GEEES: inferring cell-specific gene-enhancer interactions from multi-modal single-cell data

MOTIVATION

Gene-enhancer interactions are central to transcriptional regulation. Current multi-modal single-cell datasets that profile transcriptome and chromatin accessibility simultaneously in a single cell are yielding opportunities to infer gene-enhancer associations in a cell type specific manner. Computational efforts for such multi-modal single-cell datasets thus far focused on methods for identification and refinement of cell types and trajectory construction. While initial attempts for inferring gene-enhancer interactions have emerged, these have not been evaluated against benchmark datasets that materialized from bulk genomic experiments. Furthermore, existing approaches are limited to inferring gene-enhancer associations at the level of grouped cells as opposed to individual cells, thereby ignoring regulatory heterogeneity among the cells.

RESULTS

We present a new approach, GEEES for "Gene EnhancEr IntEractions from Multi-modal Single Cell Data," for inferring gene-enhancer associations at the single-cell level using multi-modal single-cell transcriptome and chromatin accessibility data. We evaluated GEEES alongside several multivariate regression-based alternatives we devised and state-of-the-art methods using a large number of benchmark datasets, providing a comprehensive assessment of current approaches. This analysis revealed significant discrepancies between gold-standard interactions and gene-enhancer associations derived from multi-modal single-cell data. Notably, incorporating gene-enhancer distance into the analysis markedly improved performance across all methods, positioning GEEES as a leading approach in this domain. While the overall improvement in performance metrics by GEEES is modest, it provides enhanced cell representation learning which can be leveraged for more effective downstream analysis. Furthermore, our review of existing experimentally driven benchmark datasets uncovers their limited concordance, underscoring the necessity for new high-throughput experiments to validate gene-enhancer interactions inferred from single-cell data.

AVAILABILITY AND IMPLEMENTATION

https://github.com/keleslab/GEEES.

Beyond the single-outcome approach: A comparison of outcome-wide analysis methods for exposome research

Outcome-wide analysis can offer several benefits, including increased power to detect weak signals and the ability to identify exposures with multiple effects on health, which may be good targets for preventive measures. Recently, advanced statistical multivariate techniques for outcome-wide analysis have been developed, but they have been rarely applied to exposome analysis. In this work, we provide an overview of a selection of methods that are well-suited for outcome-wide exposome analysis and are implemented in the R statistical software. Our work brings together six different methods presenting innovative solutions for typical problems arising from outcome-wide approaches in the context of the exposome, including dependencies among outcomes, high dimensionality, mixed-type outcomes, missing data records, and confounding effects. The identified methods can be grouped into four main categories: regularized multivariate regression techniques, multi-task learning approaches, dimensionality reduction approaches, and bayesian extensions of the multivariate regression framework. Here, we compare each technique presenting its main rationale, strengths, and limitations, and provide codes and guidelines for their application to exposome data. Additionally, we apply all selected methods to a real exposome dataset from the Human Early-Life Exposome (HELIX) project, demonstrating their suitability for exposome research. Although the choice of the best method will always depend on the challenges to be faced in each application, for an exposome-like analysis we find dimensionality reduction and bayesian methods such as reduced rank regression (RRR) or multivariate bayesian shrinkage priors (MBSP) particularly useful, given their ability to deal with critical issues such as collinearity, high-dimensionality, missing data or quantification of uncertainty.

New statistical selection method for pleiotropic variants associated with both quantitative and qualitative traits

BACKGROUND

Identification of pleiotropic variants associated with multiple phenotypic traits has received increasing attention in genetic association studies. Overlapping genetic associations from multiple traits help to detect weak genetic associations missed by single-trait analyses. Many statistical methods were developed to identify pleiotropic variants with most of them being limited to quantitative traits when pleiotropic effects on both quantitative and qualitative traits have been observed. This is a statistically challenging problem because there does not exist an appropriate multivariate distribution to model both quantitative and qualitative data together. Alternatively, meta-analysis methods can be applied, which basically integrate summary statistics of individual variants associated with either a quantitative or a qualitative trait without accounting for correlations among genetic variants.

RESULTS

We propose a new statistical selection method based on a unified selection score quantifying how a genetic variant, i.e., a pleiotropic variant associates with both quantitative and qualitative traits. In our extensive simulation studies where various types of pleiotropic effects on both quantitative and qualitative traits were considered, we demonstrated that the proposed method outperforms the existing meta-analysis methods in terms of true positive selection. We also applied the proposed method to a peanut dataset with 6 quantitative and 2 qualitative traits, and a cowpea dataset with 2 quantitative and 6 qualitative traits. We were able to detect some potentially pleiotropic variants missed by the existing methods in both analyses.

CONCLUSIONS

The proposed method is able to locate pleiotropic variants associated with both quantitative and qualitative traits. It has been implemented into an R package 'UNISS', which can be downloaded from http://github.com/statpng/uniss.

Joint selection of brain network nodes and edges for MCI identification

BACKGROUND AND OBJECTIVE

Functional brain graph (FBG), by describing the interactions between different brain regions, provides an effective representation of fMRI data for identifying mild cognitive impairment (MCI), an early stage of Alzheimer's Disease (AD). Prior to the identification task, selecting features from the estimated FBG is a necessary step for reducing computational cost, alleviating the risk of overfitting, and finding potential biomarkers of brain diseases. In practice, either node-based features (e.g., local clustering coefficients) or edge-based features (e.g., adjacency weights) are generally considered in current studies. Despite their popularity, these schemes can only capture one granularity (node or edge) of information in the FBG, which might be insufficient for the classification task and the interpretation of the classification result.

