Bayesian Nonparametric Ordination for the Analysis of Microbial Communities

Ren, Boyu; Bacallado, Sergio; Favaro, Stefano; Holmes, Susan; Trippa, Lorenzo

doi:10.1080/01621459.2017.1288631

Cited by 32 publications

(37 citation statements)

References 59 publications

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“…In this section, we first review the construction of the Dependent Dirichlet processes in Ren et al (2016), and then provide a new version of the model which incorporates covariates.…”

Section: Prior Modelmentioning

confidence: 99%

“…Recently, a Bayesian nonparametric model for microbiome data specified through samplespecific latent factors has been discussed in Ren et al (2016). This construction induces a marginal Dirichlet process prior for each composition P j and introduces dependences across samples by associating microbial compositions P j to linear combinations of latent factors.…”

Section: Introductionmentioning

confidence: 99%

“…This manuscript builds on the model of Ren et al (2016), linking the microbial composition P j to covariate effects as well as to the latent factors. The resulting extended model takes into account overdispersion and zero-inflation in microbiome data.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian mixed effects models for zero-inflated compositions in microbiome data analysis

Ren

Bacallado²,

Favaro³

et al. 2020

Ann. Appl. Stat.

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Detecting associations between microbial compositions and sample characteristics is one of the most important tasks in microbiome studies. Most of the existing methods apply univariate models to single microbial species separately, with adjustments for multiple hypothesis testing. We propose a Bayesian analysis for a generalized mixed effects linear model tailored to this application. The marginal prior on each microbial composition is a Dirichlet Process, and dependence across compositions is induced through a linear combination of individual covariates, such as disease biomarkers or 1 arXiv:1711.01241v2 [stat.ME] 24 Aug 2019 the subject's age, and latent factors. The latent factors capture residual variability and their dimensionality is learned from the data in a fully Bayesian procedure. The proposed model is tested in data analyses and simulation studies with zero-inflated compositions. In these settings, within each sample, a large proportion of counts per microbial species are equal to zero. In our Bayesian model a priori the probability of compositions with absent microbial species is strictly positive. We propose an efficient algorithm to sample from the posterior and visualizations of model parameters which reveal associations between covariates and microbial compositions. We evaluate the proposed method in simulation studies, and then analyze a microbiome dataset for infants with type 1 diabetes which contains a large proportion of zeros in the samplespecific microbial compositions. P j and P j are similar. When φ j,j = 0, compositions P j and P j are identical. Symmetrically, the angle ϕ i,i between X i and X i can be viewed as a measure of similarity between species Z i and Z i . When ϕ i,i decreases towards zero, the correlation between (P j ({Z i }); j ≤ J) and (P j ({Z i }; j ≤ J)) increases to one.The prior specification in the model is as follows. First σ 1 > σ 2 > σ 3 . . . are a priori ordered points from a Poisson process on (0, 1) with intensity ν(σ) = ασ −1 (1−σ) −1/2 . Second the X k,i random variables are independent Gaussian N (0, 1), i = 1, 2, . . ., k = 1, 2, . . . , K., end, we first defineP ({Z i }; w 0 ), the population average abundance of species i at a covariate value w 0 , byP

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“…In this section, we first review the construction of the Dependent Dirichlet processes in Ren et al (2016), and then provide a new version of the model which incorporates covariates.…”

Section: Prior Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian mixed effects models for zero-inflated compositions in microbiome data analysis

Ren

Bacallado²,

Favaro³

et al. 2020

Ann. Appl. Stat.

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“…We compare our method to the method of Arbel et al (2016) with respect to both estimation error and computation time in Section 5. We also note the recent method of Ren et al (2017), which incorporates an error model into ordination methods, an alternative to diversity analysis in summarizing compositional data.…”

Section: α-Diversity With Covariatesmentioning

confidence: 99%

DivNet: Estimating diversity in networked communities

Willis¹,

Bd²

2018

Preprint

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Diversity is a marker of ecosystem health in ecology, microbiology and immunology, with implications for disease diagnosis and infection resistance. However, accurately comparing diversity across environmental gradients is challenging, especially when number of different taxonomic groups in the community is large. Furthermore, existing approaches to estimating diversity do not perform well when the taxonomic groups in the community interact via an ecological network, such as by competing within their niche, or with mutualistic relationships. To address this, we propose DivNet, a method for estimating within-and between-community diversity in ecosystems where taxa interact via an ecological network. In particular, accounting for network structure permits more accurate estimates of alphaand beta-diversity, even in settings with a large number of taxa and a small number of samples. DivNet is fast, accurate, precise, performs well with large numbers of taxa, and is robust to both weakly and strongly networked communities. We show that the advantages of incorporating taxon interactions into diversity estimation are especially clear in analyzing microbiomes and other high-diversity, strongly networked ecosystems. Therefore, to illustrate the method, we analyze the microbiome of seafloor basalts based on a 16S amplicon sequencing dataset with 1490 taxa and 13 samples.

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“…Walker (2015) does include an analysis of uncertainty in indirect gradient analysis, but the scope is limited to a single dimensional projection of presence/absence data. Ren, Bacallado, Favaro, Holmes, and Trippa (2017) details an approach using a dependent Dirichlet process that implements for understanding uncertainty in projections for bacteria counts, but is limited to count data. Understanding and evaluation of uncertainty is critical, in science in general and particularly in unconstrained ordination, as estimating latent gradients with precision from abundance or presence data is a major challenge.…”

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confidence: 99%

Evaluating and presenting uncertainty in model‐based unconstrained ordination

Hoegh

Roberts

2019

Ecology and Evolution

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| INTRODUC TI ONMultivariate ordination, and in particular model-based ordination with latent factor modeling, is used by community ecologists to understand patterns in community composition. Data on species presence/absence or abundance are used in ordination methods to identify compositional similarities between sample units. With these ordination models, the goal is not necessarily to learn about Abstract Variability in ecological community composition is often analyzed by recording the presence or abundance of taxa in sample units, calculating a symmetric matrix of pairwise distances or dissimilarities among sample units and then mapping the resulting matrix to a low-dimensional representation through methods collectively called ordination. Unconstrained ordination only uses taxon composition data, without any environmental or experimental covariates, to infer latent compositional gradients associated with the sampling units. Commonly, such distance-based methods have been used for ordination, but recently there has been a shift toward model-based approaches. Model-based unconstrained ordinations are commonly formulated using a Bayesian latent factor model that permits uncertainty assessment for parameters, including the latent factors that correspond to gradients in community composition.While model-based methods have the additional benefit of addressing uncertainty in the estimated gradients, typically the current practice is to report point estimates without summarizing uncertainty. To demonstrate the uncertainty present in modelbased unconstrained ordination, the well-known spider and dune data sets were analyzed and shown to have large uncertainty in the ordination projections. Hence to understand the factors that contribute to the uncertainty, simulation studies were conducted to assess the impact of additional sampling units or species to help inform future ordination studies that seek to minimize variability in the latent factors.Accurate reporting of uncertainty is an important part of transparency in the scientific process; thus, a model-based approach that accounts for uncertainty is valuable.An R package, UncertainOrd, contains visualization tools that accurately represent estimates of the gradients in community composition in the presence of uncertainty.

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Bayesian Nonparametric Ordination for the Analysis of Microbial Communities

Cited by 32 publications

References 59 publications

Bayesian mixed effects models for zero-inflated compositions in microbiome data analysis

Bayesian mixed effects models for zero-inflated compositions in microbiome data analysis

DivNet: Estimating diversity in networked communities

Evaluating and presenting uncertainty in model‐based unconstrained ordination

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