High-dimensional Genomic Data Research Articles

Imaging Informatics: 25 Years of Progress.

The science and applications of informatics in medical imaging have advanced dramatically in the past 25 years. This article provides a selective overview of key developments in medical imaging informatics. Advances in standards and technologies for compression and transmission of digital images have enabled Picture Archiving and Communications Systems (PACS) and teleradiology. Research in speech recognition, structured reporting, ontologies, and natural language processing has improved the ability to generate and analyze the reports of imaging procedures. Informatics has provided tools to address workflow and ergonomic issues engendered by the growing volume of medical image information. Research in computeraided detection and diagnosis of abnormalities in medical images has opened new avenues to improve patient care. The growing number of medical-imaging examinations and their large volumes of information create a natural platform for "big data" analytics, particularly when joined with high-dimensional genomic data. Radiogenomics investigates relationships between a disease's genetic and gene-expression characteristics and its imaging phenotype; this emerging field promises to help us better understand disease biology, prognosis, and treatment options. The next 25 years offer remarkable opportunities for informatics and medical imaging together to lead to further advances in both disciplines and to improve health.

Context Specific and Differential Gene Co-expression Networks via Bayesian Biclustering.

Identifying latent structure in high-dimensional genomic data is essential for exploring biological processes. Here, we consider recovering gene co-expression networks from gene expression data, where each network encodes relationships between genes that are co-regulated by shared biological mechanisms. To do this, we develop a Bayesian statistical model for biclustering to infer subsets of co-regulated genes that covary in all of the samples or in only a subset of the samples. Our biclustering method, BicMix, allows overcomplete representations of the data, computational tractability, and joint modeling of unknown confounders and biological signals. Compared with related biclustering methods, BicMix recovers latent structure with higher precision across diverse simulation scenarios as compared to state-of-the-art biclustering methods. Further, we develop a principled method to recover context specific gene co-expression networks from the estimated sparse biclustering matrices. We apply BicMix to breast cancer gene expression data and to gene expression data from a cardiovascular study cohort, and we recover gene co-expression networks that are differential across ER+ and ER- samples and across male and female samples. We apply BicMix to the Genotype-Tissue Expression (GTEx) pilot data, and we find tissue specific gene networks. We validate these findings by using our tissue specific networks to identify trans-eQTLs specific to one of four primary tissues.

Comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering.

Comparing large covariance matrices has important applications in modern genomics, where scientists are often interested in understanding whether relationships (e.g., dependencies or co-regulations) among a large number of genes vary between different biological states. We propose a computationally fast procedure for testing the equality of two large covariance matrices when the dimensions of the covariance matrices are much larger than the sample sizes. A distinguishing feature of the new procedure is that it imposes no structural assumptions on the unknown covariance matrices. Hence, the test is robust with respect to various complex dependence structures that frequently arise in genomics. We prove that the proposed procedure is asymptotically valid under weak moment conditions. As an interesting application, we derive a new gene clustering algorithm which shares the same nice property of avoiding restrictive structural assumptions for high-dimensional genomics data. Using an asthma gene expression dataset, we illustrate how the new test helps compare the covariance matrices of the genes across different gene sets/pathways between the disease group and the control group, and how the gene clustering algorithm provides new insights on the way gene clustering patterns differ between the two groups. The proposed methods have been implemented in an R-package HDtest and are available on CRAN.

Genome-wide prediction using Bayesian additive regression trees

BackgroundThe goal of genome-wide prediction (GWP) is to predict phenotypes based on marker genotypes, often obtained through single nucleotide polymorphism (SNP) chips. The major problem with GWP is high-dimensional data from many thousands of SNPs scored on several thousands of individuals. A large number of methods have been developed for GWP, which are mostly parametric methods that assume statistical linearity and only additive genetic effects. The Bayesian additive regression trees (BART) method was recently proposed and is based on the sum of nonparametric regression trees with the priors being used to regularize the parameters. Each regression tree is based on a recursive binary partitioning of the predictor space that approximates an unknown function, which will automatically model nonlinearities within SNPs (dominance) and interactions between SNPs (epistasis). In this study, we introduced BART and compared its predictive performance with that of the LASSO, Bayesian LASSO (BLASSO), genomic best linear unbiased prediction (GBLUP), reproducing kernel Hilbert space (RKHS) regression and random forest (RF) methods.ResultsTests on the QTLMAS2010 simulated data, which are mainly based on additive genetic effects, show that cross-validated optimization of BART provides a smaller prediction error than the RF, BLASSO, GBLUP and RKHS methods, and is almost as accurate as the LASSO method. If dominance and epistasis effects are added to the QTLMAS2010 data, the accuracy of BART relative to the other methods was increased. We also showed that BART can produce importance measures on the SNPs through variable inclusion proportions. In evaluations using real data on pigs, the prediction error was smaller with BART than with the other methods.ConclusionsBART was shown to be an accurate method for GWP, in which the regression trees guarantee a very sparse representation of additive and complex non-additive genetic effects. Moreover, the Markov chain Monte Carlo algorithm with Bayesian back-fitting provides a computationally efficient procedure that is suitable for high-dimensional genomic data.Electronic supplementary materialThe online version of this article (doi:10.1186/s12711-016-0219-8) contains supplementary material, which is available to authorized users.

