Integrative analysis of genetical genomics data incorporating network structures

In a living organism, tens of thousands of genes are expressed and interact with each other to achieve necessary cellular functions. Gene regulatory networks contain information on regulatory mechanisms and the functions of gene expressions. Thus, incorporating network structures, discerned either through biological experiments or statistical estimations, could potentially increase the selection and estimation accuracy of genes associated with a phenotype of interest. Here, we considered a gene selection problem using gene expression data and the graphical structures found in gene networks. Because gene expression measurements are intermediate phenotypes between a trait and its associated genes, we adopted an instrumental variable regression approach. We treated genetic variants as instrumental variables to address the endogeneity issue. We proposed a two‐step estimation procedure. In the first step, we applied the LASSO algorithm to estimate the effects of genetic variants on gene expression measurements. In the second step, the projected expression measurements obtained from the first step were treated as input variables. A graph‐constrained regularization method was adopted to improve the efficiency of gene selection and estimation. We theoretically showed the selection consistency of the estimation method and derived the bound of the estimates. Simulation and real data analyses were conducted to demonstrate the effectiveness of our method and to compare it with its counterparts.     

Network Based Prediction Model for Genomics Data Analysis

Biological networks, such as genetic regulatory networks and protein interaction networks, provide important information for studying gene/protein activities. In this paper, we propose a new method, NetBoosting, for incorporating a priori biological network information in analyzing high dimensional genomics data. Specially, we are interested in constructing prediction models for disease phenotypes of interest based on genomics data, and at the same time identifying disease susceptible genes. We employ the gradient descent boosting procedure to build an additive tree model and propose a new algorithm to utilize the network structure in fitting small tree weak learners. We illustrate by simulation studies and a real data example that, by making use of the network information, NetBoosting outperforms a few existing methods in terms of accuracy of prediction and variable selection.     

Integrating external biological knowledge in the construction of regulatory networks from time-series expression data

ABSTRACT: BACKGROUND: Inference about regulatory networks from high-throughput genomics data is of great interest in systems biology. We present a Bayesian approach to infer gene regulatory networks from time series expression data by integrating various types of biological knowledge. RESULTS: We formulate network construction as a series of variable selection problems and use linear regression to model the data. Our method summarizes additional data sources with an informative prior probability distribution over candidate regression models. We extend the Bayesian model averaging (BMA) variable selection method to select regulators in the regression framework. We summarize the external biological knowledge by an informative prior probability distribution over the candidate regression models. CONCLUSIONS: We demonstrate our method on simulated data and a set of time-series microarray experiments measuring the effect of a drug perturbation on gene expression levels, and show that it outperforms leading regression-based methods in the literature.     

Diffusion kernel-based logistic regression models for protein function prediction

Assigning functions to unknown proteins is one of the most important problems in proteomics. Several approaches have used protein-protein interaction data to predict protein functions. We previously developed a Markov random field (MRF) based method to infer a protein's functions using protein-protein interaction data and the functional annotations of its protein interaction partners. In the original model, only direct interactions were considered and each function was considered separately. In this study, we develop a new model which extends direct interactions to all neighboring proteins, and one function to multiple functions. The goal is to understand a protein's function based on information on all the neighboring proteins in the interaction network. We first developed a novel kernel logistic regression (KLR) method based on diffusion kernels for protein interaction networks. The diffusion kernels provide means to incorporate all neighbors of proteins in the network. Second, we identified a set of functions that are highly correlated with the function of interest, referred to as the correlated functions, using the chi-square test. Third, the correlated functions were incorporated into our new KLR model. Fourth, we extended our model by incorporating multiple biological data sources such as protein domains, protein complexes, and gene expressions by converting them into networks. We showed that the KLR approach of incorporating all protein neighbors significantly improved the accuracy of protein function predictions over the MRF model. The incorporation of multiple data sets also improved prediction accuracy. The prediction accuracy is comparable to another protein function classifier based on the support vector machine (SVM), using a diffusion kernel. The advantages of the KLR model include its simplicity as well as its ability to explore the contribution of neighbors to the functions of proteins of interest.     

