Empirical Bayes shrinkage and false discovery rate estimation, allowing for unwanted variation.
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ABSTRACT:
SUBMITTER: Gerard D
PROVIDER: S-EPMC8204175 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:MotivationGenomic studies often involve estimation of variances of thousands of genes (or other genomic units) from just a few measurements on each. For example, variance estimation is an important step in gene expression analyses aimed at identifying differentially expressed genes. A common approach to this problem is to use an Empirical Bayes (EB) method that assumes the variances among genes follow an inverse-gamma distribution. This distributional assumption is relatively inflexible; for example, it may not capture 'outlying' genes whose variances are considerably bigger than usual. Here we describe a more flexible EB method, capable of capturing a much wider range of distributions. Indeed, the main assumption is that the distribution of the variances is unimodal (or, as an alternative, that the distribution of the precisions is unimodal). We argue that the unimodal assumption provides an attractive compromise between flexibility, computational tractability and statistical efficiency.ResultsWe show that this more flexible approach provides competitive performance with existing methods when the variances truly come from an inverse-gamma distribution, and can outperform them when the distribution of the variances is more complex. In analyses of several human gene expression datasets from the Genotype Tissues Expression consortium, we find that our more flexible model often fits the data appreciably better than the single inverse gamma distribution. At the same time we find that in these data this improved model fit leads to only small improvements in variance estimates and detection of differentially expressed genes.Availability and implementationOur methods are implemented in an R package vashr available from http://github.com/mengyin/vashr CONTACT: mstephens@uchicago.eduSupplementary information: Supplementary data are available at Bioinformatics online.
| S-EPMC5181563 | biostudies-literature
Project description:BackgroundIn investigating differentially expressed genes or other selected features, researchers conduct hypothesis tests to determine which biological categories, such as those of the Gene Ontology (GO), are enriched for the selected features. Multiple comparison procedures (MCPs) are commonly used to prevent excessive false positive rates. Traditional MCPs, e.g., the Bonferroni method, go to the opposite extreme: strictly controlling a family-wise error rate, resulting in excessive false negative rates. Researchers generally prefer the more balanced approach of instead controlling the false discovery rate (FDR). However, the q-values that methods of FDR control assign to biological categories tend to be too low to reliably estimate the probability that a biological category is not enriched for the preselected features. Thus, we study an application of the other estimators of that probability, which is called the local FDR (LFDR).ResultsWe considered five LFDR estimators for detecting enriched GO terms: a binomial-based estimator (BBE), a maximum likelihood estimator (MLE), a normalized MLE (NMLE), a histogram-based estimator assuming a theoretical null hypothesis (HBE), and a histogram-based estimator assuming an empirical null hypothesis (HBE-EN). Since NMLE depends not only on the data but also on the specified value of π0, the proportion of non-enriched GO terms, it is only advantageous when either π0 is already known with sufficient accuracy or there are data for only 1 GO term. By contrast, the other estimators work without specifying π0 but require data for at least 2 GO terms. Our simulation studies yielded the following summaries of the relative performance of each of those four estimators. HBE and HBE-EN produced larger biases for 2, 4, 8, 32, and 100 GO terms than BBE and MLE. BBE has the lowest bias if π0 is 1 and if the number of GO terms is between 2 and 32. The bias of MLE is no worse than that of BBE for 100 GO terms even when the ideal number of components in its underlying mixture model is unknown, but has high bias when the number of GO terms is small compared to the number of estimated parameters. For unknown values of π0, BBE has the lowest bias for a small number of GO terms (2-32 GO terms), and MLE has the lowest bias for a medium number of GO terms (100 GO terms).ConclusionsFor enrichment detection, we recommend estimating the LFDR by MLE given at least a medium number of GO terms, by BBE given a small number of GO terms, and by NMLE given either only 1 GO term or precise knowledge of π0.
| S-EPMC3658916 | biostudies-literature
Project description:In almost every field in genomics, large-scale biomedical datasets are used to report associations. Extracting associations that recur across multiple studies while controlling the false discovery rate is a fundamental challenge. Here, we propose a new method to allow joint analysis of multiple studies. Given a set of p-values obtained from each study, the goal is to identify associations that recur in at least k > 1 studies while controlling the false discovery rate. We propose several new algorithms that differ in how the study dependencies are modeled, and compare them and extant methods under various simulated scenarios. The top algorithm, SCREEN (Scalable Cluster-based REplicability ENhancement), is our new algorithm that works in three stages: (1) clustering an estimated correlation network of the studies, (2) learning replicability (e.g., of genes) within clusters, and (3) merging the results across the clusters. When we applied SCREEN to two real datasets it greatly outperformed the results obtained via standard meta-analysis. First, on a collection of 29 case-control gene expression cancer studies, we detected a large set of consistently up-regulated genes related to proliferation and cell cycle regulation. These genes are both consistently up-regulated across many cancer studies, and are well connected in known gene networks. Second, on a recent pan-cancer study that examined the expression profiles of patients with and without mutations in the HLA complex, we detected a large active module of up-regulated genes that are both related to immune responses and are well connected in known gene networks. This module covers thrice more genes as compared to the original study at a similar false discovery rate, demonstrating the high power of SCREEN. An implementation of SCREEN is available in the supplement.
| S-EPMC5576761 | biostudies-literature
Project description:The graphon (W-graph), including the stochastic block model as a special case, has been widely used in modeling and analyzing network data. Estimation of the graphon function has gained a lot of recent research interests. Most existing works focus on inference in the latent space of the model, while adopting simple maximum likelihood or Bayesian estimates for the graphon or connectivity parameters given the identified latent variables. In this work, we propose a hierarchical model and develop a novel empirical Bayes estimate of the connectivity matrix of a stochastic block model to approximate the graphon function. Based on our hierarchical model, we further introduce a new model selection criterion for choosing the number of communities. Numerical results on extensive simulations and two well-annotated social networks demonstrate the superiority of our approach in terms of parameter estimation and model selection.
