BACKGROUND: Gene set analysis methods have played a major role in generating biological interpretations of omics data such as gene expression datasets. However, most methods focus on detecting homogenous pattern changes in mean expression while methods detecting pattern changes in variance remain poorly explored. While a few studies attempted to use gene-level variance analysis, such approach remains under-utilized. When comparing two phenotypes, gene sets with distinct changes in subgroups under one phenotype are overlooked by available methods although they reflect meaningful biological differences between two phenotypes. Multivariate sample-level variance analysis methods are needed to detect such pattern changes. RESULTS: We used ranking schemes based on minimum spanning tree to generalize the Cramer-Von Mises and Anderson-Darling univariate statistics into multivariate gene set analysis methods to detect differential sample variance or mean. We characterized the detection power and Type I error rate of these methods in addition to two methods developed earlier using simulation results with different parameters. We applied the developed methods to microarray gene expression dataset of prednisolone-resistant and prednisolone-sensitive children diagnosed with B-lineage acute lymphoblastic leukemia and bulk RNA-sequencing gene expression dataset of benign hyperplastic polyps and potentially malignant sessile serrated adenoma/polyps. One or both of the two compared phenotypes in each of these datasets have distinct molecular subtypes that contribute to within phenotype variability and to heterogeneous differences between two compared phenotypes. Our results show that methods designed to detect differential sample variance provide meaningful biological interpretations by detecting specific hallmark gene sets associated with the two compared phenotypes as documented in available literature. CONCLUSIONS: The results of this study demonstrate the usefulness of methods designed to detect differential sample variance in providing biological interpretations when biologically relevant but heterogeneous changes between two phenotypes are prevalent in specific signaling pathways. Software implementation of the methods is available with detailed documentation from Bioconductor package GSAR. The available methods are applicable to gene expression datasets in a normalized matrix form and could be used with other omics datasets in a normalized matrix form with available collection of feature sets.

BACKGROUND: Gene set analysis (in a form of functionally related genes or pathways) has become the method of choice for analyzing omics data in general and gene expression data in particular. There are many statistical methods that either summarize gene-level statistics for a gene set or apply a multivariate statistic that accounts for intergene correlations. Most available methods detect complex departures from the null hypothesis but lack the ability to identify the specific alternative hypothesis that rejects the null. RESULTS: GSAR (Gene Set Analysis in R) is an open-source R/Bioconductor software package for gene set analysis (GSA). It implements self-contained multivariate non-parametric statistical methods testing a complex null hypothesis against specific alternatives, such as differences in mean (shift), variance (scale), or net correlation structure. The package also provides a graphical visualization tool, based on the union of two minimum spanning trees, for correlation networks to examine the change in the correlation structures of a gene set between two conditions and highlight influential genes (hubs). CONCLUSIONS: Package GSAR provides a set of multivariate non-parametric statistical methods that test a complex null hypothesis against specific alternatives. The methods in package GSAR are applicable to any type of omics data that can be represented in a matrix format. The package, with detailed instructions and examples, is freely available under the GPL (> = 2) license from the Bioconductor web site.

Transcriptome sequencing (RNA-seq) is gradually replacing microarrays for high-throughput studies of gene expression. The main challenge of analyzing microarray data is not in finding differentially expressed genes, but in gaining insights into the biological processes underlying phenotypic differences. To interpret experimental results from microarrays, gene set analysis (GSA) has become the method of choice, in particular because it incorporates pre-existing biological knowledge (in a form of functionally related gene sets) into the analysis. Here we provide a brief review of several statistically different GSA approaches (competitive and self-contained) that can be adapted from microarrays practice as well as those specifically designed for RNA-seq. We evaluate their performance (in terms of Type I error rate, power, robustness to the sample size and heterogeneity, as well as the sensitivity to different types of selection biases) on simulated and real RNA-seq data. Not surprisingly, the performance of various GSA approaches depends only on the statistical hypothesis they test and does not depend on whether the test was developed for microarrays or RNA-seq data. Interestingly, we found that competitive methods have lower power as well as robustness to the samples heterogeneity than self-contained methods, leading to poor results reproducibility. We also found that the power of unsupervised competitive methods depends on the balance between up- and down-regulated genes in tested gene sets. These properties of competitive methods have been overlooked before. Our evaluation provides a concise guideline for selecting GSA approaches, best performing under particular experimental settings in the context of RNA-seq.

