Sparse reduced-rank regression for integrating omics data

Abstract

Background: The problem of assessing associations between multiple omics data including genomics and metabolomics data to identify biomarkers potentially predictive of complex diseases has garnered considerable research interest nowadays. A popular epidemiology approach is to consider an association of each of the predictors with each of the response using a univariate linear regression model, and to select predictors that meet a priori specified significance level. Although this approach is simple and intuitive, it tends to require larger sample size which is costly. It also assumes variables for each data type are independent, and thus ignores correlations that exist between variables both within each data type and across the data types.

Results: We consider a multivariate linear regression model that relates multiple predictors with multiple responses, and to identify multiple relevant predictors that are simultaneously associated with the responses. We assume the coefficient matrix of the responses on the predictors is both row-sparse and of low-rank, and propose a group Dantzig type formulation to estimate the coefficient matrix.

Conclusion: Extensive simulations demonstrate the competitive performance of our proposed method when compared to existing methods in terms of estimation, prediction, and variable selection. We use the proposed method to integrate genomics and metabolomics data to identify genetic variants that are potentially predictive of atherosclerosis cardiovascular disease (ASCVD) beyond well-established risk factors. Our analysis shows some genetic variants that increase prediction of ASCVD beyond some well-established factors of ASCVD, and also suggest a potential utility of the identified genetic variants in explaining possible association between certain metabolites and ASCVD.

Keywords: High dimensional data; Integrative analysis; Multi-view data; Reduced rank regression.

Fig. 1

Simulation results for Gaussian errors under case 1. Reported results are 50 independent replications. Δ assesses estimation performance. MSPE is mean squared prediction error; TPR is true positive rate; FPR is false positive rate. Black for ρ=0.1,b=0.2; Red for ρ=0.1,b=0.4; Green for ρ=0.5,b=0.2; Blue for ρ=0.5,b=0.4; Cyan for ρ=0.9,b=0.2; Purple for ρ=0.9,b=0.4

Fig. 2

Simulation results for Gaussian errors under case 3. Reported results are 50 independent replications. Δ assesses estimation performance. MSPE is mean squared prediction error; TPR is true positive rate; FPR is false positive rate. Black for ρ=0.1,b=0.5; Red for ρ=0.1,b=1; Green for ρ=0.5,b=0.5; Blue for ρ=0.5,b=1; Cyan for ρ=0.9,b=0.5; Purple for ρ=0.9,b=1

Fig. 3

Simulation results for Gaussian errors under case 4. Reported results are 50 independent replications. Δ assesses estimation performance. MSPE is mean squared prediction error; TPR is true positive rate; FPR is false positive rate. Black for ρ=0.1,b=0.5; Red for ρ=0.1,b=1; Green for ρ=0.5,b=0.5; Blue for ρ=0.5,b=1; Cyan for ρ=0.9,b=0.5; Purple for ρ=0.9,b=1