Summary: Ontologies are widely used constructs for encoding and analyzing biomedical data, but the absence of simple and consistent tools has made exploratory and systematic analysis of such data unnecessarily difficult. Here we present three packages which aim to simplify such procedures. The ontologyIndex package enables arbitrary ontologies to be read into R, supports representation of ontological objects by native R types, and provides a parsimonius set of performant functions for querying ontologies. ontologySimilarity and ontologyPlot extend ontologyIndex with functionality for straightforward visualization and semantic similarity calculations, including statistical routines. Availability and Implementation: ontologyIndex , ontologyPlot and ontologySimilarity are all available on the Comprehensive R Archive Network website under https://cran.r-project.org/web/packages/ . Contact: Daniel Greene [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

MOTIVATION: Analysing the joint association between a large set of responses and predictors is a fundamental statistical task in integrative genomics, exemplified by numerous expression Quantitative Trait Loci (eQTL) studies. Of particular interest are the so-called ': hotspots ': , important genetic variants that regulate the expression of many genes. Recently, attention has focussed on whether eQTLs are common to several tissues, cell-types or, more generally, conditions or whether they are specific to a particular condition. RESULTS: We have implemented MT-HESS, a Bayesian hierarchical model that analyses the association between a large set of predictors, e.g. SNPs, and many responses, e.g. gene expression, in multiple tissues, cells or conditions. Our Bayesian sparse regression algorithm goes beyond ': one-at-a-time ': association tests between SNPs and responses and uses a fully multivariate model search across all linear combinations of SNPs, coupled with a model of the correlation between condition/tissue-specific responses. In addition, we use a hierarchical structure to leverage shared information across different genes, thus improving the detection of hotspots. We show the increase of power resulting from our new approach in an extensive simulation study. Our analysis of two case studies highlights new hotspots that would remain undetected by standard approaches and shows how greater prediction power can be achieved when several tissues are jointly considered. AVAILABILITY AND IMPLEMENTATION: C[Formula: see text] source code and documentation including compilation instructions are available under GNU licence at http://www.mrc-bsu.cam.ac.uk/software/.

Single-cell mRNA sequencing can uncover novel cell-to-cell heterogeneity in gene expression levels in seemingly homogeneous populations of cells. However, these experiments are prone to high levels of unexplained technical noise, creating new challenges for identifying genes that show genuine heterogeneous expression within the population of cells under study. BASiCS (Bayesian Analysis of Single-Cell Sequencing data) is an integrated Bayesian hierarchical model where: (i) cell-specific normalisation constants are estimated as part of the model parameters, (ii) technical variability is quantified based on spike-in genes that are artificially introduced to each analysed cell's lysate and (iii) the total variability of the expression counts is decomposed into technical and biological components. BASiCS also provides an intuitive detection criterion for highly (or lowly) variable genes within the population of cells under study. This is formalised by means of tail posterior probabilities associated to high (or low) biological cell-to-cell variance contributions, quantities that can be easily interpreted by users. We demonstrate our method using gene expression measurements from mouse Embryonic Stem Cells. Cross-validation and meaningful enrichment of gene ontology categories within genes classified as highly (or lowly) variable supports the efficacy of our approach.

Complex tissues, such as the brain, are composed of multiple different cell types, each of which have distinct and important roles, for example in neural function. Moreover, it has recently been appreciated that the cells that make up these sub-cell types themselves harbour significant cell-to-cell heterogeneity, in particular at the level of gene expression. The ability to study this heterogeneity has been revolutionised by advances in experimental technology, such as Wholemount in Situ Hybridizations (WiSH) and single-cell RNA-sequencing. Consequently, it is now possible to study gene expression levels in thousands of cells from the same tissue type. After generating such data one of the key goals is to cluster the cells into groups that correspond to both known and putatively novel cell types. Whilst many clustering algorithms exist, they are typically unable to incorporate information about the spatial dependence between cells within the tissue under study. When such information exists it provides important insights that should be directly included in the clustering scheme. To this end we have developed a clustering method that uses a Hidden Markov Random Field (HMRF) model to exploit both quantitative measures of expression and spatial information. To accurately reflect the underlying biology, we extend current HMRF approaches by allowing the degree of spatial coherency to differ between clusters. We demonstrate the utility of our method using simulated data before applying it to cluster single cell gene expression data generated by applying WiSH to study expression patterns in the brain of the marine annelid Platynereis dumereilii. Our approach allows known cell types to be identified as well as revealing new, previously unexplored cell types within the brain of this important model system.

SUMMARY: ESS++ is a C++ implementation of a fully Bayesian variable selection approach for single and multiple response linear regression. ESS++ works well both when the number of observations is larger than the number of predictors and in the 'large p, small n' case. In the current version, ESS++ can handle several hundred observations, thousands of predictors and a few responses simultaneously. The core engine of ESS++ for the selection of relevant predictors is based on Evolutionary Monte Carlo. Our implementation is open source, allowing community-based alterations and improvements. AVAILABILITY: C++ source code and documentation including compilation instructions are available under GNU licence at http://bgx.org.uk/software/ESS.html.