Complex heatmaps reveal patterns and correlations in multidimensional genomic data.

Parallel heatmaps with carefully designed annotation graphics are powerful for efficient visualization of patterns and relationships among high dimensional genomic data. Here we present the ComplexHeatmap package that provides rich functionalities for customizing heatmaps, arranging multiple parallel heatmaps and including user-defined annotation graphics. We demonstrate the power of ComplexHeatmap to easily reveal patterns and correlations among multiple sources of information with four real-world datasets. The ComplexHeatmap package and documentation are freely available from the Bioconductor project: http://www.bioconductor.org/packages/devel/bioc/html/ComplexHeatmap.html m.schlesner@dkfz.de Supplementary data are available at Bioinformatics online.

Convex biclustering.

In the biclustering problem, we seek to simultaneously group observations and features. While biclustering has applications in a wide array of domains, ranging from text mining to collaborative filtering, the problem of identifying structure in high-dimensional genomic data motivates this work. In this context, biclustering enables us to identify subsets of genes that are co-expressed only within a subset of experimental conditions. We present a convex formulation of the biclustering problem that possesses a unique global minimizer and an iterative algorithm, COBRA, that is guaranteed to identify it. Our approach generates an entire solution path of possible biclusters as a single tuning parameter is varied. We also show how to reduce the problem of selecting this tuning parameter to solving a trivial modification of the convex biclustering problem. The key contributions of our work are its simplicity, interpretability, and algorithmic guarantees-features that arguably are lacking in the current alternative algorithms. We demonstrate the advantages of our approach, which includes stably and reproducibly identifying biclusterings, on simulated and real microarray data.

High-dimensional genomic data bias correction and data integration using MANCIE.

High-dimensional genomic data analysis is challenging due to noises and biases in high-throughput experiments. We present a computational method matrix analysis and normalization by concordant information enhancement (MANCIE) for bias correction and data integration of distinct genomic profiles on the same samples. MANCIE uses a Bayesian-supported principal component analysis-based approach to adjust the data so as to achieve better consistency between sample-wise distances in the different profiles. MANCIE can improve tissue-specific clustering in ENCODE data, prognostic prediction in Molecular Taxonomy of Breast Cancer International Consortium and The Cancer Genome Atlas data, copy number and expression agreement in Cancer Cell Line Encyclopedia data, and has broad applications in cross-platform, high-dimensional data integration.

Identification of genomic markers correlated with sensitivity in solid tumors to Dasatinib using sparse principal components

ABSTRACT Differential analysis techniques are commonly used to offer scientists a dimension reduction procedure and an interpretable gateway to variable selection, especially when confronting high-dimensional genomic data. Huang et al. used a gene expression profile of breast cancer cell lines to identify genomic markers which are highly correlated with in vitro sensitivity of a drug Dasatinib. They considered three statistical methods to identify differentially expressed genes and finally used the results from the intersection. But the statistical methods that are used in the paper are not sufficient to select the genomic markers. In this paper we used three alternative statistical methods to select a combined list of genomic markers and compared the genes that were proposed by Huang et al. We then proposed to use sparse principal component analysis (Sparse PCA) to identify a final list of genomic markers. The Sparse PCA incorporates correlation into account among the genes and helps to draw a successful genomic markers discovery. We present a new and a small set of genomic markers to separate out the groups of patients effectively who are sensitive to the drug Dasatinib. The analysis procedure will also encourage scientists in identifying genomic markers that can help to separate out two groups.

