An Information-Theoretic Machine Learning Approach to Expression QTL Analysis

Expression Quantitative Trait Locus (eQTL) analysis is a powerful tool to study the biological mechanisms linking the genotype with gene expression. Such analyses can identify genomic locations where genotypic variants influence the expression of genes, both in close proximity to the variant (cis-eQTL), and on other chromosomes (trans-eQTL). Many traditional eQTL methods are based on a linear regression model. In this study, we propose a novel method by which to identify eQTL associations with information theory and machine learning approaches. Mutual Information (MI) is used to describe the association between genetic marker and gene expression. MI can detect both linear and non-linear associations. What’s more, it can capture the heterogeneity of the population. Advanced feature selection methods, Maximum Relevance Minimum Redundancy (mRMR) and Incremental Feature Selection (IFS), were applied to optimize the selection of the affected genes by the genetic marker. When we applied our method to a study of apoE-deficient mice, it was found that the cis-acting eQTLs are stronger than trans-acting eQTLs but there are more trans-acting eQTLs than cis-acting eQTLs. We compared our results (mRMR.eQTL) with R/qtl, and MatrixEQTL (modelLINEAR and modelANOVA). In female mice, 67.9% of mRMR.eQTL results can be confirmed by at least two other methods while only 14.4% of R/qtl result can be confirmed by at least two other methods. In male mice, 74.1% of mRMR.eQTL results can be confirmed by at least two other methods while only 18.2% of R/qtl result can be confirmed by at least two other methods. Our methods provide a new way to identify the association between genetic markers and gene expression. Our software is available from supporting information.     

High throughput screening of co-expressed gene pairs with controlled false discovery rate (FDR) and minimum acceptable strength (MAS).

Many exploratory microarray data analysis tools such as gene clustering and relevance networks rely on detecting pairwise gene co-expression. Traditional screening of pairwise co-expression either controls biological significance or statistical significance, but not both. The former approach does not provide stochastic error control, and the later approach screens many co-expressions with excessively low correlation. We have designed and implemented a statistically sound two-stage co-expression detection algorithm that controls both statistical significance (false discovery rate, FDR) and biological significance (minimum acceptable strength, MAS) of the discovered co-expressions. Based on estimation of pairwise gene correlation, the algorithm provides an initial co-expression discovery that controls only FDR, which is then followed by a second stage co-expression discovery which controls both FDR and MAS. It also computes and thresholds the set of FDR p-values for each correlation that satisfied the MAS criterion. Using simulated data, we validated asymptotic null distributions of the Pearson and Kendall correlation coefficients and the two-stage error-control procedure; we also compared our two-stage test procedure with another two-stage test procedure using the receiver operating characteristic (ROC) curve. We then used yeast galactose metabolism data to illustrate the advantage of our method for clustering genes and constructing a relevance network. The method has been implemented in an R package "GeneNT" that is freely available from the Comprehensive R Archive Network (CRAN): www.cran.r-project.org/.     

High-Dimensional Heteroscedastic Regression with an Application to eQTL Data Analysis

We consider the problem of high-dimensional regression under non-constant error variances. Despite being a common phenomenon in biological applications, heteroscedasticity has, so far, been largely ignored in high-dimensional analysis of genomic data sets. We propose a new methodology that allows non-constant error variances for high-dimensional estimation and model selection. Our method incorporates heteroscedasticity by simultaneously modeling both the mean and variance components via a novel doubly regularized approach. Extensive Monte Carlo simulations indicate that our proposed procedure can result in better estimation and variable selection than existing methods when heteroscedasticity arises from the presence of predictors explaining error variances and outliers. Further, we demonstrate the presence of heteroscedasticity in and apply our method to an expression quantitative trait loci (eQTLs) study of 112 yeast segregants. The new procedure can automatically account for heteroscedasticity in identifying the eQTLs that are associated with gene expression variations and lead to smaller prediction errors. These results demonstrate the importance of considering heteroscedasticity in eQTL data analysis.     

