Coronary heart disease (CHD) is one of the leading causes of mortality and morbidity in the United States. Accurate time-to-event CHD prediction models with high-dimensional DNA methylation and clinical features may assist with early prediction and intervention strategies. We developed a state-of-the-art deep learning autoencoder survival analysis model (AESurv) to effectively analyze high-dimensional blood DNA methylation features and traditional clinical risk factors by learning low-dimensional representation of participants for time-to-event CHD prediction. We demonstrated the utility of our model in two cohort studies: the Strong Heart Study cohort (SHS), a prospective cohort studying cardiovascular disease and its risk factors among American Indians adults; the Women's Health Initiative (WHI), a prospective cohort study including randomized clinical trials and observational study to improve postmenopausal women's health with one of the main focuses on cardiovascular disease. Our AESurv model effectively learned participant representations in low-dimensional latent space and achieved better model performance (concordance index-C index of 0.864 ± 0.009 and time-to-event mean area under the receiver operating characteristic curve-AUROC of 0.905 ± 0.009) than other survival analysis models (Cox proportional hazard, Cox proportional hazard deep neural network survival analysis, random survival forest, and gradient boosting survival analysis models) in the SHS. We further validated the AESurv model in WHI and also achieved the best model performance. The AESurv model can be used for accurate CHD prediction and assist health care professionals and patients to perform early intervention strategies. We suggest using AESurv model for future time-to-event CHD prediction based on DNA methylation features.

MOTIVATION: Epigenetic clocks are prediction methods based on DNA methylation levels in a given species or set of species. Defined as multivariate regression models, these DNA methylation-based biomarkers of age or mortality risk are useful in species conservation efforts and in preclinical studies. RESULTS: We present an R package called MammalMethylClock for the construction, assessment, and application of epigenetic clocks in different mammalian species. The R package includes the utility for implementing pre-existing mammalian clocks from the Mammalian Methylation Consortium. AVAILABILITY AND IMPLEMENTATION: The source code and documentation manual for MammalMethylClock, and clock coefficient .csv files that are included within this software package, can be found on Zenodo at https://doi.org/10.5281/zenodo.10971037.

The arrival of the Infinium DNA methylation BeadChips for mice and other nonhuman mammalian species has outpaced the development of the informatics that supports their use for epigenetics study in model organisms. Here, we present informatics infrastructure and methods to allow easy DNA methylation analysis on multiple species, including domesticated animals and inbred laboratory mice (in SeSAMe version 1.16.0+). First, we developed a data-driven analysis pipeline covering species inference, genome-specific data preprocessing and regression modeling. We targeted genomes of 310 species and 37 inbred mouse strains and showed that genome-specific preprocessing prevents artifacts and yields more accurate measurements than generic pipelines. Second, we uncovered the dynamics of the epigenome evolution in different genomic territories and tissue types through comparative analysis. We identified a catalog of inbred mouse strain-specific methylation differences, some of which are linked to the strains' immune, metabolic and neurological phenotypes. By streamlining DNA methylation array analysis for undesigned genomes, our methods extend epigenome research to broad species contexts.

BACKGROUND: Ensemble predictors such as the random forest are known to have superior accuracy but their black-box predictions are difficult to interpret. In contrast, a generalized linear model (GLM) is very interpretable especially when forward feature selection is used to construct the model. However, forward feature selection tends to overfit the data and leads to low predictive accuracy. Therefore, it remains an important research goal to combine the advantages of ensemble predictors (high accuracy) with the advantages of forward regression modeling (interpretability). To address this goal several articles have explored GLM based ensemble predictors. Since limited evaluations suggested that these ensemble predictors were less accurate than alternative predictors, they have found little attention in the literature. RESULTS: Comprehensive evaluations involving hundreds of genomic data sets, the UCI machine learning benchmark data, and simulations are used to give GLM based ensemble predictors a new and careful look. A novel bootstrap aggregated (bagged) GLM predictor that incorporates several elements of randomness and instability (random subspace method, optional interaction terms, forward variable selection) often outperforms a host of alternative prediction methods including random forests and penalized regression models (ridge regression, elastic net, lasso). This random generalized linear model (RGLM) predictor provides variable importance measures that can be used to define a "thinned" ensemble predictor (involving few features) that retains excellent predictive accuracy. CONCLUSION: RGLM is a state of the art predictor that shares the advantages of a random forest (excellent predictive accuracy, feature importance measures, out-of-bag estimates of accuracy) with those of a forward selected generalized linear model (interpretability). These methods are implemented in the freely available R software package randomGLM.

