The admixture model is widely applied to estimate and interpret population structure among individuals. Here we consider a "standard admixture" model that assumes the admixed populations are unrelated and also a generalized model, where the admixed populations themselves are related via coancestry (or covariance) of allele frequencies. The generalized model yields a potentially more realistic and substantially more flexible model that we call "super admixture". This super admixture model provides a one-to-one mapping in terms of probability moments with the kinship model, the latter of which is a general model of genome-wide relatedness and structure based on identity-by-descent. We introduce a method to estimate the super admixture model that is based on method of moments, does not rely on likelihoods, is computationally efficient, and scales to massive sample sizes. We apply the method to several human data sets and show that the admixed populations are indeed substantially related, implying the proposed method captures a new and important component of evolutionary history and structure in the admixture model. We show that the fitted super admixture model estimates relatedness between all pairs of individuals at a resolution similar to the kinship model. The super admixture model therefore provides a tractable, forward-generating probabilistic model of complex structure and relatedness that should be useful in a variety of scenarios.

MOTIVATION: Analysis of biological data often involves the simultaneous testing of thousands of genes. This requires two key steps: the ranking of genes and the selection of important genes based on a significance threshold. One such testing procedure, called the optimal discovery procedure (ODP), leverages information across different tests to provide an optimal ranking of genes. This approach can lead to substantial improvements in statistical power compared to other methods. However, current applications of the ODP have only been established for simple study designs using microarray technology. Here, we extend this work to the analysis of complex study designs and RNA-sequencing studies. RESULTS: We apply our extended framework to a static RNA-sequencing study, a longitudinal study, an independent sampling time-series study,and an independent sampling dose-response study. Our method shows improved performance compared to other testing procedures, finding more differentially expressed genes and increasing power for enrichment analysis. Thus, the extended ODP enables a favorable significance analysis of genome-wide gene expression studies. AVAILABILITY AND IMPLEMENTATION: The algorithm is implemented in our freely available R package called edge and can be downloaded at https://www.bioconductor.org/packages/release/bioc/html/edge.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Modern population genetics studies typically involve genome-wide genotyping of individuals from a diverse network of ancestries. An important problem is how to formulate and estimate probabilistic models of observed genotypes that account for complex population structure. The most prominent work on this problem has focused on estimating a model of admixture proportions of ancestral populations for each individual. Here, we instead focus on modeling variation of the genotypes without requiring a higher-level admixture interpretation. RESULTS: We formulate two general probabilistic models, and we propose computationally efficient algorithms to estimate them. First, we show how principal component analysis can be utilized to estimate a general model that includes the well-known Pritchard-Stephens-Donnelly admixture model as a special case. Noting some drawbacks of this approach, we introduce a new 'logistic factor analysis' framework that seeks to directly model the logit transformation of probabilities underlying observed genotypes in terms of latent variables that capture population structure. We demonstrate these advances on data from the Human Genome Diversity Panel and 1000 Genomes Project, where we are able to identify SNPs that are highly differentiated with respect to structure while making minimal modeling assumptions. AVAILABILITY AND IMPLEMENTATION: A Bioconductor R package called lfa is available at http://www.bioconductor.org/packages/release/bioc/html/lfa.html CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: There are a number of well-established methods such as principal component analysis (PCA) for automatically capturing systematic variation due to latent variables in large-scale genomic data. PCA and related methods may directly provide a quantitative characterization of a complex biological variable that is otherwise difficult to precisely define or model. An unsolved problem in this context is how to systematically identify the genomic variables that are drivers of systematic variation captured by PCA. Principal components (PCs) (and other estimates of systematic variation) are directly constructed from the genomic variables themselves, making measures of statistical significance artificially inflated when using conventional methods due to over-fitting. RESULTS: We introduce a new approach called the jackstraw that allows one to accurately identify genomic variables that are statistically significantly associated with any subset or linear combination of PCs. The proposed method can greatly simplify complex significance testing problems encountered in genomics and can be used to identify the genomic variables significantly associated with latent variables. Using simulation, we demonstrate that our method attains accurate measures of statistical significance over a range of relevant scenarios. We consider yeast cell-cycle gene expression data, and show that the proposed method can be used to straightforwardly identify genes that are cell-cycle regulated with an accurate measure of statistical significance. We also analyze gene expression data from post-trauma patients, allowing the gene expression data to provide a molecularly driven phenotype. Using our method, we find a greater enrichment for inflammatory-related gene sets compared to the original analysis that uses a clinically defined, although likely imprecise, phenotype. The proposed method provides a useful bridge between large-scale quantifications of systematic variation and gene-level significance analyses. AVAILABILITY AND IMPLEMENTATION: An R software package, called jackstraw, is available in CRAN. CONTACT: [email protected].