A statistical framework for eQTL mapping using RNA-seq data

RNA-seq may replace gene expression microarrays in the near future. Using RNA-seq, the expression of a gene can be estimated using the total number of sequence reads mapped to that gene, known as the total read count (TReC). Traditional expression quantitative trait locus (eQTL) mapping methods, such as linear regression, can be applied to TReC measurements after they are properly normalized. In this article, we show that eQTL mapping, by directly modeling TReC using discrete distributions, has higher statistical power than the two-step approach: data normalization followed by linear regression. In addition, RNA-seq provides information on allele-specific expression (ASE) that is not available from microarrays. By combining the information from TReC and ASE, we can computationally distinguish cis- and trans-eQTL and further improve the power of cis-eQTL mapping. Both simulation and real data studies confirm the improved power of our new methods. We also discuss the design issues of RNA-seq experiments. Specifically, we show that by combining TReC and ASE measurements, it is possible to minimize cost and retain the statistical power of cis-eQTL mapping by reducing sample size while increasing the number of sequence reads per sample. In addition to RNA-seq data, our method can also be employed to study the genetic basis of other types of sequencing data, such as chromatin immunoprecipitation followed by DNA sequencing data. In this article, we focus on eQTL mapping of a single gene using the association-based method. However, our method establishes a statistical framework for future developments of eQTL mapping methods using RNA-seq data (e.g., linkage-based eQTL mapping), and the joint study of multiple genetic markers and/or multiple genes.     

Genomewide association analysis in diverse inbred mice: power and population structure

The discovery of quantitative trait loci (QTL) in model organisms has relied heavily on the ability to perform controlled breeding to generate genotypic and phenotypic diversity. Recently, we and others have demonstrated the use of an existing set of diverse inbred mice (referred to here as the mouse diversity panel, MDP) as a QTL mapping population. The use of the MDP population has many advantages relative to traditional F(2) mapping populations, including increased phenotypic diversity, a higher recombination frequency, and the ability to collect genotype and phenotype data in community databases. However, these methods are complicated by population structure inherent in the MDP and the lack of an analytical framework to assess statistical power. To address these issues, we measured gene expression levels in hypothalamus across the MDP. We then mapped these phenotypes as quantitative traits with our association algorithm, resulting in a large set of expression QTL (eQTL). We utilized these eQTL, and specifically cis-eQTL, to develop a novel nonparametric method for association analysis in structured populations like the MDP. These eQTL data confirmed that the MDP is a suitable mapping population for QTL discovery and that eQTL results can serve as a gold standard for relative measures of statistical power.     

SnIPRE: Selection Inference Using a Poisson Random Effects Model

We present an approach for identifying genes under natural selection using polymorphism and divergence data from synonymous and non-synonymous sites within genes. A generalized linear mixed model is used to model the genome-wide variability among categories of mutations and estimate its functional consequence. We demonstrate how the model''s estimated fixed and random effects can be used to identify genes under selection. The parameter estimates from our generalized linear model can be transformed to yield population genetic parameter estimates for quantities including the average selection coefficient for new mutations at a locus, the synonymous and non-synynomous mutation rates, and species divergence times. Furthermore, our approach incorporates stochastic variation due to the evolutionary process and can be fit using standard statistical software. The model is fit in both the empirical Bayes and Bayesian settings using the lme4 package in R, and Markov chain Monte Carlo methods in WinBUGS. Using simulated data we compare our method to existing approaches for detecting genes under selection: the McDonald-Kreitman test, and two versions of the Poisson random field based method MKprf. Overall, we find our method universally outperforms existing methods for detecting genes subject to selection using polymorphism and divergence data.     

