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Biomedical research now commonly integrates diverse data types or views from the same individuals to better understand the pathobiology of complex diseases, but the challenge lies in meaningfully integrating these diverse views. Existing methods often require the same type of data from all views (cross-sectional data only or longitudinal data only) or do not consider any class outcome in the integration method, presenting limitations. To overcome these limitations, we have developed a pipeline that harnesses the power of statistical and deep learning methods to integrate cross-sectional and longitudinal data from multiple sources. Additionally, it identifies key variables contributing to the association between views and the separation among classes, providing deeper biological insights. This pipeline includes variable selection/ranking using linear and nonlinear methods, feature extraction using functional principal component analysis and Euler characteristics, and joint integration and classification using dense feed-forward networks and recurrent neural networks. We applied this pipeline to cross-sectional and longitudinal multi-omics data (metagenomics, transcriptomics, and metabolomics) from an inflammatory bowel disease (IBD) study and we identified microbial pathways, metabolites, and genes that discriminate by IBD status, providing information on the etiology of IBD. We conducted simulations to compare the two feature extraction methods. The proposed pipeline is available from the following GitHub repository: https://github.com/lasandrall/DeepIDA-GRU.

We develop scalable randomized kernel methods for jointly associating data from multiple sources and simultaneously predicting an outcome or classifying a unit into one of two or more classes. The proposed methods model nonlinear relationships in multiview data together with predicting a clinical outcome and are capable of identifying variables or groups of variables that best contribute to the relationships among the views. We use the idea that random Fourier bases can approximate shift-invariant kernel functions to construct nonlinear mappings of each view and we use these mappings and the outcome variable to learn view-independent low-dimensional representations. Through simulation studies, we show that the proposed methods outperform several other linear and nonlinear methods for multiview data integration. When the proposed methods were applied to gene expression, metabolomics, proteomics, and lipidomics data pertaining to COVID-19, we identified several molecular signatures forCOVID-19 status and severity. Results from our real data application and simulations with small sample sizes suggest that the proposed methods may be useful for small sample size problems. Availability: Our algorithms are implemented in Pytorch and interfaced in R and would be made available at: https://github.com/lasandrall/RandMVLearn., Comment: 24 pages, 5 figures, 4 tables

COVID-19 severity is due to complications from SARS-Cov-2 but the clinical course of the infection varies for individuals, emphasizing the need to better understand the disease at the molecular level. We use clinical and multiple molecular data (or views) obtained from patients with and without COVID-19 who were (or not) admitted to the intensive care unit to shed light on COVID-19 severity. Methods for jointly associating the views and separating the COVID-19 groups (i.e., one-step methods) have focused on linear relationships. The relationships between the views and COVID-19 patient groups, however, are too complex to be understood solely by linear methods. Existing nonlinear one-step methods cannot be used to identify signatures to aid in our understanding of the complexity of the disease. We propose Deep IDA (Integrative Discriminant Analysis) to address analytical challenges in our problem of interest. Deep IDA learns nonlinear projections of two or more views that maximally associate the views and separate the classes in each view, and permits feature ranking for interpretable findings. Our applications demonstrate that Deep IDA has competitive classification rates compared to other state-of-the-art methods and is able to identify molecular signatures that facilitate an understanding of COVID-19 severity.

Analyzing multi-source data, which are multiple views of data on the same subjects, has become increasingly common in molecular biomedical research. Recent methods have sought to uncover underlying structure and relationships within and/or between the data sources, and other methods have sought to build a predictive model for an outcome using all sources. However, existing methods that do both are presently limited because they either (1) only consider data structure shared by all datasets while ignoring structures unique to each source, or (2) they extract underlying structures first without consideration to the outcome. We propose a method called supervised joint and individual variation explained (sJIVE) that can simultaneously (1) identify shared (joint) and source-specific (individual) underlying structure and (2) build a linear prediction model for an outcome using these structures. These two components are weighted to compromise between explaining variation in the multi-source data and in the outcome. Simulations show sJIVE to outperform existing methods when large amounts of noise are present in the multi-source data. An application to data from the COPDGene study reveals gene expression and proteomic patterns that are predictive of lung function. Functions to perform sJIVE are included in the R.JIVE package, available online at http://github.com/lockEF/r.jive ., Comment: 23 pages, 8 tables, 3 figures

Cardiovascular diseases (CVD), including atherosclerosis CVD (ASCVD), are multifactorial diseases that present a major economic and social burden worldwide. Tremendous efforts have been made to understand traditional risk factors for ASCVD, but these risk factors account for only about half of all cases of ASCVD. It remains a critical need to identify nontraditional risk factors (e.g., genetic variants, genes) contributing to ASCVD. Further, incorporating functional knowledge in prediction models have the potential to reveal pathways associated with disease risk. We propose Bayesian hierarchical factor analysis models that associate multiple omics data, predict a clinical outcome, allow for prior functional information, and can accommodate clinical covariates. The models, motivated by available data and the need for other risk factors of ASCVD, are used for the integrative analysis of clinical, demographic, and multi-omics data to identify genetic variants, genes, and gene pathways potentially contributing to 10-year ASCVD risk in healthy adults. Our findings revealed several genetic variants, genes and gene pathways that were highly associated with ASCVD risk. Interestingly, some of these have been implicated in CVD risk. The others could be explored for their potential roles in CVD. Our findings underscore the merit in joint association and prediction models., Comment: 48 pages, 10 Figures

