Integrative analysis of multi-omics and imaging data with incorporation of biological information via structural Bayesian factor analysis

Abstract

Motivation: With the rapid development of modern technologies, massive data are available for the systematic study of Alzheimer's disease (AD). Though many existing AD studies mainly focus on single-modality omics data, multi-omics datasets can provide a more comprehensive understanding of AD. To bridge this gap, we proposed a novel structural Bayesian factor analysis framework (SBFA) to extract the information shared by multi-omics data through the aggregation of genotyping data, gene expression data, neuroimaging phenotypes and prior biological network knowledge. Our approach can extract common information shared by different modalities and encourage biologically related features to be selected, guiding future AD research in a biologically meaningful way.

Method: Our SBFA model decomposes the mean parameters of the data into a sparse factor loading matrix and a factor matrix, where the factor matrix represents the common information extracted from multi-omics and imaging data. Our framework is designed to incorporate prior biological network information. Our simulation study demonstrated that our proposed SBFA framework could achieve the best performance compared with the other state-of-the-art factor-analysis-based integrative analysis methods.

Results: We apply our proposed SBFA model together with several state-of-the-art factor analysis models to extract the latent common information from genotyping, gene expression and brain imaging data simultaneously from the ADNI biobank database. The latent information is then used to predict the functional activities questionnaire score, an important measurement for diagnosis of AD quantifying subjects' abilities in daily life. Our SBFA model shows the best prediction performance compared with the other factor analysis models.

Availability: Code are publicly available at https://github.com/JingxuanBao/SBFA.

Contact: qlong@upenn.edu.

Keywords: Alzheimer’s disease; biological network; multi-omics; structural Bayesian factor analysis.

Figure 1

Structural Bayesian factor analysis framework.   represents the number of multi-modal data sets with each dataset denoted as , . The concatenation of all data sets is denoted by . We assume both continuous and discrete underlying distribution for each dataset dominated by mean parameter , where is number of samples. represents the th column of factor matrix where . and represent the th row and th column of loading matrix and shrinkage parameter for Laplacian prior where and is the total number of features. represents the log-normal distribution. and denote the mean and precision matrix for log-normal prior, respectively.

Figure 2

Workflow for real data analysis. and are genotyping data encoded by the presence of homozygous major allele and the presence of homozygous alternative allele, respectively. and are normalized QTs representing the gene expression and neuroimaging data. Starting from the multi-modal data, different factor analysis methods are used to extract the latent factors. The number of latent dimensions is tuned either through the implemented function from the package or using BIC. After obtaining the latent factor, we use the latent factor as the input predictor to predict the FAQ score. Linear regression with lasso, ridge and elastic net regularizations are used. The raw data (transpose of multi-omics data), covariates and raw data plus covariates are also used for comparison purpose.

Figure 3

Groundtruth setting for factor loading matrix . Numbers labeled on each column represent the latent variable. Numbers labeled on rows represent the number of rows from the first row to the corresponding row. All shaded area represents elements generated by with probability to be multiplied by . All the other area contains only zero elements.

Figure e1

Estimated factor loadings for the simulated dataset. The heatmap shows the factor loadings from iCluster, JIVE, SLIDE and GBFA without graph information (GBFA(NE)), GBFA with graph information (GBFA(E)), SBFA without graph information (SBFA(NE)), SBFA with graph information (SBFA(E)) and the ground truth. The results are derived from one simulated dataset in the low-dimensional scenario (). The optimal latent dimension () for each model is indicated by the number of circles in the corresponding method track. Numbers beyond the range of () have the same color as the boundaries ( and 1).