| S-EPMC9299287 | biostudies-literature
Project description:The James-Stein estimator is an estimator of the multivariate normal mean and dominates the maximum likelihood estimator (MLE) under squared error loss. The original work inspired great interest in developing shrinkage estimators for a variety of problems. Nonetheless, research on shrinkage estimation for manifold-valued data is scarce. In this article, we propose shrinkage estimators for the parameters of the Log-Normal distribution defined on the manifold of N × N symmetric positive-definite matrices. For this manifold, we choose the Log-Euclidean metric as its Riemannian metric since it is easy to compute and has been widely used in a variety of applications. By using the Log-Euclidean distance in the loss function, we derive a shrinkage estimator in an analytic form and show that it is asymptotically optimal within a large class of estimators that includes the MLE, which is the sample Fréchet mean of the data. We demonstrate the performance of the proposed shrinkage estimator via several simulated data experiments. Additionally, we apply the shrinkage estimator to perform statistical inference in both diffusion and functional magnetic resonance imaging problems.
| S-EPMC11000275 | biostudies-literature
Project description:False discovery rate (FDR) estimation is a cornerstone of proteomics that has recently been adapted to cross-linking/mass spectrometry. Here we demonstrate that heterobifunctional cross-linkers, while theoretically different from homobifunctional cross-linkers, need not be considered separately in practice. We develop and then evaluate the impact of applying a correct FDR formula for use of heterobifunctional cross-linkers and conclude that there are minimal practical advantages. Hence a single formula can be applied to data generated from the many different non-cleavable cross-linkers.
| S-EPMC5944926 | biostudies-literature
Project description:Interpreting the potentially vast number of hypotheses generated by a shotgun proteomics experiment requires a valid and accurate procedure for assigning statistical confidence estimates to identified tandem mass spectra. Despite the crucial role such procedures play in most high-throughput proteomics experiments, the scientific literature has not reached a consensus about the best confidence estimation methodology. In this work, we evaluate, using theoretical and empirical analysis, four previously proposed protocols for estimating the false discovery rate (FDR) associated with a set of identified tandem mass spectra: two variants of the target-decoy competition protocol (TDC) of Elias and Gygi and two variants of the separate target-decoy search protocol of Käll et al. Our analysis reveals significant biases in the two separate target-decoy search protocols. Moreover, the one TDC protocol that provides an unbiased FDR estimate among the target PSMs does so at the cost of forfeiting a random subset of high-scoring spectrum identifications. We therefore propose the mix-max procedure to provide unbiased, accurate FDR estimates in the presence of well-calibrated scores. The method avoids biases associated with the two separate target-decoy search protocols and also avoids the propensity for target-decoy competition to discard a random subset of high-scoring target identifications.
| S-EPMC4533616 | biostudies-literature
Project description:BackgroundOne of the most important steps in peptide identification is to estimate the false discovery rate (FDR). The most commonly used method for estimating FDR is the target-decoy search strategy (TDS). While this method is simple and effective, it is time/space-inefficient because it searches a database that is twice as large as the original protein database. This inefficiency problem becomes more evident as protein databases get bigger and bigger. We propose a target-small decoy search strategy and present a rigorous verification that it reduces the database size and search time while retaining the accuracy of target-decoy search strategy (TDS).ResultsWe show that peptide spectrum matches (PSMs) obtained at 1% FDR in TDS overlap ~ 99% with those in our method. (Considering that 1% FDR is used, 99% overlap means our method is very accurate.) Moreover, our method is more time/space-efficient than TDS. The search time of our method is reduced to only 1/4 of that of TDS when UniProt and its 1/8 decoy database are used.ConclusionsWe demonstrate that our method is almost as accurate as TDS and more time/space-efficient than TDS. Since the efficiency of our method is more evident as the database size increases, our method is expected to be useful for identifying peptides in proteogenomics databases constructed from inflated databases using genomic data.
| S-EPMC6708216 | biostudies-literature
Project description:BackgroundHigh-throughtput technologies enable the testing of tens of thousands of measurements simultaneously. Identification of genes that are differentially expressed or associated with clinical outcomes invokes the multiple testing problem. False Discovery Rate (FDR) control is a statistical method used to correct for multiple comparisons for independent or weakly dependent test statistics. Although FDR control is frequently applied to microarray data analysis, gene expression is usually correlated, which might lead to inaccurate estimates. In this paper, we evaluate the accuracy of FDR estimation.MethodsUsing two real data sets, we resampled subgroups of patients and recalculated statistics of interest to illustrate the imprecision of FDR estimation. Next, we generated many simulated data sets with block correlation structures and realistic noise parameters, using the Ultimate Microarray Prediction, Inference, and Reality Engine (UMPIRE) R package. We estimated FDR using a beta-uniform mixture (BUM) model, and examined the variation in FDR estimation.ResultsThe three major sources of variation in FDR estimation are the sample size, correlations among genes, and the true proportion of differentially expressed genes (DEGs). The sample size and proportion of DEGs affect both magnitude and precision of FDR estimation, while the correlation structure mainly affects the variation of the estimated parameters.ConclusionsWe have decomposed various factors that affect FDR estimation, and illustrated the direction and extent of the impact. We found that the proportion of DEGs has a significant impact on FDR; this factor might have been overlooked in previous studies and deserves more thought when controlling FDR.
| S-EPMC3426804 | biostudies-literature
Project description: Not available
| S-EPMC8155551 | biostudies-literature