BACKGROUND: In microarray studies researchers are often interested in the comparison of relevant quantities between two or more similar experiments, involving different treatments, tissues, or species. Typically each experiment reports measures of significance (e.g. p-values) or other measures that rank its features (e.g genes). Our objective is to find a list of features that are significant in all experiments, to be further investigated. In this paper we present an R package called sdef, that allows the user to quantify the evidence of communality between the experiments using previously proposed statistical methods based on the ranked lists of p-values. sdef implements two approaches that address this objective: the first is a permutation test of the maximal ratio of observed to expected common features under the hypothesis of independence between the experiments. The second approach, set in a Bayesian framework, is more flexible as it takes into account the uncertainty on the number of genes differentially expressed in each experiment. RESULTS: We used sdef to re-analyze publicly available data i) on Type 2 diabetes susceptibility in mice on liver and skeletal muscle (two experiments); ii) on molecular similarities between mammalian sexes (three experiments). For the first example, we found between 68 and 104 genes commonly perturbed between the two tissues, using the two methods described above, and enrichment of the inflammation pathways, which are related to obesity and diabetes. For the second example, looking at three lists of features, we found 110 genes commonly perturbed between the three tissues, using the same two methods, and enrichment on genes involved in cell development. CONCLUSIONS: sdef is an R package that provides researchers with an easy and powerful methodology to find lists of features commonly perturbed in two or more experiments to be further investigated. The package is provided with plots and tables to help the user visualize and interpret the results. The Windows, Linux and MacOS versions of the package, together with the documentation are available on the website http://cran.r-project.org/web/packages/sdef/index.html.

The majority of expression quantitative trait locus (eQTL) studies have been carried out in single tissues or cell types, using methods that ignore information shared across tissues. Although global analysis of RNA expression in multiple tissues is now feasible, few integrated statistical frameworks for joint analysis of gene expression across tissues combined with simultaneous analysis of multiple genetic variants have been developed to date. Here, we propose Sparse Bayesian Regression models for mapping eQTLs within individual tissues and simultaneously across tissues. Testing these on a set of 2,000 genes in four tissues, we demonstrate that our methods are more powerful than traditional approaches in revealing the true complexity of the eQTL landscape at the systems-level. Highlighting the power of our method, we identified a two-eQTL model (cis/trans) for the Hopx gene that was experimentally validated and was not detected by conventional approaches. We showed common genetic regulation of gene expression across four tissues for approximately 27% of transcripts, providing >5 fold increase in eQTLs detection when compared with single tissue analyses at 5% FDR level. These findings provide a new opportunity to uncover complex genetic regulatory mechanisms controlling global gene expression while the generality of our modelling approach makes it adaptable to other model systems and humans, with broad application to analysis of multiple intermediate and whole-body phenotypes.

BACKGROUND: In gene expression studies a key role is played by the so called "pre-processing", a series of steps designed to extract the signal and account for the sources of variability due to the technology used rather than to biological differences between the RNA samples. At the moment there is no commonly agreed gold standard pre-processing method and each researcher has the responsibility to choose one method, incurring the risk of false positive and false negative features arising from the particular method chosen. RESULTS: We propose a Bayesian calibration model that makes use of the information provided by several pre-processing methods and we show that this model gives a better assessment of the 'true' unknown differential expression between two conditions. We demonstrate how to estimate the posterior distribution of the differential expression values of interest from the combined information. CONCLUSION: On simulated data and on the spike-in Latin Square dataset from Affymetrix the Bayesian calibration model proves to have more power than each pre-processing method. Its biological interest is demonstrated through an experimental example on publicly available data.

BACKGROUND: Affymetrix 3' GeneChip microarrays are widely used to profile the expression of thousands of genes simultaneously. They differ from many other microarray types in that GeneChips are hybridised using a single labelled extract and because they contain multiple 'match' and 'mismatch' sequences for each transcript. Most algorithms extract the signal from GeneChip experiments in a sequence of separate steps, including background correction and normalisation, which inhibits the simultaneous use of all available information. They principally provide a point estimate of gene expression and, in contrast to BGX, do not fully integrate the uncertainty arising from potentially heterogeneous responses of the probes. RESULTS: BGX is a new Bioconductor R package that implements an integrated Bayesian approach to the analysis of 3' GeneChip data. The software takes into account additive and multiplicative error, non-specific hybridisation and replicate summarisation in the spirit of the model outlined in 1. It also provides a posterior distribution for the expression of each gene. Moreover, BGX can take into account probe affinity effects from probe sequence information where available. The package employs a novel adaptive Markov chain Monte Carlo (MCMC) algorithm that raises considerably the efficiency with which the posterior distributions are sampled from. Finally, BGX incorporates various ways to analyse the results, such as ranking genes by expression level as well as statistically based methods for estimating the amount of up and down regulated genes between two conditions. CONCLUSION: BGX performs well relative to other widely used methods at estimating expression levels and fold changes. It has the advantage that it provides a statistically sound measure of uncertainty for its estimates. BGX includes various analysis functions to visualise and exploit the rich output that is produced by the Bayesian model.