METHODS

To address this issue, in this paper, we propose to jointly select nodes and edges from the estimated FBGs. Specifically, we first assign the edges to different node groups. Then, sparse group least absolute shrinkage and selection operator (sgLASSO) is used to select groups (nodes) and edges in the groups towards a better classification performance. Such a technique enables us to simultaneously locate discriminative brain regions, as well as connections between these brain regions, making the classification results more interpretable.

RESULTS

Experimental results show that the proposed method achieves better classification performance than state-of-the-art methods. Moreover, by exploring brain network "features" that contributed most to MCI identification, we discover potential biomarkers for MCI diagnosis.

CONCLUSION

A novel method for jointly selecting nodes and edges from the estimated functional brain graphs (FBGs) is proposed.

Low-rank regression models for multiple binary responses and their applications to cancer cell-line encyclopedia data

In this paper, we study high-dimensional multivariate logistic regression models in which a common set of covariates is used to predict multiple binary outcomes simultaneously. Our work is primarily motivated from many biomedical studies with correlated multiple responses such as the cancer cell-line encyclopedia project. We assume that the underlying regression coefficient matrix is simultaneously low-rank and row-wise sparse. We propose an intuitively appealing selection and estimation framework based on marginal model likelihood, and we develop an efficient computational algorithm for inference. We establish a novel high-dimensional theory for this nonlinear multivariate regression. Our theory is general, allowing for potential correlations between the binary responses. We propose a new type of nuclear norm penalty using the smooth clipped absolute deviation, filling the gap in the related non-convex penalization literature. We theoretically demonstrate that the proposed approach improves estimation accuracy by considering multiple responses jointly through the proposed estimator when the underlying coefficient matrix is low-rank and row-wise sparse. In particular, we establish the non-asymptotic error bounds, and both rank and row support consistency of the proposed method. Moreover, we develop a consistent rule to simultaneously select the rank and row dimension of the coefficient matrix. Furthermore, we extend the proposed methods and theory to a joint Ising model, which accounts for the dependence relationships. In our analysis of both simulated data and the cancer cell line encyclopedia data, the proposed methods outperform the existing methods in better predicting responses.

High-dimension to high-dimension screening for detecting genome-wide epigenetic and noncoding RNA regulators of gene expression

MOTIVATION

The advancement of high-throughput technology characterizes a wide variety of epigenetic modifications and noncoding RNAs across the genome involved in disease pathogenesis via regulating gene expression. The high dimensionality of both epigenetic/noncoding RNA and gene expression data make it challenging to identify the important regulators of genes. Conducting univariate test for each possible regulator-gene pair is subject to serious multiple comparison burden, and direct application of regularization methods to select regulator-gene pairs is computationally infeasible. Applying fast screening to reduce dimension first before regularization is more efficient and stable than applying regularization methods alone.

RESULTS

We propose a novel screening method based on robust partial correlation to detect epigenetic and noncoding RNA regulators of gene expression over the whole genome, a problem that includes both high-dimensional predictors and high-dimensional responses. Compared to existing screening methods, our method is conceptually innovative that it reduces the dimension of both predictor and response, and screens at both node (regulators or genes) and edge (regulator-gene pairs) levels. We develop data-driven procedures to determine the conditional sets and the optimal screening threshold, and implement a fast iterative algorithm. Simulations and applications to long noncoding RNA and microRNA regulation in Kidney cancer and DNA methylation regulation in Glioblastoma Multiforme illustrate the validity and advantage of our method.

AVAILABILITY AND IMPLEMENTATION

The R package, related source codes and real datasets used in this article are provided at https://github.com/kehongjie/rPCor.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

LARGE-SCALE MULTIVARIATE SPARSE REGRESSION WITH APPLICATIONS TO UK BIOBANK

In high-dimensional regression problems, often a relatively small subset of the features are relevant for predicting the outcome, and methods that impose sparsity on the solution are popular. When multiple correlated outcomes are available (multitask), reduced rank regression is an effective way to borrow strength and capture latent structures that underlie the data. Our proposal is motivated by the UK Biobank population-based cohort study, where we are faced with large-scale, ultrahigh-dimensional features, and have access to a large number of outcomes (phenotypes)-lifestyle measures, biomarkers, and disease outcomes. We are hence led to fit sparse reduced-rank regression models, using computational strategies that allow us to scale to problems of this size. We use a scheme that alternates between solving the sparse regression problem and solving the reduced rank decomposition. For the sparse regression component we propose a scalable iterative algorithm based on adaptive screening that leverages the sparsity assumption and enables us to focus on solving much smaller subproblems. The full solution is reconstructed and tested via an optimality condition to make sure it is a valid solution for the original problem. We further extend the method to cope with practical issues, such as the inclusion of confounding variables and imputation of missing values among the phenotypes. Experiments on both synthetic data and the UK Biobank data demonstrate the effectiveness of the method and the algorithm. We present multiSnpnet package, available at http://github.com/junyangq/multiSnpnet that works on top of PLINK2 files, which we anticipate to be a valuable tool for generating polygenic risk scores from human genetic studies.

