Hierarchical probabilistic models for multiple gene/variant associations based on next-generation sequencing data

Motivation: The identification of genetic variants influencing gene expression (known as expression quantitative trait loci or eQTLs) is important in unravelling the genetic basis of complex traits. Detecting multiple eQTLs simultaneously in a population based on paired DNA‐seq and RNA‐seq assays employs two competing types of models: models which rely on appropriate transformations of RNA‐seq data (and are powered by a mature mathematical theory), or count‐based models, which represent digital gene expression explicitly, thus rendering such transformations unnecessary. The latter constitutes an immensely popular methodology, which is however plagued by mathematical intractability. Results: We develop tractable count‐based models, which are amenable to efficient estimation through the introduction of latent variables and the appropriate application of recent statistical theory in a sparse Bayesian modelling framework. Furthermore, we examine several transformation methods for RNA‐seq read counts and we introduce arcsin, logit and Laplace smoothing as preprocessing steps for transformation‐based models. Using natural and carefully simulated data from the 1000 Genomes and gEUVADIS projects, we benchmark both approaches under a variety of scenarios, including the presence of noise and violation of basic model assumptions. We demonstrate that an arcsin transformation of Laplace‐smoothed data is at least as good as state‐of‐the‐art models, particularly at small samples. Furthermore, we show that an over‐dispersed Poisson model is comparable to the celebrated Negative Binomial, but much easier to estimate. These results provide strong support for transformation‐based versus count‐based (particularly Negative‐Binomial‐based) models for eQTL mapping. Availability and implementation: All methods are implemented in the free software eQTLseq: https://github.com/dvav/eQTLseq Contact: dimitris.vavoulis@well.ox.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online.

[1]  Charity W. Law,et al.  voom: precision weights unlock linear model analysis tools for RNA-seq read counts , 2014, Genome Biology.

[2]  Pedro G. Ferreira,et al.  Transcriptome and genome sequencing uncovers functional variation in humans , 2013, Nature.

[3]  F ChenStanley,et al.  An Empirical Study of Smoothing Techniques for Language Modeling , 1996, ACL.

[4]  Wei Cheng,et al.  Graph-regularized dual Lasso for robust eQTL mapping , 2014, Bioinform..

[5]  W. Huber,et al.  Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2 , 2014, Genome Biology.

[6]  Hao Wu,et al.  A new shrinkage estimator for dispersion improves differential expression detection in RNA-seq data , 2012, Biostatistics.

[7]  Charlotte Soneson,et al.  A comparison of methods for differential expression analysis of RNA-seq data , 2013, BMC Bioinformatics.

[8]  Julian Gough,et al.  DGEclust: differential expression analysis of clustered count data , 2014, Genome Biology.

[9]  Roby Joehanes,et al.  Integrated genome-wide analysis of expression quantitative trait loci aids interpretation of genomic association studies , 2017, Genome Biology.

[10]  Harald Binder,et al.  Transforming RNA-Seq Data to Improve the Performance of Prognostic Gene Signatures , 2014, PloS one.

[11]  N. Yi,et al.  Bayesian LASSO for Quantitative Trait Loci Mapping , 2008, Genetics.

[12]  Michael E. Tipping.  Sparse Bayesian Learning and the Relevance Vector Machine , 2001, J. Mach. Learn. Res..

[13]  L. Liang,et al.  Mapping complex disease traits with global gene expression , 2009, Nature Reviews Genetics.

[14]  David B. Dunson,et al.  Lognormal and Gamma Mixed Negative Binomial Regression , 2012, ICML.

[15]  Derek W Wright,et al.  Gateways to the FANTOM5 promoter level mammalian expression atlas , 2015, Genome Biology.

[16]  F. Cunningham,et al.  The Ensembl Variant Effect Predictor , 2016, Genome Biology.

[17]  Andrey A. Shabalin,et al.  Matrix eQTL: ultra fast eQTL analysis via large matrix operations , 2011, Bioinform..

[18]  G. Casella,et al.  The Bayesian Lasso , 2008 .

[19]  Dan Nettleton,et al.  SimSeq: a nonparametric approach to simulation of RNA-sequence datasets , 2015, Bioinform..

[20]  M. Gerstein,et al.  RNA-Seq: a revolutionary tool for transcriptomics , 2009, Nature Reviews Genetics.

[21]  Alyssa C. Frazee,et al.  ReCount: A multi-experiment resource of analysis-ready RNA-seq gene count datasets , 2011, BMC Bioinformatics.

[22]  Zoubin Ghahramani,et al.  Nonparametric Bayesian Sparse Factor Models with application to Gene Expression modelling , 2010, The Annals of Applied Statistics.

[23]  B. Matthews.  Comparison of the predicted and observed secondary structure of T4 phage lysozyme. , 1975, Biochimica et biophysica acta.

[24]  L. Lin,et al.  A concordance correlation coefficient to evaluate reproducibility. , 1989, Biometrics.

[25]  R. O’Hara,et al.  A review of Bayesian variable selection methods: what, how and which , 2009 .

[26]  Daniel J. Gaffney,et al.  Fine-mapping cellular QTLs with RASQUAL and ATAC-seq , 2015, Nature Genetics.

[27]  Gabor T. Marth,et al.  A global reference for human genetic variation , 2015, Nature.

[28]  Wei Sun,et al.  eQTL Mapping Using RNA-seq Data , 2012, Statistics in Biosciences.

[29]  Matthew West,et al.  Bayesian factor regression models in the''large p , 2003 .

[30]  J. S. Rao,et al.  Spike and slab variable selection: Frequentist and Bayesian strategies , 2005, math/0505633.

[31]  T Mark Beasley,et al.  Rank-Based Inverse Normal Transformations are Increasingly Used, But are They Merited? , 2009, Behavior genetics.

[32]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[33]  Nando de Freitas,et al.  An Introduction to MCMC for Machine Learning , 2004, Machine Learning.

[34]  L. Kruglyak,et al.  The role of regulatory variation in complex traits and disease , 2015, Nature Reviews Genetics.

[35]  Francis K C Hui,et al.  The arcsine is asinine: the analysis of proportions in ecology. , 2011, Ecology.

[36]  R. Guigó,et al.  Transcriptome genetics using second generation sequencing in a Caucasian population , 2010, Nature.

[37]  James G. Scott,et al.  Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables , 2012, 1205.0310.

[38]  M. Stephens,et al.  A Statistical Framework for Joint eQTL Analysis in Multiple Tissues , 2012, PLoS genetics.

[39]  Laura L. Elo,et al.  Comparison of software packages for detecting differential expression in RNA-seq studies , 2013, Briefings Bioinform..

[40]  Vanessa M Kvam,et al.  A comparison of statistical methods for detecting differentially expressed genes from RNA-seq data. , 2012, American journal of botany.

[41]  Sylvia Richardson,et al.  Bayesian Detection of Expression Quantitative Trait Loci Hot Spots , 2011, Genetics.