MicroRNA expression in abdominal and gluteal adipose tissue is associated with mRNA expression levels and partly genetically driven

To understand how miRNAs contribute to the molecular phenotype of adipose tissues and related traits, we performed global miRNA expression profiling in subcutaneous abdominal and gluteal adipose tissue of 70 human subjects and characterised which miRNAs were differentially expressed between these tissues. We found that 12% of the miRNAs were significantly differentially expressed between abdominal and gluteal adipose tissue (FDR adjusted p<0.05) in the primary study, of which 59 replicated in a follow-up study of 40 additional subjects. Further, 14 miRNAs were found to be associated with metabolic syndrome case-control status in abdominal tissue and three of these replicated (primary study: FDR adjusted p<0.05, replication: p<0.05 and directionally consistent effect). Genome-wide genotyping was performed in the 70 subjects to enable miRNA expression quantitative trait loci (eQTL) analysis. Candidate miRNA eQTLs were followed-up in the additional 40 subjects and six significant, independent cis-located miRNA eQTLs (primary study: p<0.001; replication: p<0.05 and directionally consistent effect) were identified. Finally, global mRNA expression profiling was performed in both tissues to enable association analysis between miRNA and target mRNA expression levels. We find 22% miRNAs in abdominal and 9% miRNAs in gluteal adipose tissue with expression levels significantly associated with the expression of corresponding target mRNAs (FDR adjusted p<0.05). Taken together, our results indicate a clear difference in the miRNA molecular phenotypic profile of abdominal and gluteal adipose tissue, that the expressions of some miRNAs are influenced by cis-located genetic variants and that miRNAs are associated with expression levels of their predicted mRNA targets.     

Estimation of false discovery rates in multiple testing: application to gene microarray data

Testing for significance with gene expression data from DNA microarray experiments involves simultaneous comparisons of hundreds or thousands of genes. If R denotes the number of rejections (declared significant genes) and V denotes the number of false rejections, then V/R, if R > 0, is the proportion of false rejected hypotheses. This paper proposes a model for the distribution of the number of rejections and the conditional distribution of V given R, V / R. Under the independence assumption, the distribution of R is a convolution of two binomials and the distribution of V / R has a noncentral hypergeometric distribution. Under an equicorrelated model, the distributions are more complex and are also derived. Five false discovery rate probability error measures are considered: FDR = E(V/R), pFDR = E(V/R / R > 0) (positive FDR), cFDR = E(V/R / R = r) (conditional FDR), mFDR = E(V)/E(R) (marginal FDR), and eFDR = E(V)/r (empirical FDR). The pFDR, cFDR, and mFDR are shown to be equivalent under the Bayesian framework, in which the number of true null hypotheses is modeled as a random variable. We present a parametric and a bootstrap procedure to estimate the FDRs. Monte Carlo simulations were conducted to evaluate the performance of these two methods. The bootstrap procedure appears to perform reasonably well, even when the alternative hypotheses are correlated (rho = .25). An example from a toxicogenomic microarray experiment is presented for illustration.     

Penalized Multimarker vs. Single-Marker Regression Methods for Genome-Wide Association Studies of Quantitative Traits

The data from genome-wide association studies (GWAS) in humans are still predominantly analyzed using single-marker association methods. As an alternative to single-marker analysis (SMA), all or subsets of markers can be tested simultaneously. This approach requires a form of penalized regression (PR) as the number of SNPs is much larger than the sample size. Here we review PR methods in the context of GWAS, extend them to perform penalty parameter and SNP selection by false discovery rate (FDR) control, and assess their performance in comparison with SMA. PR methods were compared with SMA, using realistically simulated GWAS data with a continuous phenotype and real data. Based on these comparisons our analytic FDR criterion may currently be the best approach to SNP selection using PR for GWAS. We found that PR with FDR control provides substantially more power than SMA with genome-wide type-I error control but somewhat less power than SMA with Benjamini–Hochberg FDR control (SMA-BH). PR with FDR-based penalty parameter selection controlled the FDR somewhat conservatively while SMA-BH may not achieve FDR control in all situations. Differences among PR methods seem quite small when the focus is on SNP selection with FDR control. Incorporating linkage disequilibrium into the penalization by adapting penalties developed for covariates measured on graphs can improve power but also generate more false positives or wider regions for follow-up. We recommend the elastic net with a mixing weight for the Lasso penalty near 0.5 as the best method.     