Gene duplication with subsequent interaction divergence is one of the primary driving forces in the evolution of genetic systems. Yet little is known about the precise mechanisms and the role of duplication divergence in the evolution of protein networks from the prokaryote and eukaryote domains. We developed a novel, model-based approach for Bayesian inference on biological network data that centres on approximate Bayesian computation, or likelihood-free inference. Instead of computing the intractable likelihood of the protein network topology, our method summarizes key features of the network and, based on these, uses a MCMC algorithm to approximate the posterior distribution of the model parameters. This allowed us to reliably fit a flexible mixture model that captures hallmarks of evolution by gene duplication and subfunctionalization to protein interaction network data of Helicobacter pylori and Plasmodium falciparum. The 80% credible intervals for the duplication-divergence component are [0.64, 0.98] for H. pylori and [0.87, 0.99] for P. falciparum. The remaining parameter estimates are not inconsistent with sequence data. An extensive sensitivity analysis showed that incompleteness of PIN data does not largely affect the analysis of models of protein network evolution, and that the degree sequence alone barely captures the evolutionary footprints of protein networks relative to other statistics. Our likelihood-free inference approach enables a fully Bayesian analysis of a complex and highly stochastic system that is otherwise intractable at present. Modelling the evolutionary history of PIN data, it transpires that only the simultaneous analysis of several global aspects of protein networks enables credible and consistent inference to be made from available datasets. Our results indicate that gene duplication has played a larger part in the network evolution of the eukaryote than in the prokaryote, and suggests that single gene duplications with immediate divergence alone may explain more than 60% of biological network data in both domains.

MOTIVATION: Comparative genomic hybridization array experiments that investigate gene copy number changes present new challenges for statistical analysis and call for methods that incorporate spatial dependence between sequences along the chromosome. For this purpose, we propose a novel method called CGHmix. It is based on a spatially structured mixture model with three states corresponding to genomic sequences that are either unmodified, deleted or amplified. Inference is performed in a Bayesian framework. From the output, posterior probabilities of belonging to each of the three states are estimated for each genomic sequence and used to classify them. RESULTS: Using simulated data, CGHmix is validated and compared with both a conventional unstructured mixture model and with a recently proposed data mining method. We demonstrate the good performance of CGHmix for classifying copy number changes. In addition, the method provides a good estimate of the false discovery rate. We also present the analysis of a cancer related dataset. SUPPLEMENTARY INFORMATION: http://www.bgx.org.uk/papers.html

BACKGROUND: Studies of differential expression that use Affymetrix GeneChip arrays are often carried out with a limited number of replicates. Reasons for this include financial considerations and limits on the available amount of RNA for sample preparation. In addition, failed hybridizations are not uncommon leading to a further reduction in the number of replicates available for analysis. Most existing methods for studying differential expression rely on the availability of replicates and the demand for alternative methods that require few or no replicates is high. RESULTS: We describe a statistical procedure for performing differential expression analysis without replicates. The procedure relies on a Bayesian integrated approach (BGX) to the analysis of Affymetrix GeneChips. The BGX method estimates a posterior distribution of expression for each gene and condition, from a simultaneous consideration of the available probe intensities representing the gene in a condition. Importantly, posterior distributions of expression are obtained regardless of the number of replicates available. We exploit these posterior distributions to create ranked gene lists that take into account the estimated expression difference as well as its associated uncertainty. We estimate the proportion of non-differentially expressed genes empirically, allowing an informed choice of cut-off for the ranked gene list, adapting an approach proposed by Efron. We assess the performance of the method, and compare it to those of other methods, on publicly available spike-in data sets, as well as in a proper biological setting. CONCLUSION: The method presented is a powerful tool for extracting information on differential expression from GeneChip expression studies with limited or no replicates.

MOTIVATION: Multiclass response (MCR) experiments are those in which there are more than two classes to be compared. In these experiments, though the null hypothesis is simple, there are typically many patterns of gene expression changes across the different classes that led to complex alternatives. In this paper, we propose a new strategy for selecting genes in MCR that is based on a flexible mixture model for the marginal distribution of a modified F-statistic. Using this model, false positive and negative discovery rates can be estimated and combined to produce a rule for selecting a subset of genes. Moreover, the method proposed allows calculation of these rates for any predefined subset of genes. RESULTS: We illustrate the performance our approach using simulated datasets and a real breast cancer microarray dataset. In this latter study, we investigate predefined subset of genes and point out interesting differences between three distinct biological pathways. AVAILABILITY: http://www.bgx.org.uk/software.html