MOTIVATION: To date, gene set analysis approaches primarily focus on identifying differentially expressed gene sets (pathways). Methods for identifying differentially coexpressed pathways also exist but are mostly based on aggregated pairwise correlations or other pairwise measures of coexpression. Instead, we propose Gene Sets Net Correlations Analysis (GSNCA), a multivariate differential coexpression test that accounts for the complete correlation structure between genes. RESULTS: In GSNCA, weight factors are assigned to genes in proportion to the genes' cross-correlations (intergene correlations). The problem of finding the weight vectors is formulated as an eigenvector problem with a unique solution. GSNCA tests the null hypothesis that for a gene set there is no difference in the weight vectors of the genes between two conditions. In simulation studies and the analyses of experimental data, we demonstrate that GSNCA captures changes in the structure of genes' cross-correlations rather than differences in the averaged pairwise correlations. Thus, GSNCA infers differences in coexpression networks, however, bypassing method-dependent steps of network inference. As an additional result from GSNCA, we define hub genes as genes with the largest weights and show that these genes correspond frequently to major and specific pathway regulators, as well as to genes that are most affected by the biological difference between two conditions. In summary, GSNCA is a new approach for the analysis of differentially coexpressed pathways that also evaluates the importance of the genes in the pathways, thus providing unique information that may result in the generation of novel biological hypotheses. AVAILABILITY AND IMPLEMENTATION: Implementation of the GSNCA test in R is available upon request from the authors.

BACKGROUND: Over the last few years transcriptome sequencing (RNA-Seq) has almost completely taken over microarrays for high-throughput studies of gene expression. Currently, the most popular use of RNA-Seq is to identify genes which are differentially expressed between two or more conditions. Despite the importance of Gene Set Analysis (GSA) in the interpretation of the results from RNA-Seq experiments, the limitations of GSA methods developed for microarrays in the context of RNA-Seq data are not well understood. RESULTS: We provide a thorough evaluation of popular multivariate and gene-level self-contained GSA approaches on simulated and real RNA-Seq data. The multivariate approach employs multivariate non-parametric tests combined with popular normalizations for RNA-Seq data. The gene-level approach utilizes univariate tests designed for the analysis of RNA-Seq data to find gene-specific P-values and combines them into a pathway P-value using classical statistical techniques. Our results demonstrate that the Type I error rate and the power of multivariate tests depend only on the test statistics and are insensitive to the different normalizations. In general standard multivariate GSA tests detect pathways that do not have any bias in terms of pathways size, percentage of differentially expressed genes, or average gene length in a pathway. In contrast the Type I error rate and the power of gene-level GSA tests are heavily affected by the methods for combining P-values, and all aforementioned biases are present in detected pathways. CONCLUSIONS: Our result emphasizes the importance of using self-contained non-parametric multivariate tests for detecting differentially expressed pathways for RNA-Seq data and warns against applying gene-level GSA tests, especially because of their high level of Type I error rates for both, simulated and real data.

MOTIVATION: The analysis of differentially expressed gene sets became a routine in the analyses of gene expression data. There is a multitude of tests available, ranging from aggregation tests that summarize gene-level statistics for a gene set to true multivariate tests, accounting for intergene correlations. Most of them detect complex departures from the null hypothesis but when the null hypothesis is rejected, the specific alternative leading to the rejection is not easily identifiable. RESULTS: In this article we compare the power and Type I error rates of minimum-spanning tree (MST)-based non-parametric multivariate tests with several multivariate and aggregation tests, which are frequently used for pathway analyses. In our simulation study, we demonstrate that MST-based tests have power that is for many settings comparable with the power of conventional approaches, but outperform them in specific regions of the parameter space corresponding to biologically relevant configurations. Further, we find for simulated and for gene expression data that MST-based tests discriminate well against shift and scale alternatives. As a general result, we suggest a two-step practical analysis strategy that may increase the interpretability of experimental data: first, apply the most powerful multivariate test to find the subset of pathways for which the null hypothesis is rejected and second, apply MST-based tests to these pathways to select those that support specific alternative hypotheses. CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

This paper provides an analytical framework to study the performance of linear companding techniques proposed in the OFDM literature, thus settling the numerous controversial claims that are based solely on simulation results. Linear companding transforms are widely employed to reduce the peak-to- average-power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. Two main linear companding classes have been considered in the literature: linear symmetrical transform (LST) and linear asymmetrical transform (LAST). In the literature, the bit error rate (BER) performance superiority of the basic LAST (with one discontinuity point) over the LST is claimed based on computer simulations. Also, it has been claimed that a LAST with two discontinuity points outperforms the basic LAST with one discontinuity point. These claims are however not substantiated with analytical results. Our analysis shows that these claims are, in general, not always true. We derive a sufficient condition, in terms of the companding parameters, under which the BER performance of a general LAST with M-1 discontinuity points is superior to that of LST. The derived condition explains the contradictions between different reported results in the literature and validates some other reported simulation results. It also serves as a guideline in the process of choosing proper values for companding parameters to obtain a specific trade-off between PAPR reduction capability and BER performance. In particular, the derived sufficient condition shows that the BER performance for LAST depends on the slopes of the LAST rather than on the number of discontinuity points as has been indicated so far. Moreover, we derive conditions for the companding parameters in order to keep the average transmitted power unchanged after companding. Our theoretical derivations are supported by simulation results.