Reliable gene signatures for microarray classification: assessment of stability and performance

MOTIVATION: Two important questions for the analysis of gene expression measurements from different sample classes are (1) how to classify samples and (2) how to identify meaningful gene signatures (ranked gene lists) exhibiting the differences between classes and sample subsets. Solutions to both questions have immediate biological and biomedical applications. To achieve optimal classification performance, a suitable combination of classifier and gene selection method needs to be specifically selected for a given dataset. The selected gene signatures can be unstable and the resulting classification accuracy unreliable, particularly when considering different subsets of samples. Both unstable gene signatures and overestimated classification accuracy can impair biological conclusions. METHODS: We address these two issues by repeatedly evaluating the classification performance of all models, i.e. pairwise combinations of various gene selection and classification methods, for random subsets of arrays (sampling). A model score is used to select the most appropriate model for the given dataset. Consensus gene signatures are constructed by extracting those genes frequently selected over many samplings. Sampling additionally permits measurement of the stability of the classification performance for each model, which serves as a measure of model reliability. RESULTS: We analyzed a large gene expression dataset with 78 measurements of four different cartilage sample classes. Classifiers trained on subsets of measurements frequently produce models with highly variable performance. Our approach provides reliable classification performance estimates via sampling. In addition to reliable classification performance, we determined stable consensus signatures (i.e. gene lists) for sample classes. Manual literature screening showed that these genes are highly relevant to our gene expression experiment with osteoarthritic cartilage. We compared our approach to others based on a publicly available dataset on breast cancer. AVAILABILITY: R package at http://www.bio.ifi.lmu.de/~davis/edaprakt     

A Novel Strategy for Gene Selection of Microarray Data Based on Gene-to-Class Sensitivity Information

To obtain predictive genes with lower redundancy and better interpretability, a hybrid gene selection method encoding prior information is proposed in this paper. To begin with, the prior information referred to as gene-to-class sensitivity (GCS) of all genes from microarray data is exploited by a single hidden layered feedforward neural network (SLFN). Then, to select more representative and lower redundant genes, all genes are grouped into some clusters by K-means method, and some low sensitive genes are filtered out according to their GCS values. Finally, a modified binary particle swarm optimization (BPSO) encoding the GCS information is proposed to perform further gene selection from the remainder genes. For considering the GCS information, the proposed method selects those genes highly correlated to sample classes. Thus, the low redundant gene subsets obtained by the proposed method also contribute to improve classification accuracy on microarray data. The experiments results on some open microarray data verify the effectiveness and efficiency of the proposed approach.     

Boosting Probabilistic Graphical Model Inference by Incorporating Prior Knowledge from Multiple Sources

Inferring regulatory networks from experimental data via probabilistic graphical models is a popular framework to gain insights into biological systems. However, the inherent noise in experimental data coupled with a limited sample size reduces the performance of network reverse engineering. Prior knowledge from existing sources of biological information can address this low signal to noise problem by biasing the network inference towards biologically plausible network structures. Although integrating various sources of information is desirable, their heterogeneous nature makes this task challenging. We propose two computational methods to incorporate various information sources into a probabilistic consensus structure prior to be used in graphical model inference. Our first model, called Latent Factor Model (LFM), assumes a high degree of correlation among external information sources and reconstructs a hidden variable as a common source in a Bayesian manner. The second model, a Noisy-OR, picks up the strongest support for an interaction among information sources in a probabilistic fashion. Our extensive computational studies on KEGG signaling pathways as well as on gene expression data from breast cancer and yeast heat shock response reveal that both approaches can significantly enhance the reconstruction accuracy of Bayesian Networks compared to other competing methods as well as to the situation without any prior. Our framework allows for using diverse information sources, like pathway databases, GO terms and protein domain data, etc. and is flexible enough to integrate new sources, if available.     

Stochastic search gene suggestion: a Bayesian hierarchical model for gene mapping

Mapping the genes for a complex disease, such as diabetes or rheumatoid arthritis (RA), involves finding multiple genetic loci that may contribute to the onset of the disease. Pairwise testing of the loci leads to the problem of multiple testing. Looking at haplotypes, or linear sets of loci, avoids multiple tests but results in a contingency table with sparse counts, especially when using marker loci with multiple alleles. We propose a hierarchical Bayesian model for case-parent triad data that uses a conditional logistic regression likelihood to model the probability of transmission to a diseased child. We define hierarchical prior distributions on the allele main effects to model the genetic dependencies present in the human leukocyte antigen (HLA) region of chromosome 6. First, we add a hierarchical level for model selection that accounts for both locus and allele selection. This allows us to cast the problem of identifying genetic loci relevant to the disease into a problem of Bayesian variable selection. Second, we attempt to include linkage disequilibrium as a covariance structure in the prior for model coefficients. We evaluate the performance of the procedure with some simulated examples and then apply our procedure to identifying genetic markers in the HLA region that influence risk for RA. Our software is available on the website http://www.epigenetic.org/Linkage/ssgs-public/.     