E-values have been the dominant statistic for protein sequence analysis for the past two decades: from identifying statistically significant local sequence alignments to evaluating matches to hidden Markov models describing protein domain families. Here we formally show that for "stratified" multiple hypothesis testing problems-that is, those in which statistical tests can be partitioned naturally-controlling the local False Discovery Rate (lFDR) per stratum, or partition, yields the most predictions across the data at any given threshold on the FDR or E-value over all strata combined. For the important problem of protein domain prediction, a key step in characterizing protein structure, function and evolution, we show that stratifying statistical tests by domain family yields excellent results. We develop the first FDR-estimating algorithms for domain prediction, and evaluate how well thresholds based on q-values, E-values and lFDRs perform in domain prediction using five complementary approaches for estimating empirical FDRs in this context. We show that stratified q-value thresholds substantially outperform E-values. Contradicting our theoretical results, q-values also outperform lFDRs; however, our tests reveal a small but coherent subset of domain families, biased towards models for specific repetitive patterns, for which weaknesses in random sequence models yield notably inaccurate statistical significance measures. Usage of lFDR thresholds outperform q-values for the remaining families, which have as-expected noise, suggesting that further improvements in domain predictions can be achieved with improved modeling of random sequences. Overall, our theoretical and empirical findings suggest that the use of stratified q-values and lFDRs could result in improvements in a host of structured multiple hypothesis testing problems arising in bioinformatics, including genome-wide association studies, orthology prediction, and motif scanning.

MOTIVATION: Next-generation sequencing experiments, such as RNA-Seq, play an increasingly important role in biological research. One complication is that the power and accuracy of such experiments depend substantially on the number of reads sequenced, so it is important and challenging to determine the optimal read depth for an experiment or to verify whether one has adequate depth in an existing experiment. RESULTS: By randomly sampling lower depths from a sequencing experiment and determining where the saturation of power and accuracy occurs, one can determine what the most useful depth should be for future experiments, and furthermore, confirm whether an existing experiment had sufficient depth to justify its conclusions. We introduce the subSeq R package, which uses a novel efficient approach to perform this subsampling and to calculate informative metrics at each depth. AVAILABILITY AND IMPLEMENTATION: The subSeq R package is available at http://github.com/StoreyLab/subSeq/.

BACKGROUND: Significance analysis plays a major role in identifying and ranking genes, transcription factor binding sites, DNA methylation regions, and other high-throughput features associated with illness. We propose a new approach, called gene set bagging, for measuring the probability that a gene set replicates in future studies. Gene set bagging involves resampling the original high-throughput data, performing gene-set analysis on the resampled data, and confirming that biological categories replicate in the bagged samples. RESULTS: Using both simulated and publicly-available genomics data, we demonstrate that significant categories in a gene set enrichment analysis may be unstable when subjected to resampling. We show our method estimates the replication probability (R), the probability that a gene set will replicate as a significant result in future studies, and show in simulations that this method reflects replication better than each set's p-value. CONCLUSIONS: Our results suggest that gene lists based on p-values are not necessarily stable, and therefore additional steps like gene set bagging may improve biological inference on gene sets.

Abstract Summary: Heterogeneity and latent variables are now widely recognized as major sources of bias and variability in high-throughput experiments. The most well-known source of latent variation in genomic experiments are batch effects—when samples are processed on different days, in different groups or by different people. However, there are also a large number of other variables that may have a major impact on high-throughput measurements. Here we describe the sva package for identifying, estimating and removing unwanted sources of variation in high-throughput experiments. The sva package supports surrogate variable estimation with the sva function, direct adjustment for known batch effects with the ComBat function and adjustment for batch and latent variables in prediction problems with the fsva function. Availability: The R package sva is freely available from http://www.bioconductor.org. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.

MOTIVATION: It is well known that patterns of differential gene expression across biological conditions are often shared by many genes, particularly those within functional groups. Taking advantage of these patterns can lead to increased statistical power and biological clarity when testing for differential expression in a microarray experiment. The optimal discovery procedure (ODP), which maximizes the expected number of true positives for each fixed number of expected false positives, is a framework aimed at this goal. Storey et al. introduced an estimator of the ODP for identifying differentially expressed genes. However, their ODP estimator grows quadratically in computational time with respect to the number of genes. Reducing this computational burden is a key step in making the ODP practical for usage in a variety of high-throughput problems. RESULTS: Here, we propose a new estimate of the ODP called the modular ODP (mODP). The existing 'full ODP' requires that the likelihood function for each gene be evaluated according to the parameter estimates for all genes. The mODP assigns genes to modules according to a Kullback-Leibler distance, and then evaluates the statistic only at the module-averaged parameter estimates. We show that the mODP is relatively insensitive to the choice of the number of modules, but dramatically reduces the computational complexity from quadratic to linear in the number of genes. We compare the full ODP algorithm and mODP on simulated data and gene expression data from a recent study of Morrocan Amazighs. The mODP and full ODP algorithm perform very similarly across a range of comparisons. AVAILABILITY: The mODP methodology has been implemented into EDGE, a comprehensive gene expression analysis software package in R, available at http://genomine.org/edge/.