Classification methods that leverage the strengths of data from multiple sources (multi-view data) simultaneously have enormous potential to yield more powerful findings than two step methods: association followed by classification. We propose two methods, sparse integrative discriminant analysis (SIDA) and SIDA with incorporation of network information (SIDANet), for joint association and classification studies. The methods consider the overall association between multi-veiw data, and the separation within each view in choosing discriminant vectors that are associated and optimally separate subjects into different classes. SIDANet is among the first methods to incorporate prior structural information in joint association and classification studies. It uses the normalized Laplacian of a graph to smooth coefficients of predictor variables, thus encouraging selection of predictors that are connected and behave similarly. We demonstrate the effectiveness of our methods on a set of synthetic and real datasets. Our findings underscore the benefit of joint association and classification methods if the goal is to correlate multi-view data and to perform classification., Comment: 40 pages, 4 figures

Missing data present challenges in data analysis. Naive analyses such as complete-case and available-case analysis may introduce bias and loss of efficiency, and produce unreliable results. Multiple imputation (MI) is one of the most widely used methods for handling missing data which can be partly attributed to its ease of use. However, existing MI methods implemented in most statistical software are not applicable to or do not perform well in high-dimensional settings where the number of predictors is large relative to the sample size. To remedy this issue, we develop an MI approach that uses dimension reduction techniques. Specifically, in constructing imputation models in the presence of high-dimensional data our approach uses sure independent screening followed by either sparse principal component analysis (sPCA) or sufficient dimension reduction (SDR) techniques. Our simulation studies, conducted for high-dimensional data, demonstrate that using SIS followed by sPCA to perform MI achieves better performance than the other imputation methods including several existing imputation approaches. We apply our approach to analysis of gene expression data from a prostate cancer study.

We present a method for individual and integrative analysis of high dimension, low sample size data that capitalizes on the recurring theme in multivariate analysis of projecting higher dimensional data onto a few meaningful directions that are solutions to a generalized eigenvalue problem. We propose a general framework, called SELP (Sparse Estimation with Linear Programming), with which one can obtain a sparse estimate for a solution vector of a generalized eigenvalue problem. We demonstrate the utility of SELP on canonical correlation analysis for an integrative analysis of methylation and gene expression profiles from a breast cancer study, and we identify some genes known to be associated with breast carcinogenesis, which indicates that the proposed method is capable of generating biologically meaningful insights. Simulation studies suggest that the proposed method performs competitive in comparison with some existing methods in identifying true signals in various underlying covariance structures.

Integrative analyses of different high dimensional data types are becoming increasingly popular. Similarly, incorporating prior functional relationships among variables in data analysis has been a topic of increasing interest as it helps elucidate underlying mechanisms among complex diseases. In this paper, the goal is to assess association between transcriptomic and metabolomic data from a Predictive Health Institute (PHI) study including healthy adults at high risk of developing cardiovascular diseases. To this end, we develop statistical methods for identifying sparse structure in canonical correlation analysis (CCA) with incorporation of biological/structural information. Our proposed methods use prior network structural information among genes and among metabolites to guide selection of relevant genes and metabolites in sparse CCA, providing insight on the molecular underpinning of cardiovascular disease. Our simulations demonstrate that the structured sparse CCA methods outperform several existing sparse CCA methods in selecting relevant genes and metabolites when structural information is informative and are robust to mis-specified structural information. Our analysis of the PHI study reveals that a number of genes and metabolic pathways including some known to be associated with cardiovascular diseases are enriched in the subset of genes and metabolites selected by our proposed approach.

The objective of many high-dimensional microarray and RNA-seq studies is to develop a classifier of cancer patients based on characteristics of their disease. The germinal center B-cell (GCB) classifier study in lymphoma and the National Cancer Institute's Director's Challenge lung (DC-lung) study are two examples. In recent years, such classifiers are often developed using regularized regression, such as the lasso. A critical question is whether a better classifier can be developed from a larger training set size and, if so, how large the training set should be. This paper examines these two questions using an existing sample size method and a novel sample size method developed here specifically for lasso logistic regression. Both methods are based on pilot data. We reexamine the lymphoma and lung cancer data sets to evaluate the sample sizes, and use resampling to assess the estimation methods. We also study application to an RNA-seq data set. We find that it is feasible to estimate sample size for regularized logistic regression if an adequate pilot data set exists. The GCB and the DC-lung data sets appear adequate, under specific assumptions. Existing human RNA-seq data sets are by and large inadequate, and cannot be used as pilot data. Pilot RNA-seq data can be simulated, and the methods in this paper can be used for sample size estimation. A MATLAB program is made available., Comment: Published at http://dx.doi.org/10.1214/15-AOAS825 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)