Wavelet thresholding with bayesian false discovery rate control

The false discovery rate (FDR) procedure has become a popular method for handling multiplicity in high-dimensional data. The definition of FDR has a natural Bayesian interpretation; it is the expected proportion of null hypotheses mistakenly rejected given a measure of evidence for their truth. In this article, we propose controlling the positive FDR using a Bayesian approach where the rejection rule is based on the posterior probabilities of the null hypotheses. Correspondence between Bayesian and frequentist measures of evidence in hypothesis testing has been studied in several contexts. Here we extend the comparison to multiple testing with control of the FDR and illustrate the procedure with an application to wavelet thresholding. The problem consists of recovering signal from noisy measurements. This involves extracting wavelet coefficients that result from true signal and can be formulated as a multiple hypotheses-testing problem. We use simulated examples to compare the performance of our approach to the Benjamini and Hochberg (1995, Journal of the Royal Statistical Society, Series B57, 289-300) procedure. We also illustrate the method with nuclear magnetic resonance spectral data from human brain.     

cn.MOPS: mixture of Poissons for discovering copy number variations in next-generation sequencing data with a low false discovery rate

Quantitative analyses of next-generation sequencing (NGS) data, such as the detection of copy number variations (CNVs), remain challenging. Current methods detect CNVs as changes in the depth of coverage along chromosomes. Technological or genomic variations in the depth of coverage thus lead to a high false discovery rate (FDR), even upon correction for GC content. In the context of association studies between CNVs and disease, a high FDR means many false CNVs, thereby decreasing the discovery power of the study after correction for multiple testing. We propose 'Copy Number estimation by a Mixture Of PoissonS' (cn.MOPS), a data processing pipeline for CNV detection in NGS data. In contrast to previous approaches, cn.MOPS incorporates modeling of depths of coverage across samples at each genomic position. Therefore, cn.MOPS is not affected by read count variations along chromosomes. Using a Bayesian approach, cn.MOPS decomposes variations in the depth of coverage across samples into integer copy numbers and noise by means of its mixture components and Poisson distributions, respectively. The noise estimate allows for reducing the FDR by filtering out detections having high noise that are likely to be false detections. We compared cn.MOPS with the five most popular methods for CNV detection in NGS data using four benchmark datasets: (i) simulated data, (ii) NGS data from a male HapMap individual with implanted CNVs from the X chromosome, (iii) data from HapMap individuals with known CNVs, (iv) high coverage data from the 1000 Genomes Project. cn.MOPS outperformed its five competitors in terms of precision (1-FDR) and recall for both gains and losses in all benchmark data sets. The software cn.MOPS is publicly available as an R package at http://www.bioinf.jku.at/software/cnmops/ and at Bioconductor.     

Hit selection with false discovery rate control in genome-scale RNAi screens

RNA interference (RNAi) is a modality in which small double-stranded RNA molecules (siRNAs) designed to lead to the degradation of specific mRNAs are introduced into cells or organisms. siRNA libraries have been developed in which siRNAs targeting virtually every gene in the human genome are designed, synthesized and are presented for introduction into cells by transfection in a microtiter plate array. These siRNAs can then be transfected into cells using high-throughput screening (HTS) methodologies. The goal of RNAi HTS is to identify a set of siRNAs that inhibit or activate defined cellular phenotypes. The commonly used analysis methods including median ± kMAD have issues about error rates in multiple hypothesis testing and plate-wise versus experiment-wise analysis. We propose a methodology based on a Bayesian framework to address these issues. Our approach allows for sharing of information across plates in a plate-wise analysis, which obviates the need for choosing either a plate-wise or experimental-wise analysis. The proposed approach incorporates information from reliable controls to achieve a higher power and a balance between the contribution from the samples and control wells. Our approach provides false discovery rate (FDR) control to address multiple testing issues and it is robust to outliers.     

cn.FARMS: a latent variable model to detect copy number variations in microarray data with a low false discovery rate

Cost-effective oligonucleotide genotyping arrays like the Affymetrix SNP 6.0 are still the predominant technique to measure DNA copy number variations (CNVs). However, CNV detection methods for microarrays overestimate both the number and the size of CNV regions and, consequently, suffer from a high false discovery rate (FDR). A high FDR means that many CNVs are wrongly detected and therefore not associated with a disease in a clinical study, though correction for multiple testing takes them into account and thereby decreases the study's discovery power. For controlling the FDR, we propose a probabilistic latent variable model, 'cn.FARMS', which is optimized by a Bayesian maximum a posteriori approach. cn.FARMS controls the FDR through the information gain of the posterior over the prior. The prior represents the null hypothesis of copy number 2 for all samples from which the posterior can only deviate by strong and consistent signals in the data. On HapMap data, cn.FARMS clearly outperformed the two most prevalent methods with respect to sensitivity and FDR. The software cn.FARMS is publicly available as a R package at http://www.bioinf.jku.at/software/cnfarms/cnfarms.html.     