BACKGROUND: Co-expression measures are often used to define networks among genes. Mutual information (MI) is often used as a generalized correlation measure. It is not clear how much MI adds beyond standard (robust) correlation measures or regression model based association measures. Further, it is important to assess what transformations of these and other co-expression measures lead to biologically meaningful modules (clusters of genes). RESULTS: We provide a comprehensive comparison between mutual information and several correlation measures in 8 empirical data sets and in simulations. We also study different approaches for transforming an adjacency matrix, e.g. using the topological overlap measure. Overall, we confirm close relationships between MI and correlation in all data sets which reflects the fact that most gene pairs satisfy linear or monotonic relationships. We discuss rare situations when the two measures disagree. We also compare correlation and MI based approaches when it comes to defining co-expression network modules. We show that a robust measure of correlation (the biweight midcorrelation transformed via the topological overlap transformation) leads to modules that are superior to MI based modules and maximal information coefficient (MIC) based modules in terms of gene ontology enrichment. We present a function that relates correlation to mutual information which can be used to approximate the mutual information from the corresponding correlation coefficient. We propose the use of polynomial or spline regression models as an alternative to MI for capturing non-linear relationships between quantitative variables. CONCLUSION: The biweight midcorrelation outperforms MI in terms of elucidating gene pairwise relationships. Coupled with the topological overlap matrix transformation, it often leads to more significantly enriched co-expression modules. Spline and polynomial networks form attractive alternatives to MI in case of non-linear relationships. Our results indicate that MI networks can safely be replaced by correlation networks when it comes to measuring co-expression relationships in stationary data.

Both avian and mammalian basal ganglia are involved in voluntary motor control. In birds, such movements include hopping, perching and flying. Two organizational features that distinguish the songbird basal ganglia are that striatal and pallidal neurons are intermingled, and that neurons dedicated to vocal-motor function are clustered together in a dense cell group known as area X that sits within the surrounding striato-pallidum. This specification allowed us to perform molecular profiling of two striato-pallidal subregions, comparing transcriptional patterns in tissue dedicated to vocal-motor function (area X) to those in tissue that contains similar cell types but supports non-vocal behaviors: the striato-pallidum ventral to area X (VSP), our focus here. Since any behavior is likely underpinned by the coordinated actions of many molecules, we constructed gene co-expression networks from microarray data to study large-scale transcriptional patterns in both subregions. Our goal was to investigate any relationship between VSP network structure and singing and identify gene co-expression groups, or modules, found in the VSP but not area X. We observed mild, but surprising, relationships between VSP modules and song spectral features, and found a group of four VSP modules that were highly specific to the region. These modules were unrelated to singing, but were composed of genes involved in many of the same biological processes as those we previously observed in area X-specific singing-related modules. The VSP-specific modules were also enriched for processes disrupted in Parkinson's and Huntington's Diseases. Our results suggest that the activation/inhibition of a single pathway is not sufficient to functionally specify area X versus the VSP and support the notion that molecular processes are not in and of themselves specialized for behavior. Instead, unique interactions between molecular pathways create functional specificity in particular brain regions during distinct behavioral states.

BACKGROUND: Genomic and other high dimensional analyses often require one to summarize multiple related variables by a single representative. This task is also variously referred to as collapsing, combining, reducing, or aggregating variables. Examples include summarizing several probe measurements corresponding to a single gene, representing the expression profiles of a co-expression module by a single expression profile, and aggregating cell-type marker information to de-convolute expression data. Several standard statistical summary techniques can be used, but network methods also provide useful alternative methods to find representatives. Currently few collapsing functions are developed and widely applied. RESULTS: We introduce the R function collapseRows that implements several collapsing methods and evaluate its performance in three applications. First, we study a crucial step of the meta-analysis of microarray data: the merging of independent gene expression data sets, which may have been measured on different platforms. Toward this end, we collapse multiple microarray probes for a single gene and then merge the data by gene identifier. We find that choosing the probe with the highest average expression leads to best between-study consistency. Second, we study methods for summarizing the gene expression profiles of a co-expression module. Several gene co-expression network analysis applications show that the optimal collapsing strategy depends on the analysis goal. Third, we study aggregating the information of cell type marker genes when the aim is to predict the abundance of cell types in a tissue sample based on gene expression data ("expression deconvolution"). We apply different collapsing methods to predict cell type abundances in peripheral human blood and in mixtures of blood cell lines. Interestingly, the most accurate prediction method involves choosing the most highly connected "hub" marker gene. Finally, to facilitate biological interpretation of collapsed gene lists, we introduce the function userListEnrichment, which assesses the enrichment of gene lists for known brain and blood cell type markers, and for other published biological pathways. CONCLUSIONS: The R function collapseRows implements several standard and network-based collapsing methods. In various genomic applications we provide evidence that both types of methods are robust and biologically relevant tools.