Sparse reduced-rank regression for simultaneous rank and variable selection via manifold optimization

We consider the problem of constructing a reduced-rank regression model whose coefficient parameter is represented as a singular value decomposition with sparse singular vectors. The traditional estimation procedure for the coefficient parameter often fails when the true rank of the parameter is high. To overcome this issue, we develop an estimation algorithm with rank and variable selection via sparse regularization and manifold optimization, which enables us to obtain an accurate estimation of the coefficient parameter even if the true rank of the coefficient parameter is high. Using sparse regularization, we can also select an optimal value of the rank. We conduct Monte Carlo experiments and a real data analysis to illustrate the effectiveness of our proposed method.

Conditional Gaussian graphical model for estimating personalized disease symptom networks

The co-occurrence of symptoms may result from the direct interactions between these symptoms and the symptoms can be treated as a system. In addition, subject-specific risk factors (eg, genetic variants, age) can also exert external influence on the system. In this work, we develop a covariate-dependent conditional Gaussian graphical model to obtain personalized symptom networks. The strengths of network connections are modeled as a function of covariates to capture the heterogeneity among individuals and subgroups of individuals. We assess the performance of our proposed method by simulation studies and an application to a large natural history study of Huntington's disease to investigate the networks of symptoms in multiple clinical domains (motor, cognitive, psychiatric) and identify important brain imaging biomarkers that are associated with the connections. We show that the symptoms in the same clinical domain interact more often with each other than cross domains and the psychiatric subnetwork is the densest network. We validate the findings using the subjects' symptom measurements at follow-up visits.

A COVARIANCE-ENHANCED APPROACH TO MULTI-TISSUE JOINT EQTL MAPPING WITH APPLICATION TO TRANSCRIPTOME-WIDE ASSOCIATION STUDIES

Transcriptome-wide association studies based on genetically predicted gene expression have the potential to identify novel regions associated with various complex traits. It has been shown that incorporating expression quantitative trait loci (eQTLs) corresponding to multiple tissue types can improve power for association studies involving complex etiology. In this article, we propose a new multivariate response linear regression model and method for predicting gene expression in multiple tissues simultaneously. Unlike existing methods for multi-tissue joint eQTL mapping, our approach incorporates tissue-tissue expression correlation, which allows us to more efficiently handle missing expression measurements and more accurately predict gene expression using a weighted summation of eQTL genotypes. We show through simulation studies that our approach performs better than the existing methods in many scenarios. We use our method to estimate eQTL weights for 29 tissues collected by GTEx, and show that our approach significantly improves expression prediction accuracy compared to competitors. Using our eQTL weights, we perform a multi-tissue-based S-MultiXcan [2] transcriptome-wide association study and show that our method leads to more discoveries in novel regions and more discoveries overall than the existing methods. Estimated eQTL weights and code for implementing the method are available for download online at github.com/ajmolstad/MTeQTLResults.

Predicting correlated outcomes from molecular data

MOTIVATION

Multivariate (multi-target) regression has the potential to outperform univariate (single-target) regression at predicting correlated outcomes, which frequently occur in biomedical and clinical research. Here we implement multivariate lasso and ridge regression using stacked generalisation.

RESULTS

Our flexible approach leads to predictive and interpretable models in high-dimensional settings, with a single estimate for each input-output effect. In the simulation, we compare the predictive performance of several state-of-the-art methods for multivariate regression. In the application, we use clinical and genomic data to predict multiple motor and non-motor symptoms in Parkinson's disease patients. We conclude that stacked multivariate regression, with our adaptations, is a competitive method for predicting correlated outcomes.

AVAILABILITY AND IMPLEMENTATION

The R package joinet is available on GitHub (https://github.com/rauschenberger/joinet) and cran (https://cran.r-project.org/package=joinet).

SUPPLEMENTARY INFORMATION

Supplementary tables and figures are available at Bioinformatics online.

Biomarker-guided heterogeneity analysis of genetic regulations via multivariate sparse fusion

Heterogeneity is a hallmark of many complex diseases. There are multiple ways of defining heterogeneity, among which the heterogeneity in genetic regulations, for example, gene expressions (GEs) by copy number variations (CNVs), and methylation, has been suggested but little investigated. Heterogeneity in genetic regulations can be linked with disease severity, progression, and other traits and is biologically important. However, the analysis can be very challenging with the high dimensionality of both sides of regulation as well as sparse and weak signals. In this article, we consider the scenario where subjects form unknown subgroups, and each subgroup has unique genetic regulation relationships. Further, such heterogeneity is "guided" by a known biomarker. We develop a multivariate sparse fusion (MSF) approach, which innovatively applies the penalized fusion technique to simultaneously determine the number and structure of subgroups and regulation relationships within each subgroup. An effective computational algorithm is developed, and extensive simulations are conducted. The analysis of heterogeneity in the GE-CNV regulations in melanoma and GE-methylation regulations in stomach cancer using the TCGA data leads to interesting findings.