A mixture model for estimating the local false discovery rate in DNA microarray analysis

MOTIVATION: Statistical methods based on controlling the false discovery rate (FDR) or positive false discovery rate (pFDR) are now well established in identifying differentially expressed genes in DNA microarray. Several authors have recently raised the important issue that FDR or pFDR may give misleading inference when specific genes are of interest because they average the genes under consideration with genes that show stronger evidence for differential expression. The paper proposes a flexible and robust mixture model for estimating the local FDR which quantifies how plausible each specific gene expresses differentially. RESULTS: We develop a special mixture model tailored to multiple testing by requiring the P-value distribution for the differentially expressed genes to be stochastically smaller than the P-value distribution for the non-differentially expressed genes. A smoothing mechanism is built in. The proposed model gives robust estimation of local FDR for any reasonable underlying P-value distributions. It also provides a single framework for estimating the proportion of differentially expressed genes, pFDR, negative predictive values, sensitivity and specificity. A cervical cancer study shows that the local FDR gives more specific and relevant quantification of the evidence for differential expression that can be substantially different from pFDR. AVAILABILITY: An R function implementing the proposed model is available at http://www.geocities.com/jg_liao/software     

Implementing false discovery rate control: increasing your power

Popular procedures to control the chance of making type I errors when multiple statistical tests are performed come at a high cost: a reduction in power. As the number of tests increases, power for an individual test may become unacceptably low. This is a consequence of minimizing the chance of making even a single type I error, which is the aim of, for instance, the Bonferroni and sequential Bonferroni procedures. An alternative approach, control of the false discovery rate (FDR), has recently been advocated for ecological studies. This approach aims at controlling the proportion of significant results that are in fact type I errors. Keeping the proportion of type I errors low among all significant results is a sensible, powerful, and easy-to-interpret way of addressing the multiple testing issue. To encourage practical use of the approach, in this note we illustrate how the proposed procedure works, we compare it to more traditional methods that control the familywise error rate, and we discuss some recent useful developments in FDR control.     

A simple procedure for estimating the false discovery rate

MOTIVATION: The most used criterion in microarray data analysis is nowadays the false discovery rate (FDR). In the framework of estimating procedures based on the marginal distribution of the P-values without any assumption on gene expression changes, estimators of the FDR are necessarily conservatively biased. Indeed, only an upper bound estimate can be obtained for the key quantity pi0, which is the probability for a gene to be unmodified. In this paper, we propose a novel family of estimators for pi0 that allows the calculation of FDR. RESULTS: The very simple method for estimating pi0 called LBE (Location Based Estimator) is presented together with results on its variability. Simulation results indicate that the proposed estimator performs well in finite sample and has the best mean square error in most of the cases as compared with the procedures QVALUE, BUM and SPLOSH. The different procedures are then applied to real datasets. AVAILABILITY: The R function LBE is available at http://ifr69.vjf.inserm.fr/lbe CONTACT: broet@vjf.inserm.fr.     

Modeling recurrent DNA copy number alterations in array CGH data

MOTIVATION: Recurrent DNA copy number alterations (CNA) measured with array comparative genomic hybridization (aCGH) reveal important molecular features of human genetics and disease. Studying aCGH profiles from a phenotypic group of individuals can determine important recurrent CNA patterns that suggest a strong correlation to the phenotype. Computational approaches to detecting recurrent CNAs from a set of aCGH experiments have typically relied on discretizing the noisy log ratios and subsequently inferring patterns. We demonstrate that this can have the effect of filtering out important signals present in the raw data. In this article we develop statistical models that jointly infer CNA patterns and the discrete labels by borrowing statistical strength across samples. RESULTS: We propose extending single sample aCGH HMMs to the multiple sample case in order to infer shared CNAs. We model recurrent CNAs as a profile encoded by a master sequence of states that generates the samples. We show how to improve on two basic models by performing joint inference of the discrete labels and providing sparsity in the output. We demonstrate on synthetic ground truth data and real data from lung cancer cell lines how these two important features of our model improve results over baseline models. We include standard quantitative metrics and a qualitative assessment on which to base our conclusions. AVAILABILITY: http://www.cs.ubc.ca/~sshah/acgh.     