In many applications, one is interested in determining which of the properties of a network module change across conditions. For example, to validate the existence of a module, it is desirable to show that it is reproducible (or preserved) in an independent test network. Here we study several types of network preservation statistics that do not require a module assignment in the test network. We distinguish network preservation statistics by the type of the underlying network. Some preservation statistics are defined for a general network (defined by an adjacency matrix) while others are only defined for a correlation network (constructed on the basis of pairwise correlations between numeric variables). Our applications show that the correlation structure facilitates the definition of particularly powerful module preservation statistics. We illustrate that evaluating module preservation is in general different from evaluating cluster preservation. We find that it is advantageous to aggregate multiple preservation statistics into summary preservation statistics. We illustrate the use of these methods in six gene co-expression network applications including 1) preservation of cholesterol biosynthesis pathway in mouse tissues, 2) comparison of human and chimpanzee brain networks, 3) preservation of selected KEGG pathways between human and chimpanzee brain networks, 4) sex differences in human cortical networks, 5) sex differences in mouse liver networks. While we find no evidence for sex specific modules in human cortical networks, we find that several human cortical modules are less preserved in chimpanzees. In particular, apoptosis genes are differentially co-expressed between humans and chimpanzees. Our simulation studies and applications show that module preservation statistics are useful for studying differences between the modular structure of networks. Data, R software and accompanying tutorials can be downloaded from the following webpage: http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/ModulePreservation.

SUMMARY: Hierarchical clustering is a widely used method for detecting clusters in genomic data. Clusters are defined by cutting branches off the dendrogram. A common but inflexible method uses a constant height cutoff value; this method exhibits suboptimal performance on complicated dendrograms. We present the Dynamic Tree Cut R package that implements novel dynamic branch cutting methods for detecting clusters in a dendrogram depending on their shape. Compared to the constant height cutoff method, our techniques offer the following advantages: (1) they are capable of identifying nested clusters; (2) they are flexible-cluster shape parameters can be tuned to suit the application at hand; (3) they are suitable for automation; and (4) they can optionally combine the advantages of hierarchical clustering and partitioning around medoids, giving better detection of outliers. We illustrate the use of these methods by applying them to protein-protein interaction network data and to a simulated gene expression data set. AVAILABILITY: The Dynamic Tree Cut method is implemented in an R package available at http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/BranchCutting.

BACKGROUND: Correlation networks are increasingly being used in bioinformatics applications. For example, weighted gene co-expression network analysis is a systems biology method for describing the correlation patterns among genes across microarray samples. Weighted correlation network analysis (WGCNA) can be used for finding clusters (modules) of highly correlated genes, for summarizing such clusters using the module eigengene or an intramodular hub gene, for relating modules to one another and to external sample traits (using eigengene network methodology), and for calculating module membership measures. Correlation networks facilitate network based gene screening methods that can be used to identify candidate biomarkers or therapeutic targets. These methods have been successfully applied in various biological contexts, e.g. cancer, mouse genetics, yeast genetics, and analysis of brain imaging data. While parts of the correlation network methodology have been described in separate publications, there is a need to provide a user-friendly, comprehensive, and consistent software implementation and an accompanying tutorial. RESULTS: The WGCNA R software package is a comprehensive collection of R functions for performing various aspects of weighted correlation network analysis. The package includes functions for network construction, module detection, gene selection, calculations of topological properties, data simulation, visualization, and interfacing with external software. Along with the R package we also present R software tutorials. While the methods development was motivated by gene expression data, the underlying data mining approach can be applied to a variety of different settings. CONCLUSION: The WGCNA package provides R functions for weighted correlation network analysis, e.g. co-expression network analysis of gene expression data. The R package along with its source code and additional material are freely available at http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/Rpackages/WGCNA.