Penalized Cox regression analysis in the high-dimensional and low-sample size settings, with applications to microarray gene expression data

MOTIVATION: An important application of microarray technology is to relate gene expression profiles to various clinical phenotypes of patients. Success has been demonstrated in molecular classification of cancer in which the gene expression data serve as predictors and different types of cancer serve as a categorical outcome variable. However, there has been less research in linking gene expression profiles to the censored survival data such as patients' overall survival time or time to cancer relapse. It would be desirable to have models with good prediction accuracy and parsimony property. RESULTS: We propose to use the L(1) penalized estimation for the Cox model to select genes that are relevant to patients' survival and to build a predictive model for future prediction. The computational difficulty associated with the estimation in the high-dimensional and low-sample size settings can be efficiently solved by using the recently developed least-angle regression (LARS) method. Our simulation studies and application to real datasets on predicting survival after chemotherapy for patients with diffuse large B-cell lymphoma demonstrate that the proposed procedure, which we call the LARS-Cox procedure, can be used for identifying important genes that are related to time to death due to cancer and for building a parsimonious model for predicting the survival of future patients. The LARS-Cox regression gives better predictive performance than the L(2) penalized regression and a few other dimension-reduction based methods. CONCLUSIONS: We conclude that the proposed LARS-Cox procedure can be very useful in identifying genes relevant to survival phenotypes and in building a parsimonious predictive model that can be used for classifying future patients into clinically relevant high- and low-risk groups based on the gene expression profile and survival times of previous patients.     

Bayesian Hierarchical Modeling and Selection of Differentially Expressed Genes for the EST Data

Summary Expressed sequence tag (EST) sequencing is a one‐pass sequencing reading of cloned cDNAs derived from a certain tissue. The frequency of unique tags among different unbiased cDNA libraries is used to infer the relative expression level of each tag. In this article, we propose a hierarchical multinomial model with a nonlinear Dirichlet prior for the EST data with multiple libraries and multiple types of tissues. A novel hierarchical prior is developed and the properties of the proposed prior are examined. An efficient Markov chain Monte Carlo algorithm is developed for carrying out the posterior computation. We also propose a new selection criterion for detecting which genes are differentially expressed between two tissue types. Our new method with the new gene selection criterion is demonstrated via several simulations to have low false negative and false positive rates. A real EST data set is used to motivate and illustrate the proposed method.     

Eigengene-based linear discriminant model for tumor classification using gene expression microarray data

MOTIVATION: The nearest shrunken centroids classifier has become a popular algorithm in tumor classification problems using gene expression microarray data. Feature selection is an embedded part of the method to select top-ranking genes based on a univariate distance statistic calculated for each gene individually. The univariate statistics summarize gene expression profiles outside of the gene co-regulation network context, leading to redundant information being included in the selection procedure. RESULTS: We propose an Eigengene-based Linear Discriminant Analysis (ELDA) to address gene selection in a multivariate framework. The algorithm uses a modified rotated Spectral Decomposition (SpD) technique to select 'hub' genes that associate with the most important eigenvectors. Using three benchmark cancer microarray datasets, we show that ELDA selects the most characteristic genes, leading to substantially smaller classifiers than the univariate feature selection based analogues. The resulting de-correlated expression profiles make the gene-wise independence assumption more realistic and applicable for the shrunken centroids classifier and other diagonal linear discriminant type of models. Our algorithm further incorporates a misclassification cost matrix, allowing differential penalization of one type of error over another. In the breast cancer data, we show false negative prognosis can be controlled via a cost-adjusted discriminant function. AVAILABILITY: R code for the ELDA algorithm is available from author upon request.     

