Dirichlet negative multinomial regression for overdispersed correlated count data.
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ABSTRACT:
SUBMITTER: Farewell DM
PROVIDER: S-EPMC3590929 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:There is heightened interest in using high-throughput sequencing technologies to quantify abundances of microbial taxa and linking the abundance to human diseases and traits. Proper modeling of multivariate taxon counts is essential to the power of detecting this association. Existing models are limited in handling excessive zero observations in taxon counts and in flexibly accommodating complex correlation structures and dispersion patterns among taxa. In this article, we develop a new probability distribution, zero-inflated generalized Dirichlet multinomial (ZIGDM), that overcomes these limitations in modeling multivariate taxon counts. Based on this distribution, we propose a ZIGDM regression model to link microbial abundances to covariates (e.g. disease status) and develop a fast expectation-maximization algorithm to efficiently estimate parameters in the model. The derived tests enable us to reveal rich patterns of variation in microbial compositions including differential mean and dispersion. The advantages of the proposed methods are demonstrated through simulation studies and an analysis of a gut microbiome dataset.
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Project description:There are many instances in genomics data analyses where measurements are made on a multivariate response. For example, alternative splicing can lead to multiple expressed isoforms from the same primary transcript. There are situations where differences (e.g. between normal and disease state) in the relative ratio of expressed isoforms may have significant phenotypic consequences or lead to prognostic capabilities. Similarly, knowledge of single nucleotide polymorphisms (SNPs) that affect splicing, so-called splicing quantitative trait loci (sQTL) will help to characterize the effects of genetic variation on gene expression. RNA sequencing (RNA-seq) has provided an attractive toolbox to carefully unravel alternative splicing outcomes and recently, fast and accurate methods for transcript quantification have become available. We propose a statistical framework based on the Dirichlet-multinomial distribution that can discover changes in isoform usage between conditions and SNPs that affect relative expression of transcripts using these quantifications. The Dirichlet-multinomial model naturally accounts for the differential gene expression without losing information about overall gene abundance and by joint modeling of isoform expression, it has the capability to account for their correlated nature. The main challenge in this approach is to get robust estimates of model parameters with limited numbers of replicates. We approach this by sharing information and show that our method improves on existing approaches in terms of standard statistical performance metrics. The framework is applicable to other multivariate scenarios, such as Poly-A-seq or where beta-binomial models have been applied (e.g., differential DNA methylation). Our method is available as a Bioconductor R package called DRIMSeq.
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Project description:IntroductionCount outcomes in tobacco research are often analyzed with the Poisson distribution. However, they often exhibit features such as overdispersion (variance larger than expected) and zero inflation (extra zeros) that violate model assumptions. Furthermore, longitudinal studies have repeated measures that generate correlated counts. Failure to account for overdispersion, zero inflation, and correlation can yield incorrect statistical inferences. Thus, it is important to familiarize researchers with proper models for such data.Aims and methodsPoisson and Negative Binomial models with correlated random effects with and without zero inflation are presented. The illustrative data comes from a study comparing a mindfulness training app (Craving to Quit [C2Q], n = 60) with a control app (experience sampling-only app, n = 66) on smoking frequency at 1, 3, and 6 months. Predictors include app, time, the app-by-time interaction, and baseline smoking. Each model is evaluated in terms of accounting for zero inflation, overdispersion, and correlation in the data. Emphasis is placed on evaluating model fit, subject-specific interpretation of effects, and choosing an appropriate model.ResultsThe hurdle Poisson model provided the best fit to the data. Smoking abstinence rates were 33%, 32%, and 28% at 1, 3, and 6 months, respectively, with variance larger than expected by a factor >7 at each follow-up. Individuals on C2Q were less likely to achieve abstinence across time but likely to smoke fewer cigarettes if smoking.ConclusionsThe models presented are specifically suited for analyzing correlated count outcomes and account for zero inflation and overdispersion. We provide guidance to researchers on the use of these models to better inform nicotine and tobacco research.ImplicationsIn tobacco research, count outcomes are often measured repeatedly on the same subject and thus correlated. Such outcomes often have many zeros and exhibit large variances relative to the mean. Analyzing such data require models specifically suited for correlated counts. The presented models and guidelines could improve the rigor of the analysis of correlated count data and thus increase the impact of studies in nicotine and tobacco research using such outcomes.
