Analyzing differences between microbiome communities using mixture distributions
In this paper, we present a method to assess differences between microbiome communities that effectively models sparse count data and accounts for presence‐absence bias frequently encountered when zeros are present. We assume that the observed data for each operational taxonomic unit is Poisson gene...
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Published in | Statistics in medicine Vol. 37; no. 27; pp. 4036 - 4053 |
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Format | Journal Article |
Language | English |
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30.11.2018
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Abstract | In this paper, we present a method to assess differences between microbiome communities that effectively models sparse count data and accounts for presence‐absence bias frequently encountered when zeros are present. We assume that the observed data for each operational taxonomic unit is Poisson generated with the rate for each sample originating from an underlying rate distribution. We propose to model this distribution using a mixture model, specifying the components based on the posterior rate distribution of a count and estimating the optimal weights using a least squares objective function. The distribution incorporates varying resolutions of samples, a point mass for differentiating structural and nonstructural zeros, and a truncation point mass to account for high values that are too sparse to model. As mixture component specification is not always straightforward, a method to estimate a joint model from several mixture distributions using minimum distances of bootstrap iterates is proposed. Once the population rate distribution is approximated, we obtain sample‐specific distributions by conditioning on the observed operational taxonomic unit count, resolution, and estimated mixture distribution and then use these to estimate pairwise distances for a permutation test. The method gives an accurate estimate of the true proportion of zeros for presence‐absence, effectively models the distribution of low counts using the mixture distribution, and achieves good power for detecting differences in a variety of scenarios. The method is tested using a simulation study and applied to two microbiome datasets. In each case, the results are compared with a number of existing methods. |
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AbstractList | In this paper, we present a method to assess differences between microbiome communities that effectively models sparse count data and accounts for presence‐absence bias frequently encountered when zeros are present. We assume that the observed data for each operational taxonomic unit is Poisson generated with the rate for each sample originating from an underlying rate distribution. We propose to model this distribution using a mixture model, specifying the components based on the posterior rate distribution of a count and estimating the optimal weights using a least squares objective function. The distribution incorporates varying resolutions of samples, a point mass for differentiating structural and nonstructural zeros, and a truncation point mass to account for high values that are too sparse to model. As mixture component specification is not always straightforward, a method to estimate a joint model from several mixture distributions using minimum distances of bootstrap iterates is proposed. Once the population rate distribution is approximated, we obtain sample‐specific distributions by conditioning on the observed operational taxonomic unit count, resolution, and estimated mixture distribution and then use these to estimate pairwise distances for a permutation test. The method gives an accurate estimate of the true proportion of zeros for presence‐absence, effectively models the distribution of low counts using the mixture distribution, and achieves good power for detecting differences in a variety of scenarios. The method is tested using a simulation study and applied to two microbiome datasets. In each case, the results are compared with a number of existing methods. |
Author | Escobar, Michael D. Shestopaloff, Konstantin Xu, Wei |
Author_xml | – sequence: 1 givenname: Konstantin orcidid: 0000-0003-3933-4967 surname: Shestopaloff fullname: Shestopaloff, Konstantin email: konstantin.shestopaloff@utoronto.ca organization: University Health Network – sequence: 2 givenname: Michael D. surname: Escobar fullname: Escobar, Michael D. organization: University of Toronto – sequence: 3 givenname: Wei surname: Xu fullname: Xu, Wei organization: University of Toronto |