A statistical method for the conservative adjustment of false discovery rate (<Emphasis Type="Italic">q</Emphasis>-value)

Background

q-value is a widely used statistical method for estimating false discovery rate (FDR), which is a conventional significance measure in the analysis of genome-wide expression data. q-value is a random variable and it may underestimate FDR in practice. An underestimated FDR can lead to unexpected false discoveries in the follow-up validation experiments. This issue has not been well addressed in literature, especially in the situation when the permutation procedure is necessary for p-value calculation.

Results

We proposed a statistical method for the conservative adjustment of q-value. In practice, it is usually necessary to calculate p-value by a permutation procedure. This was also considered in our adjustment method. We used simulation data as well as experimental microarray or sequencing data to illustrate the usefulness of our method.

Conclusions

The conservativeness of our approach has been mathematically confirmed in this study. We have demonstrated the importance of conservative adjustment of q-value, particularly in the situation that the proportion of differentially expressed genes is small or the overall differential expression signal is weak.

     

Bait-ER: A Bayesian method to detect targets of selection in Evolve-and-Resequence experiments

For over a decade, experimental evolution has been combined with high-throughput sequencing techniques. In so-called Evolve-and-Resequence (E&R) experiments, populations are kept in the laboratory under controlled experimental conditions where their genomes are sampled and allele frequencies monitored. However, identifying signatures of adaptation in E&R datasets is far from trivial, and it is still necessary to develop more efficient and statistically sound methods for detecting selection in genome-wide data. Here, we present Bait-ER – a fully Bayesian approach based on the Moran model of allele evolution to estimate selection coefficients from E&R experiments. The model has overlapping generations, a feature that describes several experimental designs found in the literature. We tested our method under several different demographic and experimental conditions to assess its accuracy and precision, and it performs well in most scenarios. Nevertheless, some care must be taken when analysing trajectories where drift largely dominates and starting frequencies are low. We compare our method with other available software and report that ours has generally high accuracy even for trajectories whose complexity goes beyond a classical sweep model. Furthermore, our approach avoids the computational burden of simulating an empirical null distribution, outperforming available software in terms of computational time and facilitating its use on genome-wide data. We implemented and released our method in a new open-source software package that can be accessed at https://doi.org/10.5281/zenodo.7351736 .     

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.     

Gene expression in skin and lymphoblastoid cells: Refined statistical method reveals extensive overlap in cis-eQTL signals

Psoriasis, an immune-mediated, inflammatory disease of the skin and joints, provides an ideal system for expression quantitative trait locus (eQTL) analysis, because it has a strong genetic basis and disease-relevant tissue (skin) is readily accessible. To better understand the role of genetic variants regulating cutaneous gene expression, we identified 841 cis-acting eQTLs using RNA extracted from skin biopsies of 53 psoriatic individuals and 57 healthy controls. We found substantial overlap between cis-eQTLs of normal control, uninvolved psoriatic, and lesional psoriatic skin. Consistent with recent studies and with the idea that control of gene expression can mediate relationships between genetic variants and disease risk, we found that eQTL SNPs are more likely to be associated with psoriasis than are randomly selected SNPs. To explore the tissue specificity of these eQTLs and hence to quantify the benefits of studying eQTLs in different tissues, we developed a refined statistical method for estimating eQTL overlap and used it to compare skin eQTLs to a published panel of lymphoblastoid cell line (LCL) eQTLs. Our method accounts for the fact that most eQTL studies are likely to miss some true eQTLs as a result of power limitations and shows that ～70% of cis-eQTLs in LCLs are shared with skin, as compared with the naive estimate of < 50% sharing. Our results provide a useful method for estimating the overlap between various eQTL studies and provide a catalog of cis-eQTLs in skin that can facilitate efforts to understand the functional impact of identified susceptibility variants on psoriasis and other skin traits.