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Project description:BACKGROUND: In addition to sequence conservation, protein multiple sequence alignments contain evolutionary signal in the form of correlated variation among amino acid positions. This signal indicates positions in the sequence that influence each other, and can be applied for the prediction of intra- or intermolecular contacts. Although various approaches exist for the detection of such correlated mutations, in general these methods utilize only pairwise correlations. Hence, they tend to conflate direct and indirect dependencies. RESULTS: We propose RMRCM, a method for Regularized Multinomial Regression in order to obtain Correlated Mutations from protein multiple sequence alignments. Importantly, our method is not restricted to pairwise (column-column) comparisons only, but takes into account the network nature of relationships between protein residues in order to predict residue-residue contacts. The use of regularization ensures that the number of predicted links between columns in the multiple sequence alignment remains limited, preventing overprediction. Using simulated datasets we analyzed the performance of our approach in predicting residue-residue contacts, and studied how it is influenced by various types of noise. For various biological datasets, validation with protein structure data indicates a good performance of the proposed algorithm for the prediction of residue-residue contacts, in comparison to previous results. RMRCM can also be applied to predict interactions (in addition to only predicting interaction sites or contact sites), as demonstrated by predicting PDZ-peptide interactions. CONCLUSIONS: A novel method is presented, which uses regularized multinomial regression in order to obtain correlated mutations from protein multiple sequence alignments. AVAILABILITY: R-code of our implementation is available via http://www.ab.wur.nl/rmrcm.
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Project description:Count datasets are traditionally analyzed using the ordinary Poisson distribution. However, said model has its applicability limited, as it can be somewhat restrictive to handling specific data structures. In this case, the need arises for obtaining alternative models that accommodate, for example, overdispersion and zero modification (inflation/deflation at the frequency of zeros). In practical terms, these are the most prevalent structures ruling the nature of discrete phenomena nowadays. Hence, this paper's primary goal was to jointly address these issues by deriving a fixed-effects regression model based on the hurdle version of the Poisson-Sujatha distribution. In this framework, the zero modification is incorporated by considering that a binary probability model determines which outcomes are zero-valued, and a zero-truncated process is responsible for generating positive observations. Posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the g-prior method. Intensive Monte Carlo simulation studies were performed to assess the Bayesian estimators' empirical properties, and the obtained results have been discussed. The proposed model was considered for analyzing a real dataset, and its competitiveness regarding some well-established fixed-effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian p-value and the randomized quantile residuals were considered for the task of model validation.
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Project description:Understanding the factors that alter the composition of the human microbiota may help personalized healthcare strategies and therapeutic drug targets. In many sequencing studies, microbial communities are characterized by a list of taxa, their counts, and their evolutionary relationships represented by a phylogenetic tree. In this article, we consider an extension of the Dirichlet multinomial distribution, called the Dirichlet-tree multinomial distribution, for multivariate, over-dispersed, and tree-structured count data. To address the relationships between these counts and a set of covariates, we propose the Dirichlet-tree multinomial regression model for which we develop a penalized likelihood method for estimating parameters and selecting covariates. For efficient optimization, we adopt the accelerated proximal gradient approach. Simulation studies are presented to demonstrate the good performance of the proposed procedure. An analysis of a data set relating dietary nutrients with bacterial counts is used to show that the incorporation of the tree structure into the model helps increase the prediction power.
| S-EPMC5587402 | biostudies-literature
Project description:BackgroundUnderstanding the relation between the human microbiome and modulating factors, such as diet, may help researchers design intervention strategies that promote and maintain healthy microbial communities. Numerous analytical tools are available to help identify these relations, oftentimes via automated variable selection methods. However, available tools frequently ignore evolutionary relations among microbial taxa, potential relations between modulating factors, as well as model selection uncertainty.ResultsWe present MicroBVS, an R package for Dirichlet-tree multinomial models with Bayesian variable selection, for the identification of covariates associated with microbial taxa abundance data. The underlying Bayesian model accommodates phylogenetic structure in the abundance data and various parameterizations of covariates' prior probabilities of inclusion.ConclusionWhile developed to study the human microbiome, our software can be employed in various research applications, where the aim is to generate insights into the relations between a set of covariates and compositional data with or without a known tree-like structure.