Abstract B24: High-dimensional genomic data integration and bias correction using MANCIE

Abstract Most genomic and epigenomic experimental data are presented as high-dimensional matrices. Integrative analysis of such high-dimensional genomic data is challenging due to noises and biases in the high-throughput experiments from different platforms. We present MANCIE (Matrix Analysis and Normalization by Concordant Information Enhancement), a computational method for integrating two genomic datasets based on a Bayesian supported principal component analysis (PCA) approach. We demonstrate that data integration using MANCIE can reduce biases and improve the identification of tissue specificity from the Encyclopedia of DNA Elements (ENCODE) data, improve prognostic prediction from The Cancer Genome Atlas (TCGA) data, and improve the identification of genetic correlation in the Cancer Cell Line Encyclopedia (CCLE) data. MANCIE has broad applications in genomic and epigenomic data analysis in cancer research. Citation Format: Chongzhi Zang, Tao Wang, Ke Deng, Bo Li, Sheng'en Hu, Qian Qin, Tengfei Xiao, Shihua Zhang, Clifford A. Meyer, Housheng Hansen He, Myles Brown, Jun S. Liu, Yang Xie, Xiaole Shirley Liu. High-dimensional genomic data integration and bias correction using MANCIE. [abstract]. In: Proceedings of the AACR Special Conference on Chromatin and Epigenetics in Cancer; Sep 24-27, 2015; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2016;76(2 Suppl):Abstract nr B24.

Efficient Regularized Regression with L0 Penalty for Variable Selection and Network Construction.

Variable selections for regression with high-dimensional big data have found many applications in bioinformatics and computational biology. One appealing approach is the L 0 regularized regression which penalizes the number of nonzero features in the model directly. However, it is well known that L 0 optimization is NP-hard and computationally challenging. In this paper, we propose efficient EM (L 0EM) and dual L 0EM (DL 0EM) algorithms that directly approximate the L 0 optimization problem. While L 0EM is efficient with large sample size, DL 0EM is efficient with high-dimensional (n ≪ m) data. They also provide a natural solution to all L p p ∈ [0,2] problems, including lasso with p = 1 and elastic net with p ∈ [1,2]. The regularized parameter λ can be determined through cross validation or AIC and BIC. We demonstrate our methods through simulation and high-dimensional genomic data. The results indicate that L 0 has better performance than lasso, SCAD, and MC+, and L 0 with AIC or BIC has similar performance as computationally intensive cross validation. The proposed algorithms are efficient in identifying the nonzero variables with less bias and constructing biologically important networks with high-dimensional big data.

Multiple Group Testing Procedures for Analysis of High-Dimensional Genomic Data.

In genetic association studies with high-dimensional genomic data, multiple group testing procedures are often required in order to identify disease/trait-related genes or genetic regions, where multiple genetic sites or variants are located within the same gene or genetic region. However, statistical testing procedures based on an individual test suffer from multiple testing issues such as the control of family-wise error rate and dependent tests. Moreover, detecting only a few of genes associated with a phenotype outcome among tens of thousands of genes is of main interest in genetic association studies. In this reason regularization procedures, where a phenotype outcome regresses on all genomic markers and then regression coefficients are estimated based on a penalized likelihood, have been considered as a good alternative approach to analysis of high-dimensional genomic data. But, selection performance of regularization procedures has been rarely compared with that of statistical group testing procedures. In this article, we performed extensive simulation studies where commonly used group testing procedures such as principal component analysis, Hotelling's T2 test, and permutation test are compared with group lasso (least absolute selection and shrinkage operator) in terms of true positive selection. Also, we applied all methods considered in simulation studies to identify genes associated with ovarian cancer from over 20,000 genetic sites generated from Illumina Infinium HumanMethylation27K Beadchip. We found a big discrepancy of selected genes between multiple group testing procedures and group lasso.

Recursive Random Lasso (RRLasso) for Identifying Anti-Cancer Drug Targets.

Uncovering driver genes is crucial for understanding heterogeneity in cancer. L 1-type regularization approaches have been widely used for uncovering cancer driver genes based on genome-scale data. Although the existing methods have been widely applied in the field of bioinformatics, they possess several drawbacks: subset size limitations, erroneous estimation results, multicollinearity, and heavy time consumption. We introduce a novel statistical strategy, called a Recursive Random Lasso (RRLasso), for high dimensional genomic data analysis and investigation of driver genes. For time-effective analysis, we consider a recursive bootstrap procedure in line with the random lasso. Furthermore, we introduce a parametric statistical test for driver gene selection based on bootstrap regression modeling results. The proposed RRLasso is not only rapid but performs well for high dimensional genomic data analysis. Monte Carlo simulations and analysis of the “Sanger Genomics of Drug Sensitivity in Cancer dataset from the Cancer Genome Project” show that the proposed RRLasso is an effective tool for high dimensional genomic data analysis. The proposed methods provide reliable and biologically relevant results for cancer driver gene selection.

A novel sparse coding algorithm for classification of tumors based on gene expression data.