BackLink | https://www.ncbi.nlm.nih.gov/pubmed/30039541$$D View this record in MEDLINE/PubMed |
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Cites_doi | 10.1073/pnas.1116053109 10.1093/nar/gkq865 10.1038/ng.3693 10.1038/nature10213 10.1111/j.2517-6161.1968.tb00743.x 10.1002/(SICI)1097-0258(19960715)15:13<1365::AID-SIM232>3.0.CO;2-J 10.1002/bimj.200810452 10.1016/S1369-5274(99)80052-6 10.1093/nar/21.13.3021 10.1090/S0025-5718-1980-0572855-7 10.1128/mSystems.00022-16 10.1093/nar/gkm864 10.1038/nature11711 10.1007/s10651-005-6817-1 10.2307/1942268 10.1093/bioinformatics/btw311 10.1007/s11894-008-0075-y 10.1128/AEM.03006-05 10.1128/AEM.71.12.8228-8235.2005 10.1038/nrg3182 10.1099/ijs.0.64915-0 10.1016/S0378-1097(03)00717-1 10.1093/biomet/asq026 10.1137/0728030 10.1098/rstb.2005.1725 10.1371/journal.pone.0129606 10.1186/gb-2012-13-9-r79 10.1101/gr.131029.111 |
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References_xml | – volume: 26 start-page: 32 issue: 1 year: 2001 end-page: 46 article-title: A new method for non‐parametric multivariate analysis of variance publication-title: Austral Ecol – volume: 27 start-page: 325 issue: 4 year: 1957 end-page: 349 article-title: An ordination of the upland forest communities of Southern Wisconsin publication-title: Ecol Monogr – volume: 71 start-page: 8228 issue: 12 year: 2005 end-page: 8235 article-title: UniFrac: a new phylogenetic method for comparing microbial communities publication-title: Appl Environ Microbiol – year: 2005 – volume: 109 start-page: 594 issue: 2 year: 2012 end-page: 599 article-title: Metagenomic systems biology of the human gut microbiome reveals topological shifts associated with obesity and inflammatory bowel disease publication-title: Proc Natl Acad Sci – volume: 493 start-page: 45 issue: 7430 year: 2013 end-page: 50 article-title: Genomic variation landscape of the human gut microbiome publication-title: Nature – volume: 97 start-page: 727 issue: 3 year: 2010 end-page: 740 article-title: Estimating species richness by a Poisson‐compound gamma model publication-title: Biometrika – volume: 57 start-page: 2259 issue: 10 year: 2007 end-page: 2261 article-title: EzTaxon: a web‐based tool for the identification of prokaryotes based on 16S ribosomal RNA gene sequences publication-title: Int J Syst Evol Microbiol – volume: 35 start-page: 7188 issue: 21 year: 2007 end-page: 7196 article-title: SILVA: a comprehensive online resource for quality checked and aligned ribosomal RNA sequence data compatible with ARB publication-title: Nucleic Acids Res – start-page: 3 year: 2003 end-page: 6 – volume: 48 start-page: 1413 issue: 11 year: 2016 end-page: 1417 article-title: Association of host genome with intestinal microbial composition in a large healthy cohort publication-title: Nat Genet – volume: 360 start-page: 1935 issue: 1462 year: 2005 end-page: 1943 article-title: Defining operational taxonomic units using DNA barcode data publication-title: Philos Trans R Soc B Biol Sci – volume: 32 start-page: 2618 issue: 17 year: 2016 end-page: 2625 article-title: PERMANOVA‐S: association test for microbial community composition that accommodates confounders and multiple distances publication-title: Bioinformatics – volume: 72 start-page: 5069 issue: 7 year: 2006 end-page: 5072 article-title: Greengenes, a chimera‐checked 16S rRNA gene database and workbench compatible with ARB publication-title: Appl Environ Microbiol – volume: 21 start-page: 3021 issue: 13 year: 1993 end-page: 3023 article-title: The ribosomal database project publication-title: Nucleic Acids Res – year: 2014 – year: 1998 – volume: 50 start-page: 971 issue: 6 year: 2008 end-page: 982 article-title: Parametric models for estimating the number of classes publication-title: Biom J – volume: 22 start-page: 850 issue: 5 year: 2012 end-page: 859 article-title: Temporal shifts in the skin microbiome associated with disease flares and treatment in children with atopic dermatitis publication-title: Genome Res – volume: 228 start-page: 45 issue: 1 year: 2003 end-page: 49 article-title: Intragenomic heterogeneity between multiple 16S ribosomal RNA operons in sequenced bacterial genomes publication-title: FEMS Microbiol Lett – volume: 10 start-page: 396 issue: 4 year: 2008 end-page: 403 article-title: The human gut microbiome: implications for future health care publication-title: Curr Gastroenterol Rep – volume: 15 start-page: 1365 issue: 13 year: 1996 