Gene selection: a Bayesian variable selection approach

Selection of significant genes via expression patterns is an important problem in microarray experiments. Owing to small sample size and the large number of variables (genes), the selection process can be unstable. This paper proposes a hierarchical Bayesian model for gene (variable) selection. We employ latent variables to specialize the model to a regression setting and uses a Bayesian mixture prior to perform the variable selection. We control the size of the model by assigning a prior distribution over the dimension (number of significant genes) of the model. The posterior distributions of the parameters are not in explicit form and we need to use a combination of truncated sampling and Markov Chain Monte Carlo (MCMC) based computation techniques to simulate the parameters from the posteriors. The Bayesian model is flexible enough to identify significant genes as well as to perform future predictions. The method is applied to cancer classification via cDNA microarrays where the genes BRCA1 and BRCA2 are associated with a hereditary disposition to breast cancer, and the method is used to identify a set of significant genes. The method is also applied successfully to the leukemia data. SUPPLEMENTARY INFORMATION: http://stat.tamu.edu/people/faculty/bmallick.html.     

Disease gene identification by using graph kernels and Markov random fields

Genes associated with similar diseases are often functionally related. This principle is largely supported by many biological data sources, such as disease phenotype similarities, protein complexes, protein-protein interactions, pathways and gene expression profiles. Integrating multiple types of biological data is an effective method to identify disease genes for many genetic diseases. To capture the gene-disease associations based on biological networks, a kernel-based MRF method is proposed by combining graph kernels and the Markov random field (MRF) method. In the proposed method, three kinds of kernels are employed to describe the overall relationships of vertices in five biological networks, respectively, and a novel weighted MRF method is developed to integrate those data. In addition, an improved Gibbs sampling procedure and a novel parameter estimation method are proposed to generate predictions from the kernel-based MRF method. Numerical experiments are carried out by integrating known gene-disease associations, protein complexes, protein-protein interactions, pathways and gene expression profiles. The proposed kernel-based MRF method is evaluated by the leave-one-out cross validation paradigm, achieving an AUC score of 0.771 when integrating all those biological data in our experiments, which indicates that our proposed method is very promising compared with many existing methods.     

A Regression-Based Differential Expression Detection Algorithm for Microarray Studies with Ultra-Low Sample Size

Global gene expression analysis using microarrays and, more recently, RNA-seq, has allowed investigators to understand biological processes at a system level. However, the identification of differentially expressed genes in experiments with small sample size, high dimensionality, and high variance remains challenging, limiting the usability of these tens of thousands of publicly available, and possibly many more unpublished, gene expression datasets. We propose a novel variable selection algorithm for ultra-low-n microarray studies using generalized linear model-based variable selection with a penalized binomial regression algorithm called penalized Euclidean distance (PED). Our method uses PED to build a classifier on the experimental data to rank genes by importance. In place of cross-validation, which is required by most similar methods but not reliable for experiments with small sample size, we use a simulation-based approach to additively build a list of differentially expressed genes from the rank-ordered list. Our simulation-based approach maintains a low false discovery rate while maximizing the number of differentially expressed genes identified, a feature critical for downstream pathway analysis. We apply our method to microarray data from an experiment perturbing the Notch signaling pathway in Xenopus laevis embryos. This dataset was chosen because it showed very little differential expression according to limma, a powerful and widely-used method for microarray analysis. Our method was able to detect a significant number of differentially expressed genes in this dataset and suggest future directions for investigation. Our method is easily adaptable for analysis of data from RNA-seq and other global expression experiments with low sample size and high dimensionality.     

A top-r feature selection algorithm for microarray gene expression data

Most of the conventional feature selection algorithms have a drawback whereby a weakly ranked gene that could perform well in terms of classification accuracy with an appropriate subset of genes will be left out of the selection. Considering this shortcoming, we propose a feature selection algorithm in gene expression data analysis of sample classifications. The proposed algorithm first divides genes into subsets, the sizes of which are relatively small (roughly of size h), then selects informative smaller subsets of genes (of size r < h) from a subset and merges the chosen genes with another gene subset (of size r) to update the gene subset. We repeat this process until all subsets are merged into one informative subset. We illustrate the effectiveness of the proposed algorithm by analyzing three distinct gene expression data sets. Our method shows promising classification accuracy for all the test data sets. We also show the relevance of the selected genes in terms of their biological functions.     