MOTIVATION: A major challenge in utilizing microarray technologies to measure nucleic acid abundances is 'normalization', the goal of which is to separate biologically meaningful signal from other confounding sources of signal, often due to unavoidable technical factors. It is intuitively clear that true biological signal and confounding factors need to be simultaneously considered when performing normalization. However, the most popular normalization approaches do not utilize what is known about the study, both in terms of the biological variables of interest and the known technical factors in the study, such as batch or array processing date. RESULTS: We show here that failing to include all study-specific biological and technical variables when performing normalization leads to biased downstream analyses. We propose a general normalization framework that fits a study-specific model employing every known variable that is relevant to the expression study. The proposed method is generally applicable to the full range of existing probe designs, as well as to both single-channel and dual-channel arrays. We show through real and simulated examples that the method has favorable operating characteristics in comparison to some of the most highly used normalization methods. AVAILABILITY: An R package called snm implementing the methodology will be made available from Bioconductor (http://bioconductor.org). CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

UNLABELLED: Qvality is a C++ program for estimating two types of standard statistical confidence measures: the q-value, which is an analog of the p-value that incorporates multiple testing correction, and the posterior error probability (PEP, also known as the local false discovery rate), which corresponds to the probability that a given observation is drawn from the null distribution. In computing q-values, qvality employs a standard bootstrap procedure to estimate the prior probability of a score being from the null distribution; for PEP estimation, qvality relies upon non-parametric logistic regression. Relative to other tools for estimating statistical confidence measures, qvality is unique in its ability to estimate both types of scores directly from a null distribution, without requiring the user to calculate p-values. AVAILABILITY: A web server, C++ source code and binaries are available under MIT license at http://noble.gs.washington.edu/proj/qvality. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Abstract Summary: We provide a new statistical algorithm and software package called ‘eigen-R2’ for dissecting the variation of a high-dimensional biological dataset with respect to other measured variables of interest. We apply eigen-R2 to two real-life examples and compare it with simply averaging R2 over many features. Availability: An R-package eigenR2 is available at http://www.genomine.org/eigenr2/ and will be made publicly available via Bioconductor. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.

BACKGROUND: The combination of gene expression profiling with linkage analysis has become a powerful paradigm for mapping gene expression quantitative trait loci (eQTL). To date, most studies have searched for eQTL by analyzing gene expression traits one at a time. As thousands of expression traits are typically analyzed, this can reduce power because of the need to correct for the number of hypothesis tests performed. In addition, gene expression traits exhibit a complex correlation structure, which is ignored when analyzing traits individually. RESULTS: To address these issues, we applied two different multivariate dimension reduction techniques, the Singular Value Decomposition (SVD) and Independent Component Analysis (ICA) to gene expression traits derived from a cross between two strains of Saccharomyces cerevisiae. Both methods decompose the data into a set of meta-traits, which are linear combinations of all the expression traits. The meta-traits were enriched for several Gene Ontology categories including metabolic pathways, stress response, RNA processing, ion transport, retro-transposition and telomeric maintenance. Genome-wide linkage analysis was performed on the top 20 meta-traits from both techniques. In total, 21 eQTL were found, of which 11 are novel. Interestingly, both cis and trans-linkages to the meta-traits were observed. CONCLUSION: These results demonstrate that dimension reduction methods are a useful and complementary approach for probing the genetic architecture of gene expression variation.

Abstract Summary: EDGE (Extraction of Differential Gene Expression) is an open source, point-and-click software program for the significance analysis of DNA microarray experiments. EDGE can perform both standard and time course differential expression analysis. The functions are based on newly developed statistical theory and methods. This document introduces the EDGE software package. Availability: EDGE is freely available for non-commercial users. EDGE can be downloaded for Windows, Macintosh and Linux/UNIX from Contact: [email protected]

The authors would like to apologise for the omission of John D. Storey's email address, as he is a corresponding author for the article. He can be contacted by [email protected]. The authors would also like to apologise for an incorrect reference given in the article. The reference cited by Storey et al. (2005b) should be as follows: Storey,J.D. et al. (2005b) Significance analysis of time course microarray experiments. Proc. Natl Acad. Sci. USA, 102, 12837–12842.