A Novel Method for Identifying a Parsimonious and Accurate Predictive Model for Multiple Clinical Outcomes

BACKGROUND AND OBJECTIVE

Most methods for developing clinical prognostic models focus on identifying parsimonious and accurate models to predict a single outcome; however, patients and providers often want to predict multiple outcomes simultaneously. As an example, for older adults one is often interested in predicting nursing home admission as well as mortality. We propose and evaluate a novel predictor-selection computing method for multiple outcomes and provide the code for its implementation.

METHODS

Our proposed algorithm selected the best subset of common predictors based on the minimum average normalized Bayesian Information Criterion (BIC) across outcomes: the Best Average BIC (baBIC) method. We compared the predictive accuracy (Harrell's C-statistic) and parsimony (number of predictors) of the model obtained using the baBIC method with: 1) a subset of common predictors obtained from the union of optimal models for each outcome (Union method), 2) a subset obtained from the intersection of optimal models for each outcome (Intersection method), and 3) a model with no variable selection (Full method). We used a case-study data from the Health and Retirement Study (HRS) to demonstrate our method and conducted a simulation study to investigate performance.

RESULTS

In the case-study data and simulations, the average Harrell's C-statistics across outcomes of the models obtained with the baBIC and Union methods were comparable. Despite the similar discrimination, the baBIC method produced more parsimonious models than the Union method. In contrast, the models selected with the Intersection method were the most parsimonious, but with worst predictive accuracy, and the opposite was true in the Full method. In the simulations, the baBIC method performed well by identifying many of the predictors selected in the baBIC model of the case-study data most of the time and excluding those not selected in the majority of the simulations.

CONCLUSIONS

Our method identified a common subset of variables to predict multiple clinical outcomes with superior balance between parsimony and predictive accuracy to current methods.

Structural factor equation models for causal network construction via directed acyclic mixed graphs

Directed acyclic mixed graphs (DAMGs) provide a useful representation of network topology with both directed and undirected edges subject to the restriction of no directed cycles in the graph. This graphical framework may arise in many biomedical studies, for example, when a directed acyclic graph (DAG) of interest is contaminated with undirected edges induced by some unobserved confounding factors (eg, unmeasured environmental factors). Directed edges in a DAG are widely used to evaluate causal relationships among variables in a network, but detecting them is challenging when the underlying causality is obscured by some shared latent factors. The objective of this paper is to develop an effective structural equation model (SEM) method to extract reliable causal relationships from a DAMG. The proposed approach, termed structural factor equation model (SFEM), uses the SEM to capture the network topology of the DAG while accounting for the undirected edges in the graph with a factor analysis model. The latent factors in the SFEM enable the identification and removal of undirected edges, leading to a simpler and more interpretable causal network. The proposed method is evaluated and compared to existing methods through extensive simulation studies, and illustrated through the construction of gene regulatory networks related to breast cancer.

TPQCI: A topology potential-based method to quantify functional influence of copy number variations

Copy number variation (CNV) is a major type of chromosomal structural variation that play important roles in many diseases including cancers. Due to genome instability, a large number of CNV events can be detected in diseases such as cancer. Therefore, it is important to identify the functionally important CNVs in diseases, which currently still poses a challenge in genomics. One of the critical steps to solve the problem is to define the influence of CNV. In this paper, we provide a topology potential based method, TPQCI, to quantify this kind of influence by integrating statistics, gene regulatory associations, and biological function information. We used this metric to detect functionally enriched genes on genomic segments with CNV in breast cancer and multiple myeloma and discovered biological functions influenced by CNV. Our results demonstrate that, by using our proposed TPQCI metric, we can detect disease-specific genes that are influenced by CNVs. Source codes of TPQCI are provided in Github (https://github.com/usos/TPQCI).

L2,1-norm regularized multivariate regression model with applications to genomic prediction

MOTIVATION

Genomic selection (GS) is currently deemed the most effective approach to speed up breeding of agricultural varieties. It has been recognized that consideration of multiple traits in GS can improve accuracy of prediction for traits of low heritability. However, since GS forgoes statistical testing with the idea of improving predictions, it does not facilitate mechanistic understanding of the contribution of particular single nucleotide polymorphisms (SNP).

RESULTS

Here, we propose a L2,1-norm regularized multivariate regression model and devise a fast and efficient iterative optimization algorithm, called L2,1-joint, applicable in multi-trait GS. The usage of the L2,1-norm facilitates variable selection in a penalized multivariate regression that considers the relation between individuals, when the number of SNPs is much larger than the number of individuals. The capacity for variable selection allows us to define master regulators that can be used in a multi-trait GS setting to dissect the genetic architecture of the analyzed traits. Our comparative analyses demonstrate that the proposed model is a favorable candidate compared to existing state-of-the-art approaches. Prediction and variable selection with datasets from Brassica napus, wheat and Arabidopsis thaliana diversity panels are conducted to further showcase the performance of the proposed model.

AVAILABILITY AND IMPLEMENTATION

: The model is implemented using R programming language and the code is freely available from https://github.com/alainmbebi/L21-norm-GS.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Integration of Proteomics and Other Omics Data

In recent biomedical studies, multidimensional profiling, which collects proteomics as well as other types of omics data on the same subjects, is getting increasingly popular. Proteomics, transcriptomics, genomics, epigenomics, and other types of data contain overlapping as well as independent information, which suggests the possibility of integrating multiple types of data to generate more reliable findings/models with better classification/prediction performance. In this chapter, a selective review is conducted on recent data integration techniques for both unsupervised and supervised analysis. The main objective is to provide the "big picture" of data integration that involves proteomics data and discuss the "intuition" beneath the recently developed approaches without invoking too many mathematical details. Potential pitfalls and possible directions for future developments are also discussed.

