Quantitative set analysis for gene expression: a method to quantify gene set differential expression including gene-gene correlations

Enrichment analysis of gene sets is a popular approach that provides a functional interpretation of genome-wide expression data. Existing tests are affected by inter-gene correlations, resulting in a high Type I error. The most widely used test, Gene Set Enrichment Analysis, relies on computationally intensive permutations of sample labels to generate a null distribution that preserves gene–gene correlations. A more recent approach, CAMERA, attempts to correct for these correlations by estimating a variance inflation factor directly from the data. Although these methods generate P-values for detecting gene set activity, they are unable to produce confidence intervals or allow for post hoc comparisons. We have developed a new computational framework for Quantitative Set Analysis of Gene Expression (QuSAGE). QuSAGE accounts for inter-gene correlations, improves the estimation of the variance inflation factor and, rather than evaluating the deviation from a null hypothesis with a P-value, it quantifies gene-set activity with a complete probability density function. From this probability density function, P-values and confidence intervals can be extracted and post hoc analysis can be carried out while maintaining statistical traceability. Compared with Gene Set Enrichment Analysis and CAMERA, QuSAGE exhibits better sensitivity and specificity on real data profiling the response to interferon therapy (in chronic Hepatitis C virus patients) and Influenza A virus infection. QuSAGE is available as an R package, which includes the core functions for the method as well as functions to plot and visualize the results.     

EDDY: a novel statistical gene set test method to detect differential genetic dependencies

Identifying differential features between conditions is a popular approach to understanding molecular features and their mechanisms underlying a biological process of particular interest. Although many tests for identifying differential expression of gene or gene sets have been proposed, there was limited success in developing methods for differential interactions of genes between conditions because of its computational complexity. We present a method for Evaluation of Dependency DifferentialitY (EDDY), which is a statistical test for differential dependencies of a set of genes between two conditions. Unlike previous methods focused on differential expression of individual genes or correlation changes of individual gene–gene interactions, EDDY compares two conditions by evaluating the probability distributions of dependency networks from genes. The method has been evaluated and compared with other methods through simulation studies, and application to glioblastoma multiforme data resulted in informative cancer and glioblastoma multiforme subtype-related findings. The comparison with Gene Set Enrichment Analysis, a differential expression-based method, revealed that EDDY identifies the gene sets that are complementary to those identified by Gene Set Enrichment Analysis. EDDY also showed much lower false positives than Gene Set Co-expression Analysis, a method based on correlation changes of individual gene–gene interactions, thus providing more informative results. The Java implementation of the algorithm is freely available to noncommercial users. Download from: http://biocomputing.tgen.org/software/EDDY.     

A computational approach to measuring coherence of gene expression in pathways

This study uses a computational approach to analyze coherence of expression of genes in pathways. Microarray data were analyzed with respect to coherent gene expression in a group of genes defined as a pathway in the Kyoto Encyclopedia of Genes and Genomes (KEGG) database. Our hypothesis is that genes in the same pathway are more likely to be coordinately regulated than a randomly selected gene set. A correlation coefficient for each pair of genes in a pathway was estimated based on gene expression in normal or tumor samples, and statistically significant correlation coefficients were identified. The coherence indicator was defined as the ratio of the number of gene pairs in the pathway whose correlation coefficients are significant, divided by the total number of gene pairs in the pathway. We defined all genes that appeared in the KEGG pathways as a reference gene set. Our analysis indicated that the mean coherence indicator of pathways is significantly larger than the mean coherence indicator of random gene sets drawn from the reference gene set. Thus, the result supports our hypothesis. The significance of each individual pathway of n genes was evaluated by comparing its coherence indicator with coherence indicators of 1000 random permutation sets of n genes chosen from the reference gene set. We analyzed three data sets: two Affymetrix microarrays and one cDNA microarray. For each of the three data sets, statistically significant pathways were identified among all KEGG pathways. Seven of 96 pathways had a significant coherence indicator in normal tissue and 14 of 96 pathways had a significant coherence indicator in tumor tissue in all three data sets. The increase in the number of pathways with significant coherence indicators may reflect the fact that tumor cells have a higher rate of metabolism than normal cells. Five pathways involved in oxidative phosphorylation, ATP synthesis, protein synthesis, or RNA synthesis were coherent in both normal and tumor tissue, demonstrating that these are essential genes, a high level of expression of which is required regardless of cell type.     

