MIMIX: A Bayesian Mixed-Effects Model for Microbiome Data From Designed Experiments

Grantham, Neal S.; Guan, Yawen; Reich, Brian J.; Borer, Elizabeth T.; Gross, Kevin

doi:10.1080/01621459.2019.1626242

“…This is therefore a type of partial technical process (Class IIa) as more of one transcript partially (not completely) inhibits our ability to measure another transcript. This competition to be counted has been successfully measured using multinomial based models [20,18,31]. As multinomial models model both this multivariate partial technical process (Class IIa) and sampling zeros (Class I) we consider multinomial models to be a hybrid of Class IIa and Class I models.…”

Section: Multivariate Count Modelsmentioning

confidence: 99%

“…Class II models go beyond modeling stochastic sampling by considering that zero values may arise due to secondary sources. Class IIa models, such as the multinomial-Dirichlet [17,11,12] or multinomial-logistic normal [18,19,20] based models represent sources of technical variation beyond stochastic sampling that can introduce zeros into the data. In contrast, class IIb models such as zero inflated models [18,21,22,23] or hurdle models [24,13], consider secondary sources of technical variation or bias that specifically add zero values into observed data.…”

Section: Introductionmentioning

confidence: 99%

Naught all zeros in sequence count data are the same

Silverman

¹

,

Roche

²

,

Mukherjee

³

et al. 2018

Preprint

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Due to the advent and utility of high-throughput sequencing, modern biomedical research abounds with multivariate count data. Yet such sequence count data is often extremely sparse; that is, much of the data is zero values. Such zero values are well known to cause problems for statistical analyses. In this work we provide a systematic description of different processes that can give rise to zero values as well as the types of methods for addressing zeros in sequence count studies. Importantly, we systematically review how various models perform on each type of zero generating process. Our results demonstrate that zero-inflated models can have substantial biases in both simulated and real data settings. Additionally, we find that zeros due to biological absences can, for many applications, be approximated as originating from under sampling. Beyond these results, this work provides a paired categorization scheme for models and zero generating processes to facilitate discussions and future research into the analysis of sequence count data.

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“…Some authors have suggested that the expected negative covariance of feature proportions (

\overset{p}{true}

) in a Dirichlet distribution is a drawback that makes this distribution undesirable (Grantham, Guan, Reich, Borer, & Gross, ; Mandal et al, ; Weiss et al, ). Specifically, the elements of

\overset{p}{true}

in a deviate from a Dirichlet distribution are expected to negatively covary (Mosimann, ) according to:

C o v [p_{i}, p_{j}] = \frac{- α_{i} α_{j}}{α_{0}^{2} (α_{0} + 1)}

, where

\overset{p}{true}

is the vector of expected proportions for features in the composition and

\overset{α}{true}

represents the Dirichlet parameter vector.…”

Section: Discussionmentioning

confidence: 99%

“…Some authors have suggested that the expected negative covariance of feature proportions (⃗ p) in a Dirichlet distribution is a drawback that makes this distribution undesirable (Grantham, Guan, Reich, Borer, & Gross, 2019). ; Mandal et al, 2015;Weiss et al, 2016).…”

Section: Additional Considerations Pertaining To Dirichlet-multinommentioning

confidence: 99%

Dirichlet‐multinomial modelling outperforms alternatives for analysis of microbiome and other ecological count data