An efficient framework to identify key miRNA-mRNA regulatory modules in cancer

MOTIVATION

Micro-RNAs (miRNAs) are known as the important components of RNA silencing and post-transcriptional gene regulation, and they interact with messenger RNAs (mRNAs) either by degradation or by translational repression. miRNA alterations have a significant impact on the formation and progression of human cancers. Accordingly, it is important to establish computational methods with high predictive performance to identify cancer-specific miRNA-mRNA regulatory modules.

RESULTS

We presented a two-step framework to model miRNA-mRNA relationships and identify cancer-specific modules between miRNAs and mRNAs from their matched expression profiles of more than 9000 primary tumors. We first estimated the regulatory matrix between miRNA and mRNA expression profiles by solving multiple linear programming problems. We then formulated a unified regularized factor regression (RFR) model that simultaneously estimates the effective number of modules (i.e. latent factors) and extracts modules by decomposing regulatory matrix into two low-rank matrices. Our RFR model groups correlated miRNAs together and correlated mRNAs together, and also controls sparsity levels of both matrices. These attributes lead to interpretable results with high predictive performance. We applied our method on a very comprehensive data collection by including 32 TCGA cancer types. To find the biological relevance of our approach, we performed functional gene set enrichment and survival analyses. A large portion of the identified modules are significantly enriched in Hallmark, PID and KEGG pathways/gene sets. To validate the identified modules, we also performed literature validation as well as validation using experimentally supported miRTarBase database.

AVAILABILITY AND IMPLEMENTATION

Our implementation of proposed two-step RFR algorithm in R is available at https://github.com/MiladMokhtaridoost/2sRFR together with the scripts that replicate the reported experiments.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Set-Wise Differential Interaction Between Copy Number Alterations and Gene Expressions of Lower-Grade Glioma Reveals Prognosis-Associated Pathways

The integrative analysis of copy number alteration (CNA) and gene expression (GE) is an essential part of cancer research considering the impact of CNAs on cancer progression and prognosis. In this research, an integrative analysis was performed with generalized differentially coexpressed gene sets (gdCoxS), which is a modification of dCoxS. In gdCoxS, set-wise interaction is measured using the correlation of sample-wise distances with Renyi’s relative entropy, which requires an estimation of sample density based on omics profiles. To capture correlations between the variables, multivariate density estimation with covariance was applied. In the simulation study, the power of gdCoxS outperformed dCoxS that did not use the correlations in the density estimation explicitly. In the analysis of the lower-grade glioma of the cancer genome atlas program (TCGA-LGG) data, the gdCoxS identified 577 pathway CNAs and GEs pairs that showed significant changes of interaction between the survival and non-survival group, while other benchmark methods detected lower numbers of such pathways. The biological implications of the significant pathways were well consistent with previous reports of the TCGA-LGG. Taken together, the gdCoxS is a useful method for an integrative analysis of CNAs and GEs.

Time-Varying Gene Network Analysis of Human Prefrontal Cortex Development

The prefrontal cortex (PFC) constitutes a large part of the human central nervous system and is essential for the normal social affection and executive function of humans and other primates. Despite ongoing research in this region, the development of interactions between PFC genes over the lifespan is still unknown. To investigate the conversion of PFC gene interaction networks and further identify hub genes, we obtained time-series gene expression data of human PFC tissues from the Gene Expression Omnibus (GEO) database. A statistical model, loggle, was used to construct time-varying networks and several common network attributes were used to explore the development of PFC gene networks with age. Network similarity analysis showed that the development of human PFC is divided into three stages, namely, fast development period, deceleration to stationary period, and recession period. We identified some genes related to PFC development at these different stages, including genes involved in neuronal differentiation or synapse formation, genes involved in nerve impulse transmission, and genes involved in the development of myelin around neurons. Some of these genes are consistent with findings in previous reports. At the same time, we explored the development of several known KEGG pathways in PFC and corresponding hub genes. This study clarified the development trajectory of the interaction between PFC genes, and proposed a set of candidate genes related to PFC development, which helps further study of human brain development at the genomic level supplemental to regular anatomical analyses. The analytical process used in this study, involving the loggle model, similarity analysis, and central analysis, provides a comprehensive strategy to gain novel insights into the evolution and development of brain networks in other organisms.

Sparse Single Index Models for Multivariate Responses

Joint models are popular for analyzing data with multivariate responses. We propose a sparse multivariate single index model, where responses and predictors are linked by unspecified smooth functions and multiple matrix level penalties are employed to select predictors and induce low-rank structures across responses. An alternating direction method of multipliers (ADMM) based algorithm is proposed for model estimation. We demonstrate the effectiveness of proposed model in simulation studies and an application to a genetic association study.

Sparse reduced-rank regression for integrating omics data

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.