High-dimensional genomic and proteomic data play an important role in many applications in medicine such as prognosis of diseases, diagnosis, prevention and molecular biology, to name a few. Classifying such data is a challenging task due to the various issues such as curse of dimensionality, noise and redundancy. Recently, some researchers have used the sparse representation (SR) techniques to analyze high-dimensional biological data in various applications in classification of cancer patients based on gene expression datasets. A common problem with all SR-based biological data classification methods is that they cannot utilize the topological (geometrical) structure of data. More precisely, these methods transfer the data into sparse feature space without preserving the local structure of data points. In this paper, we proposed a novel SR-based cancer classification algorithm based on gene expression data that takes into account the geometrical information of all data. Precisely speaking, we incorporate the local linear embedding algorithm into the sparse coding framework, by which we can preserve the geometrical structure of all data. For performance comparison, we applied our algorithm on six tumor gene expression datasets, by which we demonstrate that the proposed method achieves higher classification accuracy than state-of-the-art SR-based tumor classification algorithms.

An Independent Filter for Gene Set Testing Based on Spectral Enrichment.

Gene set testing has become an indispensable tool for the analysis of high-dimensional genomic data. An important motivation for testing gene sets, rather than individual genomic variables, is to improve statistical power by reducing the number of tested hypotheses. Given the dramatic growth in common gene set collections, however, testing is often performed with nearly as many gene sets as underlying genomic variables. To address the challenge to statistical power posed by large gene set collections, we have developed spectral gene set filtering (SGSF), a novel technique for independent filtering of gene set collections prior to gene set testing. The SGSF method uses as a filter statistic the p-value measuring the statistical significance of the association between each gene set and the sample principal components (PCs), taking into account the significance of the associated eigenvalues. Because this filter statistic is independent of standard gene set test statistics under the null hypothesis but dependent under the alternative, the proportion of enriched gene sets is increased without impacting the type I error rate. As shown using simulated and real gene expression data, the SGSF algorithm accurately filters gene sets unrelated to the experimental outcome resulting in significantly increased gene set testing power.

Principal component gene set enrichment (PCGSE).

BackgroundAlthough principal component analysis (PCA) is widely used for the dimensional reduction of biomedical data, interpretation of PCA results remains daunting. Most existing interpretation methods attempt to explain each principal component (PC) in terms of a small number of variables by generating approximate PCs with mainly zero loadings. Although useful when just a few variables dominate the population PCs, these methods can perform poorly on genomic data, where interesting biological features are frequently represented by the combined signal of functionally related sets of genes. While gene set testing methods have been widely used in supervised settings to quantify the association of groups of genes with clinical outcomes, these methods have seen only limited application for testing the enrichment of gene sets relative to sample PCs.ResultsWe describe a novel approach, principal component gene set enrichment (PCGSE), for unsupervised gene set testing relative to the sample PCs of genomic data. The PCGSE method computes the statistical association between gene sets and individual PCs using a two-stage competitive gene set test. To demonstrate the efficacy of the PCGSE method, we use simulated and real gene expression data to evaluate the performance of various gene set test statistics and significance tests.ConclusionsGene set testing is an effective approach for interpreting the PCs of high-dimensional genomic data. As shown using both simulated and real datasets, the PCGSE method can generate biologically meaningful and computationally efficient results via a two-stage, competitive parametric test that correctly accounts for inter-gene correlation.Electronic supplementary materialThe online version of this article (doi:10.1186/s13040-015-0059-z) contains supplementary material, which is available to authorized users.

MAD Bayes for Tumor Heterogeneity—Feature Allocation With Exponential Family Sampling

We propose small-variance asymptotic approximations for inference on tumor heterogeneity (TH) using next-generation sequencing data. Understanding TH is an important and open research problem in biology. The lack of appropriate statistical inference is a critical gap in existing methods that the proposed approach aims to fill. We build on a hierarchical model with an exponential family likelihood and a feature allocation prior. The proposed implementation of posterior inference generalizes similar small-variance approximations proposed by Kulis and Jordan and Broderick, Kulis, and Jordan for inference with Dirichlet process mixture and Indian buffet process prior models under normal sampling. We show that the new algorithm can successfully recover latent structures of different haplotypes and subclones and is magnitudes faster than available Markov chain Monte Carlo samplers. The latter are practically infeasible for high-dimensional genomics data. The proposed approach is scalable, easy to implement, and benefits from the flexibility of Bayesian nonparametric models. More importantly, it provides a useful tool for applied scientists to estimate cell subtypes in tumor samples. R code is available on http://www.ma.utexas.edu/users/yxu/. Supplementary materials for this article are available online.

Spectral gene set enrichment (SGSE).