Detection of differentially expressed gene sets in a partially paired microarray data set

Partially paired data sets often occur in microarray experiments (Kim et al., 2005; Liu, Liang and Jang, 2006). Discussions of testing with partially paired data are found in the literature (Lin and Stivers 1974; Ekbohm, 1976; Bhoj, 1978). Bhoj (1978) initially proposed a test statistic that uses a convex combination of paired and unpaired t statistics. Kim et al. (2005) later proposed the t3 statistic, which is a linear combination of paired and unpaired t statistics, and then used it to detect differentially expressed (DE) genes in colorectal cancer (CRC) cDNA microarray data. In this paper, we extend Kim et al.'s t3 statistic to the Hotelling's T2 type statistic Tp for detecting DE gene sets of size p. We employ Efron's empirical null principle to incorporate inter-gene correlation in the estimation of the false discovery rate. Then, the proposed Tp statistic is applied to Kim et al's CRC data to detect the DE gene sets of sizes p=2 and p=3. Our results show that for small p, particularly for p=2 and marginally for p=3, the proposed Tp statistic compliments the univariate procedure by detecting additional DE genes that were undetected in the univariate test procedure. We also conduct a simulation study to demonstrate that Efron's empirical null principle is robust to the departure from the normal assumption.     

Normality of oligonucleotide microarray data and implications for parametric statistical analyses

MOTIVATION: Experimental limitations have resulted in the popularity of parametric statistical tests as a method for identifying differentially regulated genes in microarray data sets. However, these tests assume that the data follow a normal distribution. To date, the assumption that replicate expression values for any gene are normally distributed, has not been critically addressed for Affymetrix GeneChip data. RESULTS: The normality of the expression values calculated using four different commercial and academic software packages was investigated using a data set consisting of the same target RNA applied to 59 human Affymetrix U95A GeneChips using a combination of statistical tests and visualization techniques. For the majority of probe sets obtained from each analysis suite, the expression data showed a good correlation with normality. The exception was a large number of low-expressed genes in the data set produced using Affymetrix Microarray Suite 5.0, which showed a striking non-normal distribution. In summary, our data provide strong support for the application of parametric tests to GeneChip data sets without the need for data transformation.     

Genome-wide co-expression based prediction of differential expressions

MOTIVATION: Microarrays have been widely used for medical studies to detect novel disease-related genes. They enable us to study differential gene expressions at a genomic level. They also provide us with informative genome-wide co-expressions. Although many statistical methods have been proposed for identifying differentially expressed genes, genome-wide co-expressions have not been well considered for this issue. Incorporating genome-wide co-expression information in the differential expression analysis may improve the detection of disease-related genes. RESULTS: In this study, we proposed a statistical method for predicting differential expressions through the local regression between differential expression and co-expression measures. The smoother span parameter was determined by optimizing the rank correlation between the observed and predicted differential expression measures. A mixture normal quantile-based method was used to transform data. We used the gene-specific permutation procedure to evaluate the significance of a prediction. Two published microarray data sets were analyzed for applications. For the data set collected for a prostate cancer study, the proposed method identified many genes with weak differential expressions. Several of these genes have been shown in literature to be associated with the disease. For the data set collected for a type 2 diabetes study, no significant genes could be identified by the traditional methods. However, the proposed method identified many genes with significantly low false discovery rates. AVAILABILITY: The R codes are freely available at http://home.gwu.edu/~ylai/research/CoDiff, where the gene lists ranked by our method are also provided as the Supplementary Material.     