Augmenting Microarray Data with Literature-Based Knowledge to Enhance Gene Regulatory Network Inference

Gene regulatory networks are a crucial aspect of systems biology in describing molecular mechanisms of the cell. Various computational models rely on random gene selection to infer such networks from microarray data. While incorporation of prior knowledge into data analysis has been deemed important, in practice, it has generally been limited to referencing genes in probe sets and using curated knowledge bases. We investigate the impact of augmenting microarray data with semantic relations automatically extracted from the literature, with the view that relations encoding gene/protein interactions eliminate the need for random selection of components in non-exhaustive approaches, producing a more accurate model of cellular behavior. A genetic algorithm is then used to optimize the strength of interactions using microarray data and an artificial neural network fitness function. The result is a directed and weighted network providing the individual contribution of each gene to its target. For testing, we used invasive ductile carcinoma of the breast to query the literature and a microarray set containing gene expression changes in these cells over several time points. Our model demonstrates significantly better fitness than the state-of-the-art model, which relies on an initial random selection of genes. Comparison to the component pathways of the KEGG Pathways in Cancer map reveals that the resulting networks contain both known and novel relationships. The p53 pathway results were manually validated in the literature. 60% of non-KEGG relationships were supported (74% for highly weighted interactions). The method was then applied to yeast data and our model again outperformed the comparison model. Our results demonstrate the advantage of combining gene interactions extracted from the literature in the form of semantic relations with microarray analysis in generating contribution-weighted gene regulatory networks. This methodology can make a significant contribution to understanding the complex interactions involved in cellular behavior and molecular physiology.     

Bayesian interaction selection model for multimodal neuroimaging data analysis

Multimodality or multiconstruct data arise increasingly in functional neuroimaging studies to characterize brain activity under different cognitive states. Relying on those high-resolution imaging collections, it is of great interest to identify predictive imaging markers and intermodality interactions with respect to behavior outcomes. Currently, most of the existing variable selection models do not consider predictive effects from interactions, and the desired higher-order terms can only be included in the predictive mechanism following a two-step procedure, suffering from potential misspecification. In this paper, we propose a unified Bayesian prior model to simultaneously identify main effect features and intermodality interactions within the same inference platform in the presence of high-dimensional data. To accommodate the brain topological information and correlation between modalities, our prior is designed by compiling the intermediate selection status of sequential partitions in light of the data structure and brain anatomical architecture, so that we can improve posterior inference and enhance biological plausibility. Through extensive simulations, we show the superiority of our approach in main and interaction effects selection, and prediction under multimodality data. Applying the method to the Adolescent Brain Cognitive Development (ABCD) study, we characterize the brain functional underpinnings with respect to general cognitive ability under different memory load conditions.     

Incorporating prior knowledge of gene functional groups into regularized discriminant analysis of microarray data

MOTIVATION: Discriminant analysis for high-dimensional and low-sample-sized data has become a hot research topic in bioinformatics, mainly motivated by its importance and challenge in applications to tumor classifications for high-dimensional microarray data. Two of the popular methods are the nearest shrunken centroids, also called predictive analysis of microarray (PAM), and shrunken centroids regularized discriminant analysis (SCRDA). Both methods are modifications to the classic linear discriminant analysis (LDA) in two aspects tailored to high-dimensional and low-sample-sized data: one is the regularization of the covariance matrix, and the other is variable selection through shrinkage. In spite of their usefulness, there are potential limitations with each method. The main concern is that both PAM and SCRDA are possibly too extreme: the covariance matrix in the former is restricted to be diagonal while in the latter there is barely any restriction. Based on the biology of gene functions and given the feature of the data, it may be beneficial to estimate the covariance matrix as an intermediate between the two; furthermore, more effective shrinkage schemes may be possible. RESULTS: We propose modified LDA methods to integrate biological knowledge of gene functions (or variable groups) into classification of microarray data. Instead of simply treating all the genes independently or imposing no restriction on the correlations among the genes, we group the genes according to their biological functions extracted from existing biological knowledge or data, and propose regularized covariance estimators that encourages between-group gene independence and within-group gene correlations while maintaining the flexibility of any general covariance structure. Furthermore, we propose a shrinkage scheme on groups of genes that tends to retain or remove a whole group of the genes altogether, in contrast to the standard shrinkage on individual genes. We show that one of the proposed methods performed better than PAM and SCRDA in a simulation study and several real data examples.