Harrison

¹

,

Calder

²

,

Shastry

³

et al. 2020

Molecular Ecology Resources

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Molecular ecology regularly requires the analysis of count data that reflect the relative abundance of features of a composition (e.g., taxa in a community, gene transcripts in a tissue). The sampling process that generates these data can be modelled using the multinomial distribution. Replicate multinomial samples inform the relative abundances of features in an underlying Dirichlet distribution. These distributions together form a hierarchical model for relative abundances among replicates and sampling groups. This type of Dirichlet‐multinomial modelling (DMM) has been described previously, but its benefits and limitations are largely untested. With simulated data, we quantified the ability of DMM to detect differences in proportions between treatment and control groups, and compared the efficacy of three computational methods to implement DMM—Hamiltonian Monte Carlo (HMC), variational inference (VI), and Gibbs Markov chain Monte Carlo. We report that DMM was better able to detect shifts in relative abundances than analogous analytical tools, while identifying an acceptably low number of false positives. Among methods for implementing DMM, HMC provided the most accurate estimates of relative abundances, and VI was the most computationally efficient. The sensitivity of DMM was exemplified through analysis of previously published data describing lung microbiomes. We report that DMM identified several potentially pathogenic, bacterial taxa as more abundant in the lungs of children who aspirated foreign material during swallowing; these differences went undetected with different statistical approaches. Our results suggest that DMM has strong potential as a statistical method to guide inference in molecular ecology.

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“…3). Computational implementations of VI are a topic of current research 573 and will undoubtedly improve over coming years (Blei et al 2017 (Grantham et al 2017, Weiss et al 2016. Specifically, the elements of p in a deviate from a Dirichlet distribution are expected to negatively covary (Mosimann show two hypothetical compositions that differ between those sampling groups.…”

mentioning

confidence: 99%

Dirichlet-multinomial modelling outperforms alternatives for analysis of microbiome and other ecological count data

Harrison

¹

,

Calder

²

,

Shastry

³

et al. 2019

Preprint

View full text Add to dashboard Cite

Molecular ecology regularly requires the analysis of count data that reflect the relative abundance of features of a composition (e.g., taxa in a community, gene transcripts in a tissue).The sampling process that generates these data can be modeled using the multinomial distribution. Replicate multinomial samples inform the relative abundances of features in an underlying Dirichlet distribution. These distributions together form a hierarchical model for relative abundances among replicates and sampling groups. This type of Dirichletmultinomial modelling (DMM) has been described previously, but its benefits and limitations are largely untested. With simulated data, we quantified the ability of DMM to detect differences in proportions between treatment and control groups, and compared the efficiency of three computational methods to implement DMM-Hamiltonian Monte Carlo (HMC), variational inference (VI), and Gibbs Markov chain Monte Carlo. We report that DMM was better able to detect shifts in relative abundances than analogous analytical tools, while identifying an acceptably low number of false positives. Among methods for implementing DMM, HMC provided the most accurate estimates of relative abundances, and VI was the most computationally efficient. The sensitivity of DMM was exemplified through analysis of previously published data describing lung microbiomes. We report that DMM identified several potentially pathogenic, bacterial taxa as more abundant in the lungs of children who aspirated foreign material during swallowing; these differences went undetected with different statistical approaches. Our results suggest that DMM has strong potential as a statistical method to guide inference in molecular ecology.In many scientific disciplines, data from both manipulative experiments and surveys of nat-2 ural variation are often counts of observations that are assigned to categories. Given some 3 total level of observational effort, the counts of the different features in the sample (e.g., 4 2 taxa or transcripts) reflect the underlying proportions of those features in the sampled com-5 position (e.g., an assemblage of organisms or collection of molecules). In molecular ecology, 6 such sampling can take the form of detecting and counting taxa based on observed DNA 7 sequences (e.g., in molecular barcoding or microbial ecology) or counting the reads assigned 8 to specific transcripts in studies of gene expression , Gloor et al. 2017 Tsilimigras and Fodor 2016). For these applications, sampling effort corresponds to the total 10 number of sequence reads, and the count of reads assigned to a taxon or gene supports infer-11 ence of their true proportion in the composition. Moreover, the total number of reads that 12 can be obtained is constrained by the sequencing instrument, with reads ascribed to samples 13 and features within each sample. Due to this constant sum constraint, compositional data 14 have the important quality that as the relative abundance of one feature in the composition 15 increases, other featur...

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MIMIX: A Bayesian Mixed-Effects Model for Microbiome Data From Designed Experiments

Cited by 36 publications

References 37 publications

Naught all zeros in sequence count data are the same

Naught all zeros in sequence count data are the same

Dirichlet‐multinomial modelling outperforms alternatives for analysis of microbiome and other ecological count data

Dirichlet-multinomial modelling outperforms alternatives for analysis of microbiome and other ecological count data

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