THE MERGING OF NETWORK THEORY AND MICROARRAY DATA ANALYSIS TECHNIQUES HAS SPAWNED A NEW FIELD: gene coexpression network analysis. While network methods are increasingly used in biology, the network vocabulary of computational biologists tends to be far more limited than that of, say, social network theorists. Here we review and propose several potentially useful network concepts. We take advantage of the relationship between network theory and the field of microarray data analysis to clarify the meaning of and the relationship among network concepts in gene coexpression networks. Network theory offers a wealth of intuitive concepts for describing the pairwise relationships among genes, which are depicted in cluster trees and heat maps. Conversely, microarray data analysis techniques (singular value decomposition, tests of differential expression) can also be used to address difficult problems in network theory. We describe conditions when a close relationship exists between network analysis and microarray data analysis techniques, and provide a rough dictionary for translating between the two fields. Using the angular interpretation of correlations, we provide a geometric interpretation of network theoretic concepts and derive unexpected relationships among them. We use the singular value decomposition of module expression data to characterize approximately factorizable gene coexpression networks, i.e., adjacency matrices that factor into node specific contributions. High and low level views of coexpression networks allow us to study the relationships among modules and among module genes, respectively. We characterize coexpression networks where hub genes are significant with respect to a microarray sample trait and show that the network concept of intramodular connectivity can be interpreted as a fuzzy measure of module membership. We illustrate our results using human, mouse, and yeast microarray gene expression data. The unification of coexpression network methods with traditional data mining methods can inform the application and development of systems biologic methods.

MOTIVATION: The goal of neighborhood analysis is to find a set of genes (the neighborhood) that is similar to an initial 'seed' set of genes. Neighborhood analysis methods for network data are important in systems biology. If individual network connections are susceptible to noise, it can be advantageous to define neighborhoods on the basis of a robust interconnectedness measure, e.g. the topological overlap measure. Since the use of multiple nodes in the seed set may lead to more informative neighborhoods, it can be advantageous to define multi-node similarity measures. RESULTS: The pairwise topological overlap measure is generalized to multiple network nodes and subsequently used in a recursive neighborhood construction method. A local permutation scheme is used to determine the neighborhood size. Using four network applications and a simulated example, we provide empirical evidence that the resulting neighborhoods are biologically meaningful, e.g. we use neighborhood analysis to identify brain cancer related genes. AVAILABILITY: An executable Windows program and tutorial for multi-node topological overlap measure (MTOM) based analysis can be downloaded from the webpage (http://www.genetics.ucla.edu/labs/horvath/MTOM/).

BACKGROUND: Network methods are increasingly used to represent the interactions of genes and/or proteins. Genes or proteins that are directly linked may have a similar biological function or may be part of the same biological pathway. Since the information on the connection (adjacency) between 2 nodes may be noisy or incomplete, it can be desirable to consider alternative measures of pairwise interconnectedness. Here we study a class of measures that are proportional to the number of neighbors that a pair of nodes share in common. For example, the topological overlap measure by Ravasz et al. 1 can be interpreted as a measure of agreement between the m = 1 step neighborhoods of 2 nodes. Several studies have shown that two proteins having a higher topological overlap are more likely to belong to the same functional class than proteins having a lower topological overlap. Here we address the question whether a measure of topological overlap based on higher-order neighborhoods could give rise to a more robust and sensitive measure of interconnectedness. RESULTS: We generalize the topological overlap measure from m = 1 step neighborhoods to m > or = 2 step neighborhoods. This allows us to define the m-th order generalized topological overlap measure (GTOM) by (i) counting the number of m-step neighbors that a pair of nodes share and (ii) normalizing it to take a value between 0 and 1. Using theoretical arguments, a yeast co-expression network application, and a fly protein network application, we illustrate the usefulness of the proposed measure for module detection and gene neighborhood analysis. CONCLUSION: Topological overlap can serve as an important filter to counter the effects of spurious or missing connections between network nodes. The m-th order topological overlap measure allows one to trade-off sensitivity versus specificity when it comes to defining pairwise interconnectedness and network modules.