Combinatorial and statistical prediction of gene expression from haplotype sequence

MOTIVATION

Genome-wide association studies (GWAS) have discovered thousands of significant genetic effects on disease phenotypes. By considering gene expression as the intermediary between genotype and disease phenotype, expression quantitative trait loci studies have interpreted many of these variants by their regulatory effects on gene expression. However, there remains a considerable gap between genotype-to-gene expression association and genotype-to-gene expression prediction. Accurate prediction of gene expression enables gene-based association studies to be performed post hoc for existing GWAS, reduces multiple testing burden, and can prioritize genes for subsequent experimental investigation.

RESULTS

In this work, we develop gene expression prediction methods that relax the independence and additivity assumptions between genetic markers. First, we consider gene expression prediction from a regression perspective and develop the HAPLEXR algorithm which combines haplotype clusterings with allelic dosages. Second, we introduce the new gene expression classification problem, which focuses on identifying expression groups rather than continuous measurements; we formalize the selection of an appropriate number of expression groups using the principle of maximum entropy. Third, we develop the HAPLEXD algorithm that models haplotype sharing with a modified suffix tree data structure and computes expression groups by spectral clustering. In both models, we penalize model complexity by prioritizing genetic clusters that indicate significant effects on expression. We compare HAPLEXR and HAPLEXD with three state-of-the-art expression prediction methods and two novel logistic regression approaches across five GTEx v8 tissues. HAPLEXD exhibits significantly higher classification accuracy overall; HAPLEXR shows higher prediction accuracy on approximately half of the genes tested and the largest number of best predicted genes (r2>0.1) among all methods. We show that variant and haplotype features selected by HAPLEXR are smaller in size than competing methods (and thus more interpretable) and are significantly enriched in functional annotations related to gene regulation. These results demonstrate the importance of explicitly modeling non-dosage dependent and intragenic epistatic effects when predicting expression.

AVAILABILITY AND IMPLEMENTATION

Source code and binaries are freely available at https://github.com/rapturous/HAPLEX.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Variable Selection in Threshold Regression Model with Applications to HIV Drug Adherence Data

The threshold regression model is an effective alternative to the Cox proportional hazards regression model when the proportional hazards assumption is not met. This paper considers variable selection for threshold regression. This model has separate regression functions for the initial health status and the speed of degradation in health. This flexibility is an important advantage when considering relevant risk factors for a complex time-to-event model where one needs to decide which variables should be included in the regression function for the initial health status, in the function for the speed of degradation in health, or in both functions. In this paper, we extend the broken adaptive ridge (BAR) method, originally designed for variable selection for one regression function, to simultaneous variable selection for both regression functions needed in the threshold regression model. We establish variable selection consistency of the proposed method and asymptotic normality of the estimator of non-zero regression coefficients. Simulation results show that our method outperformed threshold regression without variable selection and variable selection based on the Akaike information criterion. We apply the proposed method to data from an HIV drug adherence study in which electronic monitoring of drug intake is used to identify risk factors for non- adherence.

L2RM: Low-rank Linear Regression Models for High-dimensional Matrix Responses

The aim of this paper is to develop a low-rank linear regression model (L2RM) to correlate a high-dimensional response matrix with a high dimensional vector of covariates when coefficient matrices have low-rank structures. We propose a fast and efficient screening procedure based on the spectral norm of each coefficient matrix in order to deal with the case when the number of covariates is extremely large. We develop an efficient estimation procedure based on the trace norm regularization, which explicitly imposes the low rank structure of coefficient matrices. When both the dimension of response matrix and that of covariate vector diverge at the exponential order of the sample size, we investigate the sure independence screening property under some mild conditions. We also systematically investigate some theoretical properties of our estimation procedure including estimation consistency, rank consistency and non-asymptotic error bound under some mild conditions. We further establish a theoretical guarantee for the overall solution of our two-step screening and estimation procedure. We examine the finite-sample performance of our screening and estimation methods using simulations and a large-scale imaging genetic dataset collected by the Philadelphia Neurodevelopmental Cohort (PNC) study.

Microbiome Multi-Omics Network Analysis: Statistical Considerations, Limitations, and Opportunities

The advent of large-scale microbiome studies affords newfound analytical opportunities to understand how these communities of microbes operate and relate to their environment. However, the analytical methodology needed to model microbiome data and integrate them with other data constructs remains nascent. This emergent analytical toolset frequently ports over techniques developed in other multi-omics investigations, especially the growing array of statistical and computational techniques for integrating and representing data through networks. While network analysis has emerged as a powerful approach to modeling microbiome data, oftentimes by integrating these data with other types of omics data to discern their functional linkages, it is not always evident if the statistical details of the approach being applied are consistent with the assumptions of microbiome data or how they impact data interpretation. In this review, we overview some of the most important network methods for integrative analysis, with an emphasis on methods that have been applied or have great potential to be applied to the analysis of multi-omics integration of microbiome data. We compare advantages and disadvantages of various statistical tools, assess their applicability to microbiome data, and discuss their biological interpretability. We also highlight on-going statistical challenges and opportunities for integrative network analysis of microbiome data.