A unified approach to false discovery rate estimation

Background  

False discovery rate (FDR) methods play an important role in analyzing high-dimensional data. There are two types of FDR, tail area-based FDR and local FDR, as well as numerous statistical algorithms for estimating or controlling FDR. These differ in terms of underlying test statistics and procedures employed for statistical learning.     

Multidimensional local false discovery rate for microarray studies

MOTIVATION: The false discovery rate (fdr) is a key tool for statistical assessment of differential expression (DE) in microarray studies. Overall control of the fdr alone, however, is not sufficient to address the problem of genes with small variance, which generally suffer from a disproportionally high rate of false positives. It is desirable to have an fdr-controlling procedure that automatically accounts for gene variability. METHODS: We generalize the local fdr as a function of multiple statistics, combining a common test statistic for assessing DE with its standard error information. We use a non-parametric mixture model for DE and non-DE genes to describe the observed multi-dimensional statistics, and estimate the distribution for non-DE genes via the permutation method. We demonstrate this fdr2d approach for simulated and real microarray data. RESULTS: The fdr2d allows objective assessment of DE as a function of gene variability. We also show that the fdr2d performs better than commonly used modified test statistics. AVAILABILITY: An R-package OCplus containing functions for computing fdr2d() and other operating characteristics of microarray data is available at http://www.meb.ki.se/~yudpaw.     

Marginal false discovery rate control for likelihood‐based penalized regression models

The popularity of penalized regression in high‐dimensional data analysis has led to a demand for new inferential tools for these models. False discovery rate control is widely used in high‐dimensional hypothesis testing, but has only recently been considered in the context of penalized regression. Almost all of this work, however, has focused on lasso‐penalized linear regression. In this paper, we derive a general method for controlling the marginal false discovery rate that can be applied to any penalized likelihood‐based model, such as logistic regression and Cox regression. Our approach is fast, flexible and can be used with a variety of penalty functions including lasso, elastic net, MCP, and MNet. We derive theoretical results under which the proposed method is valid, and use simulation studies to demonstrate that the approach is reasonably robust, albeit slightly conservative, when these assumptions are violated. Despite being conservative, we show that our method often offers more power to select causally important features than existing approaches. Finally, the practical utility of the method is demonstrated on gene expression datasets with binary and time‐to‐event outcomes.     

Sample size determination for the false discovery rate

MOTIVATION: There is not a widely applicable method to determine the sample size for experiments basing statistical significance on the false discovery rate (FDR). RESULTS: We propose and develop the anticipated FDR (aFDR) as a conceptual tool for determining sample size. We derive mathematical expressions for the aFDR and anticipated average statistical power. These expressions are used to develop a general algorithm to determine sample size. We provide specific details on how to implement the algorithm for a k-group (k > or = 2) comparisons. The algorithm performs well for k-group comparisons in a series of traditional simulations and in a real-data simulation conducted by resampling from a large, publicly available dataset. AVAILABILITY: Documented S-plus and R code libraries are freely available from www.stjuderesearch.org/depts/biostats.     

A hierarchical clustering method for estimating copy number variation

Microarray technologies allow for simultaneous measurement of DNA copy number at thousands of positions in a genome. Gains and losses of DNA sequences reveal themselves through characteristic patterns of hybridization intensity. To identify change points along the chromosomes, we develop a marker clustering method which consists of 2 parts. First, a "circular clustering tree test statistic" attaches a statistic to each marker that measures the likelihood that it is a change point. Then construction of the marker statistics is followed by outlier detection approaches. The method provides a new way to build up a binary tree that can accurately capture change-point signals and is easy to perform. A simulation study shows good performance in change-point detection, and cancer cell line data are used to illustrate performance when regions of true copy number changes are known.     

fdrMotif: identifying cis-elements by an EM algorithm coupled with false discovery rate control