BackgroundGene set testing is typically performed in a supervised context to quantify the association between groups of genes and a clinical phenotype. In many cases, however, a gene set-based interpretation of genomic data is desired in the absence of a phenotype variable. Although methods exist for unsupervised gene set testing, they predominantly compute enrichment relative to clusters of the genomic variables with performance strongly dependent on the clustering algorithm and number of clusters.ResultsWe propose a novel method, spectral gene set enrichment (SGSE), for unsupervised competitive testing of the association between gene sets and empirical data sources. SGSE first computes the statistical association between gene sets and principal components (PCs) using our principal component gene set enrichment (PCGSE) method. The overall statistical association between each gene set and the spectral structure of the data is then computed by combining the PC-level p-values using the weighted Z-method with weights set to the PC variance scaled by Tracy-Widom test p-values. Using simulated data, we show that the SGSE algorithm can accurately recover spectral features from noisy data. To illustrate the utility of our method on real data, we demonstrate the superior performance of the SGSE method relative to standard cluster-based techniques for testing the association between MSigDB gene sets and the variance structure of microarray gene expression data.ConclusionsUnsupervised gene set testing can provide important information about the biological signal held in high-dimensional genomic data sets. Because it uses the association between gene sets and samples PCs to generate a measure of unsupervised enrichment, the SGSE method is independent of cluster or network creation algorithms and, most importantly, is able to utilize the statistical significance of PC eigenvalues to ignore elements of the data most likely to represent noise.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0490-7) contains supplementary material, which is available to authorized users.

Assessing the effects of multiple markers in genetic association studies.

Assessing the effects of multiple markers in genetic association studies.

HCsnip: An R Package for Semi-supervised Snipping of the Hierarchical Clustering Tree.

Hierarchical clustering (HC) is one of the most frequently used methods in computational biology in the analysis of high-dimensional genomics data. Given a data set, HC outputs a binary tree leaves of which are the data points and internal nodes represent clusters of various sizes. Normally, a fixed-height cut on the HC tree is chosen, and each contiguous branch of data points below that height is considered as a separate cluster. However, the fixed-height branch cut may not be ideal in situations where one expects a complicated tree structure with nested clusters. Furthermore, due to lack of utilization of related background information in selecting the cutoff, induced clusters are often difficult to interpret. This paper describes a novel procedure that aims to automatically extract meaningful clusters from the HC tree in a semi-supervised way. The procedure is implemented in the R package HCsnip available from Bioconductor. Rather than cutting the HC tree at a fixed-height, HCsnip probes the various way of snipping, possibly at variable heights, to tease out hidden clusters ensconced deep down in the tree. The cluster extraction process utilizes, along with the data set from which the HC tree is derived, commonly available background information. Consequently, the extracted clusters are highly reproducible and robust against various sources of variations that “haunted” high-dimensional genomics data. Since the clustering process is guided by the background information, clusters are easy to interpret. Unlike existing packages, no constraint is placed on the data type on which clustering is desired. Particularly, the package accepts patient follow-up data for guiding the cluster extraction process. To our knowledge, HCsnip is the first package that is able to decomposes the HC tree into clusters with piecewise snipping under the guidance of patient time-to-event information. Our implementation of the semi-supervised HC tree snipping framework is generic, and can be combined with other algorithms that operate on detected clusters.

Comparison of dimension reduction-based logistic regression models for case-control genome-wide association study: principal components analysis vs. partial least squares.

With recent advances in biotechnology, genome-wide association study (GWAS) has been widely used to identify genetic variants that underlie human complex diseases and traits. In case-control GWAS, typical statistical strategy is traditional logistical regression (LR) based on single-locus analysis. However, such a single-locus analysis leads to the well-known multiplicity problem, with a risk of inflating type I error and reducing power. Dimension reduction-based techniques, such as principal component-based logistic regression (PC-LR), partial least squares-based logistic regression (PLS-LR), have recently gained much attention in the analysis of high dimensional genomic data. However, the performance of these methods is still not clear, especially in GWAS. We conducted simulations and real data application to compare the type I error and power of PC-LR, PLS-LR and LR applicable to GWAS within a defined single nucleotide polymorphism (SNP) set region. We found that PC-LR and PLS can reasonably control type I error under null hypothesis. On contrast, LR, which is corrected by Bonferroni method, was more conserved in all simulation settings. In particular, we found that PC-LR and PLS-LR had comparable power and they both outperformed LR, especially when the causal SNP was in high linkage disequilibrium with genotyped ones and with a small effective size in simulation. Based on SNP set analysis, we applied all three methods to analyze non-small cell lung cancer GWAS data.