Smooth and Locally Sparse Estimation for Multiple-Output Functional Linear Regression

Functional data analysis has attracted substantial research interest and the goal of functional sparsity is to produce a sparse estimate which assigns zero values over regions where the true underlying function is zero, i.e., no relationship between the response variable and the predictor variable. In this paper, we consider a functional linear regression models that explicitly incorporates the interconnections among the responses. We propose a locally sparse (i.e., zero on some subregions) estimator, multiple-smooth and locally sparse (m-SLoS) estimator, for coefficient functions base on the interconnections among the responses. This method is based on a combination of smooth and locally sparse (SLoS) estimator and Laplacian quadratic penalty function, where we used SLoS for encouraging locally sparse and Laplacian quadratic penalty for promoting similar locally sparse among coefficient functions associated with the interconnections among the responses. Simulations show excellent numerical performance of the proposed method in terms of the estimation of coefficient functions especially the coefficient functions are same for all multivariate responses. Practical merit of this modeling is demonstrated by one real application and the prediction shows significant improvements.

An embedded method for gene identification problems involving unwanted data heterogeneity

BACKGROUND

Modern applications such as bioinformatics collecting data in various ways can easily result in heterogeneous data. Traditional variable selection methods assume samples are independent and identically distributed, which however is not suitable for these applications. Some existing statistical models capable of taking care of unwanted variation were developed for gene identification involving heterogeneous data, but they lack model predictability and suffer from variable redundancy.

RESULTS

By accounting for the unwanted heterogeneity effectively, our method have shown its superiority over several state-of-the art methods, which is validated by the experimental results in both unsupervised and supervised gene identification problems. Moreover, we also applied our method to a pan-cancer study where our method can identify the most discriminative genes best distinguishing different cancer types.

CONCLUSIONS

This article provides an alternative gene identification method that can accounting for unwanted data heterogeneity. It is a promising method to provide new insights into the complex cancer biology and clues for understanding tumorigenesis and tumor progression.

A flexible and parallelizable approach to genome-wide polygenic risk scores

The heritability of most complex traits is driven by variants throughout the genome. Consequently, polygenic risk scores, which combine information on multiple variants genome-wide, have demonstrated improved accuracy in genetic risk prediction. We present a new two-step approach to constructing genome-wide polygenic risk scores from meta-GWAS summary statistics. Local linkage disequilibrium (LD) is adjusted for in Step 1, followed by, uniquely, long-range LD in Step 2. Our algorithm is highly parallelizable since block-wise analyses in Step 1 can be distributed across a high-performance computing cluster, and flexible, since sparsity and heritability are estimated within each block. Inference is obtained through a formal Bayesian variable selection framework, meaning final risk predictions are averaged over competing models. We compared our method to two alternative approaches: LDPred and lassosum using all seven traits in the Welcome Trust Case Control Consortium as well as meta-GWAS summaries for type 1 diabetes (T1D), coronary artery disease, and schizophrenia. Performance was generally similar across methods, although our framework provided more accurate predictions for T1D, for which there are multiple heterogeneous signals in regions of both short- and long-range LD. With sufficient compute resources, our method also allows the fastest runtimes.

Integration of Multiple Data Sources for Gene Network Inference Using Genetic Perturbation Data

The inference of gene networks from large-scale human genomic data is challenging due to the difficulty in identifying correct regulators for each gene in a high-dimensional search space. We present a Bayesian approach integrating external data sources with knockdown data from human cell lines to infer gene regulatory networks. In particular, we assemble multiple data sources, including gene expression data, genome-wide binding data, gene ontology, and known pathways, and use a supervised learning framework to compute prior probabilities of regulatory relationships. We show that our integrated method improves the accuracy of inferred gene networks as well as extends some previous Bayesian frameworks both in theory and applications. We apply our method to two different human cell lines, namely skin melanoma cell line A375 and lung cancer cell line A549, to illustrate the capabilities of our method. Our results show that the improvement in performance could vary from cell line to cell line and that we might need to choose different external data sources serving as prior knowledge if we hope to obtain better accuracy for different cell lines.

Estimating Time-Varying Graphical Models

In this paper, we study time-varying graphical models based on data measured over a temporal grid. Such models are motivated by the needs to describe and understand evolving interacting relationships among a set of random variables in many real applications, for instance the study of how stock prices interact with each other and how such interactions change over time. We propose a new model, LOcal Group Graphical Lasso Estimation (loggle), under the assumption that the graph topology changes gradually over time. Specifically, loggle uses a novel local group-lasso type penalty to efficiently incorporate information from neighboring time points and to impose structural smoothness of the graphs. We implement an ADMM based algorithm to fit the loggle model. This algorithm utilizes blockwise fast computation and pseudo-likelihood approximation to improve computational efficiency. An R package loggle has also been developed and is available on https://cran.r-project.org/. We evaluate the performance of loggle by simulation experiments. We also apply loggle to S&P 500 stock price data and demonstrate that loggle is able to reveal the interacting relationships among stock prices and among industrial sectors in a time period that covers the recent global financial crisis. The supplemental materials for this paper are also available online.

A new method for constructing tumor specific gene co-expression networks based on samples with tumor purity heterogeneity

Motivation

Tumor tissue samples often contain an unknown fraction of stromal cells. This problem is widely known as tumor purity heterogeneity (TPH) was recently recognized as a severe issue in omics studies. Specifically, if TPH is ignored when inferring co-expression networks, edges are likely to be estimated among genes with mean shift between non-tumor- and tumor cells rather than among gene pairs interacting with each other in tumor cells. To address this issue, we propose Tumor Specific Net (TSNet), a new method which constructs tumor-cell specific gene/protein co-expression networks based on gene/protein expression profiles of tumor tissues. TSNet treats the observed expression profile as a mixture of expressions from different cell types and explicitly models tumor purity percentage in each tumor sample.