Pathway-directed weighted testing procedures for the integrative analysis of gene expression and metabolomic data

We explore the utility of p-value weighting for enhancing the power to detect differential metabolites in a two-sample setting. Related gene expression information is used to assign an a priori importance level to each metabolite being tested. We map the gene expression to a metabolite through pathways and then gene expression information is summarized per-pathway using gene set enrichment tests. Through simulation we explore four styles of enrichment tests and four weight functions to convert the gene information into a meaningful p-value weight. We implement the p-value weighting on a prostate cancer metabolomic dataset. Gene expression on matched samples is used to construct the weights. Under certain regulatory conditions, the use of weighted p-values does not inflate the type I error above what we see for the un-weighted tests except in high correlation situations. The power to detect differential metabolites is notably increased in situations with disjoint pathways and shows moderate improvement, relative to the proportion of enriched pathways, when pathway membership overlaps.     

Analysis of sample set enrichment scores: assaying the enrichment of sets of genes for individual samples in genome-wide expression profiles

MOTIVATION: Gene expression profiling experiments in cell lines and animal models characterized by specific genetic or molecular perturbations have yielded sets of genes annotated by the perturbation. These gene sets can serve as a reference base for interrogating other expression datasets. For example, a new dataset in which a specific pathway gene set appears to be enriched, in terms of multiple genes in that set evidencing expression changes, can then be annotated by that reference pathway. We introduce in this paper a formal statistical method to measure the enrichment of each sample in an expression dataset. This allows us to assay the natural variation of pathway activity in observed gene expression data sets from clinical cancer and other studies. RESULTS: Validation of the method and illustrations of biological insights gleaned are demonstrated on cell line data, mouse models, and cancer-related datasets. Using oncogenic pathway signatures, we show that gene sets built from a model system are indeed enriched in the model system. We employ ASSESS for the use of molecular classification by pathways. This provides an accurate classifier that can be interpreted at the level of pathways instead of individual genes. Finally, ASSESS can be used for cross-platform expression models where data on the same type of cancer are integrated over different platforms into a space of enrichment scores. AVAILABILITY: Versions are available in Octave and Java (with a graphical user interface). Software can be downloaded at http://people.genome.duke.edu/assess.     

MetaGSCA: A tool for meta-analysis of gene set differential coexpression

Analyses of gene set differential coexpression may shed light on molecular mechanisms underlying phenotypes and diseases. However, differential coexpression analyses of conceptually similar individual studies are often inconsistent and underpowered to provide definitive results. Researchers can greatly benefit from an open-source application facilitating the aggregation of evidence of differential coexpression across studies and the estimation of more robust common effects. We developed Meta Gene Set Coexpression Analysis (MetaGSCA), an analytical tool to systematically assess differential coexpression of an a priori defined gene set by aggregating evidence across studies to provide a definitive result. In the kernel, a nonparametric approach that accounts for the gene-gene correlation structure is used to test whether the gene set is differentially coexpressed between two comparative conditions, from which a permutation test p-statistic is computed for each individual study. A meta-analysis is then performed to combine individual study results with one of two options: a random-intercept logistic regression model or the inverse variance method. We demonstrated MetaGSCA in case studies investigating two human diseases and identified pathways highly relevant to each disease across studies. We further applied MetaGSCA in a pan-cancer analysis with hundreds of major cellular pathways in 11 cancer types. The results indicated that a majority of the pathways identified were dysregulated in the pan-cancer scenario, many of which have been previously reported in the cancer literature. Our analysis with randomly generated gene sets showed excellent specificity, indicating that the significant pathways/gene sets identified by MetaGSCA are unlikely false positives. MetaGSCA is a user-friendly tool implemented in both forms of a Web-based application and an R package “MetaGSCA”. It enables comprehensive meta-analyses of gene set differential coexpression data, with an optional module of post hoc pathway crosstalk network analysis to identify and visualize pathways having similar coexpression profiles.     

