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Compositional Data Analysis of Microbiome and Any-Omics Datasets: A Validation of the Additive Logratio Transformation

Microbiome and omics datasets are, by their intrinsic biological nature, of high dimensionality, characterized by counts of large numbers of components (microbial genes, operational taxonomic units, RNA transcripts, etc.). These data are generally regarded as compositional since the total number of...

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Autores principales: Greenacre, Michael, Martínez-Álvaro, Marina, Blasco, Agustín
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Frontiers Media S.A. 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8561721/
https://www.ncbi.nlm.nih.gov/pubmed/34737726
http://dx.doi.org/10.3389/fmicb.2021.727398
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author Greenacre, Michael
Martínez-Álvaro, Marina
Blasco, Agustín
author_facet Greenacre, Michael
Martínez-Álvaro, Marina
Blasco, Agustín
author_sort Greenacre, Michael
collection PubMed
description Microbiome and omics datasets are, by their intrinsic biological nature, of high dimensionality, characterized by counts of large numbers of components (microbial genes, operational taxonomic units, RNA transcripts, etc.). These data are generally regarded as compositional since the total number of counts identified within a sample is irrelevant. The central concept in compositional data analysis is the logratio transformation, the simplest being the additive logratios with respect to a fixed reference component. A full set of additive logratios is not isometric, that is they do not reproduce the geometry of all pairwise logratios exactly, but their lack of isometry can be measured by the Procrustes correlation. The reference component can be chosen to maximize the Procrustes correlation between the additive logratio geometry and the exact logratio geometry, and for high-dimensional data there are many potential references. As a secondary criterion, minimizing the variance of the reference component's log-transformed relative abundance values makes the subsequent interpretation of the logratios even easier. On each of three high-dimensional omics datasets the additive logratio transformation was performed, using references that were identified according to the abovementioned criteria. For each dataset the compositional data structure was successfully reproduced, that is the additive logratios were very close to being isometric. The Procrustes correlations achieved for these datasets were 0.9991, 0.9974, and 0.9902, respectively. We thus demonstrate, for high-dimensional compositional data, that additive logratios can provide a valid choice as transformed variables, which (a) are subcompositionally coherent, (b) explain 100% of the total logratio variance and (c) come measurably very close to being isometric. The interpretation of additive logratios is much simpler than the complex isometric alternatives and, when the variance of the log-transformed reference is very low, it is even simpler since each additive logratio can be identified with a corresponding compositional component.
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spelling pubmed-85617212021-11-03 Compositional Data Analysis of Microbiome and Any-Omics Datasets: A Validation of the Additive Logratio Transformation Greenacre, Michael Martínez-Álvaro, Marina Blasco, Agustín Front Microbiol Microbiology Microbiome and omics datasets are, by their intrinsic biological nature, of high dimensionality, characterized by counts of large numbers of components (microbial genes, operational taxonomic units, RNA transcripts, etc.). These data are generally regarded as compositional since the total number of counts identified within a sample is irrelevant. The central concept in compositional data analysis is the logratio transformation, the simplest being the additive logratios with respect to a fixed reference component. A full set of additive logratios is not isometric, that is they do not reproduce the geometry of all pairwise logratios exactly, but their lack of isometry can be measured by the Procrustes correlation. The reference component can be chosen to maximize the Procrustes correlation between the additive logratio geometry and the exact logratio geometry, and for high-dimensional data there are many potential references. As a secondary criterion, minimizing the variance of the reference component's log-transformed relative abundance values makes the subsequent interpretation of the logratios even easier. On each of three high-dimensional omics datasets the additive logratio transformation was performed, using references that were identified according to the abovementioned criteria. For each dataset the compositional data structure was successfully reproduced, that is the additive logratios were very close to being isometric. The Procrustes correlations achieved for these datasets were 0.9991, 0.9974, and 0.9902, respectively. We thus demonstrate, for high-dimensional compositional data, that additive logratios can provide a valid choice as transformed variables, which (a) are subcompositionally coherent, (b) explain 100% of the total logratio variance and (c) come measurably very close to being isometric. The interpretation of additive logratios is much simpler than the complex isometric alternatives and, when the variance of the log-transformed reference is very low, it is even simpler since each additive logratio can be identified with a corresponding compositional component. Frontiers Media S.A. 2021-10-11 /pmc/articles/PMC8561721/ /pubmed/34737726 http://dx.doi.org/10.3389/fmicb.2021.727398 Text en Copyright © 2021 Greenacre, Martínez-Álvaro and Blasco. https://creativecommons.org/licenses/by/4.0/This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
spellingShingle Microbiology
Greenacre, Michael
Martínez-Álvaro, Marina
Blasco, Agustín
Compositional Data Analysis of Microbiome and Any-Omics Datasets: A Validation of the Additive Logratio Transformation
title Compositional Data Analysis of Microbiome and Any-Omics Datasets: A Validation of the Additive Logratio Transformation
title_full Compositional Data Analysis of Microbiome and Any-Omics Datasets: A Validation of the Additive Logratio Transformation
title_fullStr Compositional Data Analysis of Microbiome and Any-Omics Datasets: A Validation of the Additive Logratio Transformation
title_full_unstemmed Compositional Data Analysis of Microbiome and Any-Omics Datasets: A Validation of the Additive Logratio Transformation
title_short Compositional Data Analysis of Microbiome and Any-Omics Datasets: A Validation of the Additive Logratio Transformation
title_sort compositional data analysis of microbiome and any-omics datasets: a validation of the additive logratio transformation
topic Microbiology
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8561721/
https://www.ncbi.nlm.nih.gov/pubmed/34737726
http://dx.doi.org/10.3389/fmicb.2021.727398
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