end-page: 1376 article-title: Mixture models for eye‐tracking data: a case study publication-title: Statist Med – volume: 12 start-page: 45 issue: 1 year: 2005 end-page: 54 article-title: Modelling skewed data with many zeros: a simple approach combining ordinary and logistic regression publication-title: Environ Ecol Stat – volume: 35 start-page: 773 issue: 151 year: 1980 end-page: 782 article-title: Updating quasi‐Newton matrices with limited storage publication-title: Math Comp – volume: 13 start-page: 1 issue: 9 year: 2012 article-title: Dysfunction of the intestinal microbiome in inflammatory bowel disease and treatment publication-title: Genome Biol – volume: 474 start-page: 327 issue: 7351 year: 2011 end-page: 336 article-title: Human nutrition, the gut microbiome and the immune system publication-title: Nature – volume: 28 start-page: 545 issue: 2 year: 1991 end-page: 572 article-title: A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds publication-title: SIAM J Numer Anal – volume: 30 start-page: 444 issue: 3 year: 1968 end-page: 460 article-title: An estimation procedure for mixtures of distributions publication-title: J R Stat Soc Ser B Methodol – volume: 38 issue: 22 year: 2010 article-title: Identification of species by multiplex analysis of variable‐length sequences publication-title: Nucleic Acids Res – year: 2017 – volume: 2 start-page: 299 issue: 3 year: 1999 end-page: 305 article-title: Ribosomal DNA sequencing as a tool for identification of bacterial pathogens publication-title: Curr Opin Microbiol – volume: 13 start-page: 260 issue: 4 year: 2012 end-page: 270 article-title: The human microbiome: at the interface of health and disease publication-title: Nat Rev Genet – year: 2015 – volume: 1 issue: 2 year: 2016 article-title: Geography and location are the primary drivers of office microbiome composition publication-title: MSystems – volume: 10 issue: 7 year: 2015 article-title: Assessment and selection of competing models for zero‐inflated microbiome data publication-title: PLOS One – ident: e_1_2_10_4_1 doi: 10.1073/pnas.1116053109 – ident: e_1_2_10_11_1 doi: 10.1093/nar/gkq865 – ident: e_1_2_10_8_1 doi: 10.1038/ng.3693 – ident: e_1_2_10_7_1 doi: 10.1038/nature10213 – volume: 30 start-page: 444 issue: 3 year: 1968 ident: e_1_2_10_27_1 article-title: An estimation procedure for mixtures of distributions publication-title: J R Stat Soc Ser B Methodol doi: 10.1111/j.2517-6161.1968.tb00743.x contributor: fullname: Choi K – ident: e_1_2_10_32_1 doi: 10.1002/(SICI)1097-0258(19960715)15:13<1365::AID-SIM232>3.0.CO;2-J – ident: e_1_2_10_29_1 doi: 10.1002/bimj.200810452 – ident: e_1_2_10_13_1 doi: 10.1016/S1369-5274(99)80052-6 – ident: e_1_2_10_18_1 doi: 10.1093/nar/21.13.3021 – ident: e_1_2_10_36_1 – ident: e_1_2_10_33_1 doi: 10.1090/S0025-5718-1980-0572855-7 – ident: e_1_2_10_10_1 doi: 10.1128/mSystems.00022-16 – ident: e_1_2_10_16_1 doi: 10.1093/nar/gkm864 – ident: e_1_2_10_35_1 – ident: e_1_2_10_9_1 doi: 10.1038/nature11711 – volume-title: Linear and Nonlinear Programming year: 2005 ident: e_1_2_10_30_1 contributor: fullname: Luenberger DG – ident: e_1_2_10_25_1 doi: 10.1007/s10651-005-6817-1 – ident: e_1_2_10_23_1 doi: 10.2307/1942268 – ident: e_1_2_10_24_1 doi: 10.1093/bioinformatics/btw311 – volume: 26 start-page: 32 issue: 1 year: 2001 ident: e_1_2_10_20_1 article-title: A new method for non‐parametric multivariate analysis of variance publication-title: Austral Ecol contributor: fullname: Anderson MJ – ident: e_1_2_10_3_1 doi: 10.1007/s11894-008-0075-y – ident: e_1_2_10_15_1 doi: 10.1128/AEM.03006-05 – ident: e_1_2_10_21_1 doi: 10.1128/AEM.71.12.8228-8235.2005 – ident: e_1_2_10_2_1 doi: 10.1038/nrg3182 – ident: e_1_2_10_31_1 – ident: e_1_2_10_17_1 doi: 10.1099/ijs.0.64915-0 – ident: e_1_2_10_12_1 doi: 10.1016/S0378-1097(03)00717-1 – ident: e_1_2_10_28_1 doi: 10.1093/biomet/asq026 – ident: e_1_2_10_34_1 doi: 10.1137/0728030 – ident: e_1_2_10_19_1 doi: 10.1098/rstb.2005.1725 – start-page: 3 volume-title: PCR Protocols year: 2003 ident: e_1_2_10_14_1 contributor: fullname: Bartlett JMS – ident: e_1_2_10_22_1 – ident: e_1_2_10_26_1 doi: 10.1371/journal.pone.0129606 – ident: e_1_2_10_5_1 doi: 10.1186/gb-2012-13-9-r79 – ident: e_1_2_10_6_1 doi: 10.1101/gr.131029.111 |
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SubjectTerms | Ecology microbiome Microorganisms mixture models sparsity statistical ecology Taxonomy zero inflation |
Title | Analyzing differences between microbiome communities using mixture distributions |
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