MOTIVATION: Most de novo motif identification methods optimize the motif model first and then separately test the statistical significance of the motif score. In the first stage, a motif abundance parameter needs to be specified or modeled. In the second stage, a Z-score or P-value is used as the test statistic. Error rates under multiple comparisons are not fully considered. Methodology: We propose a simple but novel approach, fdrMotif, that selects as many binding sites as possible while controlling a user-specified false discovery rate (FDR). Unlike existing iterative methods, fdrMotif combines model optimization [e.g. position weight matrix (PWM)] and significance testing at each step. By monitoring the proportion of binding sites selected in many sets of background sequences, fdrMotif controls the FDR in the original data. The model is then updated using an expectation (E)- and maximization (M)-like procedure. We propose a new normalization procedure in the E-step for updating the model. This process is repeated until either the model converges or the number of iterations exceeds a maximum. RESULTS: Simulation studies suggest that our normalization procedure assigns larger weights to the binding sites than do two other commonly used normalization procedures. Furthermore, fdrMotif requires only a user-specified FDR and an initial PWM. When tested on 542 high confidence experimental p53 binding loci, fdrMotif identified 569 p53 binding sites in 505 (93.2%) sequences. In comparison, MEME identified more binding sites but in fewer ChIP sequences than fdrMotif. When tested on 500 sets of simulated 'ChIP' sequences with embedded known p53 binding sites, fdrMotif, compared to MEME, has higher sensitivity with similar positive predictive value. Furthermore, fdrMotif is robust to noise: it selected nearly identical binding sites in data adulterated with 50% added background sequences and the unadulterated data. We suggest that fdrMotif represents an improvement over MEME. AVAILABILITY: C code can be found at: http://www.niehs.nih.gov/research/resources/software/fdrMotif/.     

Number matters: control of mammalian mitochondrial DNA copy number

Regulation of mitochondrial biogenesis is essential for proper cellular functioning. Mitochondrial DNA （mtDNA） depletion and the resulting mitochondrial malfunction have been implicated in cancer, neurodegeneration, diabetes, aging, and many other human diseases. Although it is known that the dynamics of the mammalian mitochondrial genome are not linked with that of the nuclear genome, very little is known about the mechanism of mtDNA propagation. Nevertheless, our understanding of the mode of mtDNA replication has ad- vanced in recent years, though not without some controversies. This review summarizes our current knowledge of mtDNA copy number control in mammalian cells, while focusing on both mtDNA replication and turnover. Although mtDNA copy number is seemingly in excess, we reason that mtDNA copy number control is an important aspect of mitochondrial genetics and biogenesis and is essential for normal cellular function.     

A new method for determining ribosomal DNA copy number shows differences between Saccharomyces cerevisiae populations

Ribosomal DNA genes (rDNA) encode the major ribosomal RNAs and in eukaryotes typically form tandem repeat arrays. Species have characteristic rDNA copy numbers, but there is substantial intra-species variation in copy number that results from frequent rDNA recombination. Copy number differences can have phenotypic consequences, however difficulties in quantifying copy number mean we lack a comprehensive understanding of how copy number evolves and the consequences. Here we present a genomic sequence read approach to estimate rDNA copy number based on modal coverage to help overcome limitations with existing mean coverage-based approaches. We validated our method using Saccharomyces cerevisiae strains with known rDNA copy numbers. Application of our pipeline to a global sample of S. cerevisiae isolates showed that different populations have different rDNA copy numbers. Our results demonstrate the utility of the modal coverage method, and highlight the high level of rDNA copy number variation within and between populations.     

A powerful procedure that controls the false discovery rate with directional information

In many multiple testing applications in genetics, the signs of the test statistics provide useful directional information, such as whether genes are potentially up‐ or down‐regulated between two experimental conditions. However, most existing procedures that control the false discovery rate (FDR) are P‐value based and ignore such directional information. We introduce a novel procedure, the signed‐knockoff procedure, to utilize the directional information and control the FDR in finite samples. We demonstrate the power advantage of our procedure through simulation studies and two real applications.     

GEAR: genomic enrichment analysis of regional DNA copy number changes

We developed an algorithm named GEAR (genomic enrichment analysis of regional DNA copy number changes) for functional interpretation of genome-wide DNA copy number changes identified by array-based comparative genomic hybridization. GEAR selects two types of chromosomal alterations with potential biological relevance, i.e. recurrent and phenotype-specific alterations. Then it performs functional enrichment analysis using a priori selected functional gene sets to identify primary and clinical genomic signatures. The genomic signatures identified by GEAR represent functionally coordinated genomic changes, which can provide clues on the underlying molecular mechanisms related to the phenotypes of interest. GEAR can help the identification of key molecular functions that are activated or repressed in the tumor genomes leading to the improved understanding on the tumor biology. AVAILABILITY: GEAR software is available with online manual in the website, http://www.systemsbiology.co.kr/GEAR/.