Results

Using extensive synthetic data experiments, we demonstrate that TSNet outperforms a standard graphical model which does not account for TPH. We then apply TSNet to estimate tumor specific gene co-expression networks based on TCGA ovarian cancer RNAseq data. We identify novel co-expression modules and hub structure specific to tumor cells.

Availability and implementation

R codes can be found at https://github.com/petraf01/TSNet.

Supplementary information

Supplementary data are available at Bioinformatics online.

Integrative Proteo-genomic Analysis to Construct CNA-protein Regulatory Map in Breast and Ovarian Tumors

Recent development in high throughput proteomics and genomics profiling enable one to study regulations of genome alterations on protein activities in a systematic manner. In this article, we propose a new statistical method, ProMAP, to systematically characterize the regulatory relationships between proteins and DNA copy number alterations (CNA) in breast and ovarian tumors based on proteogenomic data from the CPTAC-TCGA studies. Because of the dynamic nature of mass spectrometry instruments, proteomics data from labeled mass spectrometry experiments usually have non-ignorable batch effects. Moreover, mass spectrometry based proteomic data often possesses high percentages of missing values and non-ignorable missing-data patterns. Thus, we use a linear mixed effects model to account for the batch structure and explicitly incorporate the abundance-dependent-missing-data mechanism of proteomic data in ProMAP. In addition, we employ a multivariate regression framework to characterize the multiple-to-multiple regulatory relationships between CNA and proteins. Further, we use proper statistical regularization to facilitate the detection of master genetic regulators, which affect the activities of many proteins and often play important roles in genetic regulatory networks. Improved performance of ProMAP over existing methods were illustrated through extensive simulation studies and real data examples. Applying ProMAP to the CPTAC-TCGA breast and ovarian cancer data sets, we identified many genome regions, including a few novel ones, whose CNA were associated with protein and or phosphoprotein abundances. For example, in breast tumors, a small region in 8p11.21 was recognized as the second biggest hub in the CNA-phosphoprotein regulatory map, and further investigation of the regulatory targets suggests the potential role of 8p11.21 CNA in perturbing oxygen binding and transport activities in tumor cells. This and other findings from our analyses help to characterize the impacts of CNAs on protein activity landscapes and cast light on the genetic regulation mechanisms underlying these tumors.

SOFAR: Large-Scale Association Network Learning

Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network structures via layers of sparse latent factors ranked by importance. Yet sparsity and orthogonality have been two largely incompatible goals. To accommodate both features, in this paper we suggest the method of sparse orthogonal factor regression (SOFAR) via the sparse singular value decomposition with orthogonality constrained optimization to learn the underlying association networks, with broad applications to both unsupervised and supervised learning tasks such as biclustering with sparse singular value decomposition, sparse principal component analysis, sparse factor analysis, and spare vector autoregression analysis. Exploiting the framework of convexity-assisted nonconvex optimization, we derive nonasymptotic error bounds for the suggested procedure characterizing the theoretical advantages. The statistical guarantees are powered by an efficient SOFAR algorithm with convergence property. Both computational and theoretical advantages of our procedure are demonstrated with several simulations and real data examples.

Integrative multi-view regression: Bridging group-sparse and low-rank models

Multi-view data have been routinely collected in various fields of science and engineering. A general problem is to study the predictive association between multivariate responses and multi-view predictor sets, all of which can be of high dimensionality. It is likely that only a few views are relevant to prediction, and the predictors within each relevant view contribute to the prediction collectively rather than sparsely. We cast this new problem under the familiar multivariate regression framework and propose an integrative reduced-rank regression (iRRR), where each view has its own low-rank coefficient matrix. As such, latent features are extracted from each view in a supervised fashion. For model estimation, we develop a convex composite nuclear norm penalization approach, which admits an efficient algorithm via alternating direction method of multipliers. Extensions to non-Gaussian and incomplete data are discussed. Theoretically, we derive non-asymptotic oracle bounds of iRRR under a restricted eigenvalue condition. Our results recover oracle bounds of several special cases of iRRR including Lasso, group Lasso, and nuclear norm penalized regression. Therefore, iRRR seamlessly bridges group-sparse and low-rank methods and can achieve substantially faster convergence rate under realistic settings of multi-view learning. Simulation studies and an application in the Longitudinal Studies of Aging further showcase the efficacy of the proposed methods.

Robust network-based regularization and variable selection for high-dimensional genomic data in cancer prognosis

In cancer genomic studies, an important objective is to identify prognostic markers associated with patients' survival. Network-based regularization has achieved success in variable selections for high-dimensional cancer genomic data, because of its ability to incorporate the correlations among genomic features. However, as survival time data usually follow skewed distributions, and are contaminated by outliers, network-constrained regularization that does not take the robustness into account leads to false identifications of network structure and biased estimation of patients' survival. In this study, we develop a novel robust network-based variable selection method under the accelerated failure time model. Extensive simulation studies show the advantage of the proposed method over the alternative methods. Two case studies of lung cancer datasets with high-dimensional gene expression measurements demonstrate that the proposed approach has identified markers with important implications.