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Project description:MotivationResearch on epigenetic modifications and other chromatin features at genomic regulatory elements elucidates essential biological mechanisms including the regulation of gene expression. Despite the growing number of epigenetic datasets, new tools are still needed to discover novel distinctive patterns of heterogeneous epigenetic signals at regulatory elements.ResultsWe introduce ChromDMM, a product Dirichlet-multinomial mixture model for clustering genomic regions that are characterized by multiple chromatin features. ChromDMM extends the mixture model framework by profile shifting and flipping that can probabilistically account for inaccuracies in the position and strand-orientation of the genomic regions. Owing to hyper-parameter optimization, ChromDMM can also regularize the smoothness of the epigenetic profiles across the consecutive genomic regions. With simulated data, we demonstrate that ChromDMM clusters, shifts and strand-orients the profiles more accurately than previous methods. With ENCODE data, we show that the clustering of enhancer regions in the human genome reveals distinct patterns in several chromatin features. We further validate the enhancer clusters by their enrichment for transcriptional regulatory factor binding sites.Availability and implementationChromDMM is implemented as an R package and is available at https://github.com/MariaOsmala/ChromDMM.Supplementary informationSupplementary data are available at Bioinformatics online.
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Project description:Studying the human microbiome has gained substantial interest in recent years, and a common task in the analysis of these data is to cluster microbiome compositions into subtypes. This subdivision of samples into subgroups serves as an intermediary step in achieving personalized diagnosis and treatment. In applying existing clustering methods to modern microbiome studies including the American Gut Project (AGP) data, we found that this seemingly standard task, however, is very challenging in the microbiome composition context due to several key features of such data. Standard distance-based clustering algorithms generally do not produce reliable results as they do not take into account the heterogeneity of the cross-sample variability among the bacterial taxa, while existing model-based approaches do not allow sufficient flexibility for the identification of complex within-cluster variation from cross-cluster variation. Direct applications of such methods generally lead to overly dispersed clusters in the AGP data and such phenomenon is common for other microbiome data. To overcome these challenges, we introduce Dirichlet-tree multinomial mixtures (DTMM) as a Bayesian generative model for clustering amplicon sequencing data in microbiome studies. DTMM models the microbiome population with a mixture of Dirichlet-tree kernels that utilizes the phylogenetic tree to offer a more flexible covariance structure in characterizing within-cluster variation, and it provides a means for identifying a subset of signature taxa that distinguish the clusters. We perform extensive simulation studies to evaluate the performance of DTMM and compare it to state-of-the-art model-based and distance-based clustering methods in the microbiome context, and carry out a validation study on a publicly available longitudinal data set to confirm the biological relevance of the clusters. Finally, we report a case study on the fecal data from the AGP to identify compositional clusters among individuals with inflammatory bowel disease and diabetes. Among our most interesting findings is that enterotypes (i.e., gut microbiome clusters) are not always defined by the most dominant species as previous analyses had assumed, but can involve a number of less abundant OTUs, which cannot be identified with existing distance-based and method-based approaches.
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Project description:Understanding why a random variable is actually random has been in the core of Statistics from its beginnings. The generalized Waring regression model for count data explains that inherent variability is given by three possible sources: randomness, liability and proneness. The model extends the negative binomial regression model and it is not included in the family of generalized linear models. In order to avoid that shortcoming, we developed the GWRM R package for fitting, describing and validating the model. The version we introduce in this communication provides a new design of the modelling function as well as new methods operating on the associated fitted model objects, so that the new software integrates easily into the computational toolbox for modelling count data in R. The release of a plug-in in order to use the package from the interface R Commander tries to contribute to the spreading of the model among non-advanced users. We illustrate the usage and the possibilities of the software with two examples from the fields of health and sport.
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