 × 46). Traditional CCA will perform poorly in such a case due to the multi-collinearity (linear dependence) problem, and thus having computational difficulty (Parkhomenko et al., 2009). To address above issue, sparse CCA (sCCA) methods, mostly using the l − 1 norm (CCA-l1) or the combination of l − 1 and l − 2 norm (CCA-elastic net) penalties, have been developed by introducing the sparse penalties into the traditional CCA model (Waaijenborg et al., 2008, Le Cao et al., 2009, Parkhomenko et al., 2009, Witten et al., 2009, Witten and Tibshirani, 2009, Boutte and Liu, 2010). Despite the success, they didn’t account for group structures within the data in the analysis (e.g., multiple SNPs within the same gene, a group of voxels within the same region, a group of voxels within the same ROI, etc.), which often exist or are implied by the biological mechanism. For example, SNPs within the same gene have similar functions and act together at the gene or pathway level to affect the brain activity. These SNP effects can be added up to a larger difference (Tyekucheva et al., 2011). Several previous works have shown the benefit of accounting for the group effect of features in the sCCA models (Chen and Liu, 2012, Chen et al., 2013, Lin et al., 2013). However, to our knowledge, little work has been reported to incorporate the group effect into the sCCA model for fMRI and SNP data integration. Motivated by this fact, in this paper, we developed a group sparse CCA model based integration method by imposing the sparse group lasso penalty on the CCA model for the integrative analysis of SNP and fMRI data; please refer to Fig. 1 for illustration. This method has the following advantages: (1) A group of features (voxels/SNPs) will be inspected during the correlation analysis, which can study the joint effects of multiple SNPs on the regions of voxels; (2) feature selection will be performed at both group and single feature level. Irrelevant groups of features as well as single feature within each group can be removed. Our group sparse CCA method can both exploit group information in the correlation analysis while filter out noisy features within the group simultaneously.

The group sparse CCA can estimate the correlation between canonical variates, corresponding to a set of significant SNPs or brain imaging voxels. Based on the estimates, we provided a gene-ROI correlation analysis to further confirm the significance of the correlations between genes and brain functions in ROIs.

The rest of the paper is organized as follows. The proposed group sparse CCA model and algorithm are introduced in the section of theory. The group sparse CCA based integration method for SNP and fMRI data is described in the section of method. The validation and comparison of our model with other sCCA models on both simulated and real data analysis are presented in the section of results. The pathway analysis results and limitations of the proposed method are discussed finally.