Analyzing gene expression data in terms of gene sets: methodological issues

MOTIVATION: Many statistical tests have been proposed in recent years for analyzing gene expression data in terms of gene sets, usually from Gene Ontology. These methods are based on widely different methodological assumptions. Some approaches test differential expression of each gene set against differential expression of the rest of the genes, whereas others test each gene set on its own. Also, some methods are based on a model in which the genes are the sampling units, whereas others treat the subjects as the sampling units. This article aims to clarify the assumptions behind different approaches and to indicate a preferential methodology of gene set testing. RESULTS: We identify some crucial assumptions which are needed by the majority of methods. P-values derived from methods that use a model which takes the genes as the sampling unit are easily misinterpreted, as they are based on a statistical model that does not resemble the biological experiment actually performed. Furthermore, because these models are based on a crucial and unrealistic independence assumption between genes, the P-values derived from such methods can be wildly anti-conservative, as a simulation experiment shows. We also argue that methods that competitively test each gene set against the rest of the genes create an unnecessary rift between single gene testing and gene set testing.     

Nonparametric testing for DNA copy number induced differential mRNA gene expression

Summary .  The central dogma of molecular biology relates DNA with mRNA. Array CGH measures DNA copy number and gene expression microarrays measure the amount of mRNA. Methods that integrate data from these two platforms may uncover meaningful biological relationships that further our understanding of cancer. We develop nonparametric tests for the detection of copy number induced differential gene expression. The tests incorporate the uncertainty of the calling of genomic aberrations. The test is preceded by a "tuning algorithm" that discards certain genes to improve the overall power of the false discovery rate selection procedure. Moreover, the test statistics are "shrunken" to borrow information across neighboring genes that share the same array CGH signature. For each gene we also estimate its effect, its amount of differential expression due to copy number changes, and calculate the coefficient of determination. The method is illustrated on breast cancer data, in which it confirms previously reported findings, now with a more profound statistical underpinning.     

Dissection of Regulatory Networks that Are Altered in Disease via Differential Co-expression

Comparing the gene-expression profiles of sick and healthy individuals can help in understanding disease. Such differential expression analysis is a well-established way to find gene sets whose expression is altered in the disease. Recent approaches to gene-expression analysis go a step further and seek differential co-expression patterns, wherein the level of co-expression of a set of genes differs markedly between disease and control samples. Such patterns can arise from a disease-related change in the regulatory mechanism governing that set of genes, and pinpoint dysfunctional regulatory networks.Here we present DICER, a new method for detecting differentially co-expressed gene sets using a novel probabilistic score for differential correlation. DICER goes beyond standard differential co-expression and detects pairs of modules showing differential co-expression. The expression profiles of genes within each module of the pair are correlated across all samples. The correlation between the two modules, however, differs markedly between the disease and normal samples.We show that DICER outperforms the state of the art in terms of significance and interpretability of the detected gene sets. Moreover, the gene sets discovered by DICER manifest regulation by disease-specific microRNA families. In a case study on Alzheimer''s disease, DICER dissected biological processes and protein complexes into functional subunits that are differentially co-expressed, thereby revealing inner structures in disease regulatory networks.     

Estimation of false discovery proportion under general dependence

MOTIVATION: Wide-scale correlations between genes are commonly observed in gene expression data, due to both biological and technical reasons. These correlations increase the variability of the standard estimate of the false discovery rate (FDR). We highlight the false discovery proportion (FDP, instead of the FDR) as the suitable quantity for assessing differential expression in microarray data, demonstrate the deleterious effects of correlation on FDP estimation and propose an improved estimation method that accounts for the correlations. METHODS: We analyse the variation pattern of the distribution of test statistics under permutation using the singular value decomposition. The results suggest a latent FDR model that accounts for the effects of correlation, and is statistically closer to the FDP. We develop a procedure for estimating the latent FDR (ELF) based on a Poisson regression model. RESULTS: For simulated data based on the correlation structure of real datasets, we find that ELF performs substantially better than the standard FDR approach in estimating the FDP. We illustrate the use of ELF in the analysis of breast cancer and lymphoma data. AVAILABILITY: R code to perform ELF is available in http://www.meb.ki.se/~yudpaw.     

