Tree-guided group lasso for multi-response regression with structured sparsity, with an application to eQTL mapping

We consider the problem of estimating a sparse multi-response regression function, with an application to expression quantitative trait locus (eQTL) mapping, where the goal is to discover genetic variations that influence gene-expression levels. In particular, we investigate a shrinkage technique capable of capturing a given hierarchical structure over the responses, such as a hierarchical clustering tree with leaf nodes for responses and internal nodes for clusters of related responses at multiple granularity, and we seek to leverage this structure to recover covariates relevant to each hierarchically-defined cluster of responses. We propose a tree-guided group lasso, or tree lasso, for estimating such structured sparsity under multi-response regression by employing a novel penalty function constructed from the tree. We describe a systematic weighting scheme for the overlapping groups in the tree-penalty such that each regression coefficient is penalized in a balanced manner despite the inhomogeneous multiplicity of group memberships of the regression coefficients due to overlaps among groups. For efficient optimization, we employ a smoothing proximal gradient method that was originally developed for a general class of structured-sparsity-inducing penalties. Using simulated and yeast data sets, we demonstrate that our method shows a superior performance in terms of both prediction errors and recovery of true sparsity patterns, compared to other methods for learning a multivariate-response regression.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS549 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Robust Detection of Hierarchical Communities from Escherichia coli Gene Expression Data

Determining the functional structure of biological networks is a central goal of systems biology. One approach is to analyze gene expression data to infer a network of gene interactions on the basis of their correlated responses to environmental and genetic perturbations. The inferred network can then be analyzed to identify functional communities. However, commonly used algorithms can yield unreliable results due to experimental noise, algorithmic stochasticity, and the influence of arbitrarily chosen parameter values. Furthermore, the results obtained typically provide only a simplistic view of the network partitioned into disjoint communities and provide no information of the relationship between communities. Here, we present methods to robustly detect coregulated and functionally enriched gene communities and demonstrate their application and validity for Escherichia coli gene expression data. Applying a recently developed community detection algorithm to the network of interactions identified with the context likelihood of relatedness (CLR) method, we show that a hierarchy of network communities can be identified. These communities significantly enrich for gene ontology (GO) terms, consistent with them representing biologically meaningful groups. Further, analysis of the most significantly enriched communities identified several candidate new regulatory interactions. The robustness of our methods is demonstrated by showing that a core set of functional communities is reliably found when artificial noise, modeling experimental noise, is added to the data. We find that noise mainly acts conservatively, increasing the relatedness required for a network link to be reliably assigned and decreasing the size of the core communities, rather than causing association of genes into new communities.Comment: Due to appear in PLoS Computational Biology. Supplementary Figure S1 was not uploaded but is available by contacting the author. 27 pages, 5 figures, 15 supplementary file

Integrative Model-based clustering of microarray methylation and expression data

In many fields, researchers are interested in large and complex biological processes. Two important examples are gene expression and DNA methylation in genetics. One key problem is to identify aberrant patterns of these processes and discover biologically distinct groups. In this article we develop a model-based method for clustering such data. The basis of our method involves the construction of a likelihood for any given partition of the subjects. We introduce cluster specific latent indicators that, along with some standard assumptions, impose a specific mixture distribution on each cluster. Estimation is carried out using the EM algorithm. The methods extend naturally to multiple data types of a similar nature, which leads to an integrated analysis over multiple data platforms, resulting in higher discriminating power.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS533 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A statistical framework for joint eQTL analysis in multiple tissues

Mapping expression Quantitative Trait Loci (eQTLs) represents a powerful and widely-adopted approach to identifying putative regulatory variants and linking them to specific genes. Up to now eQTL studies have been conducted in a relatively narrow range of tissues or cell types. However, understanding the biology of organismal phenotypes will involve understanding regulation in multiple tissues, and ongoing studies are collecting eQTL data in dozens of cell types. Here we present a statistical framework for powerfully detecting eQTLs in multiple tissues or cell types (or, more generally, multiple subgroups). The framework explicitly models the potential for each eQTL to be active in some tissues and inactive in others. By modeling the sharing of active eQTLs among tissues this framework increases power to detect eQTLs that are present in more than one tissue compared with "tissue-by-tissue" analyses that examine each tissue separately. Conversely, by modeling the inactivity of eQTLs in some tissues, the framework allows the proportion of eQTLs shared across different tissues to be formally estimated as parameters of a model, addressing the difficulties of accounting for incomplete power when comparing overlaps of eQTLs identified by tissue-by-tissue analyses. Applying our framework to re-analyze data from transformed B cells, T cells and fibroblasts we find that it substantially increases power compared with tissue-by-tissue analysis, identifying 63% more genes with eQTLs (at FDR=0.05). Further the results suggest that, in contrast to previous analyses of the same data, the majority of eQTLs detectable in these data are shared among all three tissues.Comment: Summitted to PLoS Genetic

Learning the optimal scale for GWAS through hierarchical SNP aggregation

Motivation: Genome-Wide Association Studies (GWAS) seek to identify causal genomic variants associated with rare human diseases. The classical statistical approach for detecting these variants is based on univariate hypothesis testing, with healthy individuals being tested against affected individuals at each locus. Given that an individual's genotype is characterized by up to one million SNPs, this approach lacks precision, since it may yield a large number of false positives that can lead to erroneous conclusions about genetic associations with the disease. One way to improve the detection of true genetic associations is to reduce the number of hypotheses to be tested by grouping SNPs. Results: We propose a dimension-reduction approach which can be applied in the context of GWAS by making use of the haplotype structure of the human genome. We compare our method with standard univariate and multivariate approaches on both synthetic and real GWAS data, and we show that reducing the dimension of the predictor matrix by aggregating SNPs gives a greater precision in the detection of associations between the phenotype and genomic regions