Rotation gene set testing for longitudinal expression data

Gene set analysis methods are popular tools for identifying differentially expressed gene sets in microarray data. Most existing methods use a permutation test to assess significance for each gene set. The permutation test's assumption of exchangeable samples is often not satisfied for time‐series data and complex experimental designs, and in addition it requires a certain number of samples to compute p‐values accurately. The method presented here uses a rotation test rather than a permutation test to assess significance. The rotation test can compute accurate p‐values also for very small sample sizes. The method can handle complex designs and is particularly suited for longitudinal microarray data where the samples may have complex correlation structures. Dependencies between genes, modeled with the use of gene networks, are incorporated in the estimation of correlations between samples. In addition, the method can test for both gene sets that are differentially expressed and gene sets that show strong time trends. We show on simulated longitudinal data that the ability to identify important gene sets may be improved by taking the correlation structure between samples into account. Applied to real data, the method identifies both gene sets with constant expression and gene sets with strong time trends.     

Detection of coregulation in differential gene expression profiles

Genomics and proteomics approaches generate distinct gene expression and protein profiles, listing individual genes embedded in broad functional terms as gene ontologies. However, interpretation of gene profiles in a regulatory and functional context remains a major issue. Elucidation of regulatory mechanisms at the gene expression level via analysis of promoter regions is a prominent procedure to decipher such gene regulatory networks. We propose a novel genetic algorithm (GA) to extract joint promoter modules in a set of coexpressed genes as resulting from differential gene expression experiments. Algorithm design has focused on the following constraints: (I) identification of the major promoter modules, which are (II) characterized by a maximum number of joint motifs and (III) are found in a maximum number of coexpressed genes. The capability of the GA in detecting multiple modules was evaluated on various test data sets, analyzing the impact of the number of motifs per promoter module, the number of genes associated with a module, as well as the total number of distinct promoter modules encoded in a sequence set. In addition to the test data sets, the GA was evaluated on two biological examples, namely a muscle-specific data set and the upstream sequences of the beta-actin gene (ACTB) derived from different species, complemented by a comparison to alternative promoter module identification routines.     

Bayesian Joint Analysis of Gene Expression Data and Gene Functional Annotations

Identifying which genes and which gene sets are differentially expressed (DE) under two experimental conditions are both key questions in microarray analysis. Although closely related and seemingly similar, they cannot replace each other, due to their own importance and merits in scientific discoveries. Existing approaches have been developed to address only one of the two questions. Further, most of the methods for detecting DE genes purely rely on gene expression analysis, without using the information about gene functional grouping. Methods for detecting altered gene sets often use a two-step procedure, of which the first step conducts differential expression analysis using expression data only, and the second step takes results from the first step and tries to examine whether each predefined gene set is overrepresented by DE genes through some testing procedure. Such a sequential manner in analysis might cause information loss by just focusing on summary results without using the entire expression data in the second step. Here, we propose a Bayesian joint modeling approach to address the two key questions in parallel, which incorporates the information of functional annotations into expression data analysis and meanwhile infer the enrichment of functional groups. Simulation results and analysis of experimental data obtained for E.?coli show improved statistical power of our integrated approach in both identifying DE genes and altered gene sets, when compared to conventional methods.     

Comparative genomic analysis of eutherian Mas-related G protein-coupled receptor genes

The present study made attempts to update comprehensive eutherian Mas-related G protein-coupled receptor gene data sets, using public eutherian genomic sequence data sets and new genomics and molecular evolution tests. Among 254 potential coding sequences, the most comprehensive gene data set of eutherian Mas-related G protein-coupled receptor genes included 119 complete coding sequences that described eight major gene clusters. The present analysis integrated gene annotations, phylogenetic analysis and protein molecular evolution analysis and first explained differential gene expansion patterns of eutherian Mas-related G protein-coupled receptor genes. The updated classification and nomenclature of eutherian Mas-related G protein-coupled receptor genes were proposed as new framework of future experiments.