scholarly journals High-dimensional Log-Error-in-Variable Regression with Applications to Microbial Compositional Data Analysis

Biometrika ◽  
2021 ◽  
Author(s):  
Pixu Shi ◽  
Yuchen Zhou ◽  
Anru R Zhang
Keyword(s):  
Data Analysis ◽  
Compositional Data ◽  
Estimation Error ◽  
Real Data ◽  
Upper And Lower Bounds ◽  
High Dimensional ◽  
Compositional Data Analysis ◽  
Sequencing Data ◽  
Contrast Model ◽  
Critical Issues

Abstract In microbiome and genomic studies, the regression of compositional data has been a crucial tool for identifying microbial taxa or genes that are associated with clinical phenotypes. To account for the variation in sequencing depth, the classic log-contrast model is often used where read counts are normalized into compositions. However, zero read counts and the randomness in covariates remain critical issues. In this article, we introduce a surprisingly simple, interpretable, and efficient method for the estimation of compositional data regression through the lens of a novel high-dimensional log-error-in-variable regression model. The proposed method provides both corrections on sequencing data with possible overdispersion and simultaneously avoids any subjective imputation of zero read counts. We provide theoretical justifications with matching upper and lower bounds for the estimation error. The merit of the procedure is illustrated through real data analysis and simulation studies.

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

2021 ◽  
Vol 12 ◽  
Author(s):  
Michael Greenacre ◽  
Marina Martínez-Álvaro ◽  
Agustín Blasco
Keyword(s):  
Data Analysis ◽  
Compositional Data ◽  
High Dimensional ◽  
Compositional Data Analysis ◽  
Rna Transcripts ◽  
Operational Taxonomic Units ◽  
Logratio Transformation ◽  
Large Numbers ◽  
Fixed Reference ◽  
Reference Component

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.

scholarly journals Compositional analysis: a valid approach to analyze microbiome high-throughput sequencing data

2016 ◽  
Vol 62 (8) ◽  
pp. 692-703 ◽  
Author(s):  
Gregory B. Gloor ◽  
Gregor Reid
Keyword(s):  
Data Analysis ◽  
High Throughput ◽  
High Throughput Sequencing ◽  
Compositional Data ◽  
Critical Role ◽  
Compositional Data Analysis ◽  
Data Sets ◽  
Clear Understanding ◽  
Sequencing Data ◽  
Microbiome Data

A workshop held at the 2015 annual meeting of the Canadian Society of Microbiologists highlighted compositional data analysis methods and the importance of exploratory data analysis for the analysis of microbiome data sets generated by high-throughput DNA sequencing. A summary of the content of that workshop, a review of new methods of analysis, and information on the importance of careful analyses are presented herein. The workshop focussed on explaining the rationale behind the use of compositional data analysis, and a demonstration of these methods for the examination of 2 microbiome data sets. A clear understanding of bioinformatics methodologies and the type of data being analyzed is essential, given the growing number of studies uncovering the critical role of the microbiome in health and disease and the need to understand alterations to its composition and function following intervention with fecal transplant, probiotics, diet, and pharmaceutical agents.

scholarly journals Compositional Data Analysis using Kernels in Mass Cytometry Data

2021 ◽  
Author(s):  
Pratyaydipta Rudra ◽  
Ryan Baxter ◽  
Elena WY Hsieh ◽  
Debashis Ghosh
Keyword(s):  
Data Analysis ◽  
Lupus Erythematosus ◽  
Compositional Data ◽  
Small Sample ◽  
Supplementary Information ◽  
High Dimensional ◽  
Compositional Data Analysis ◽  
Cell Type ◽  
Mass Cytometry ◽  
Abundance Data

Motivation: Cell type abundance data arising from mass cytometry experiments are compositional in nature. Classical association tests do not apply to the compositional data due to their non-Euclidean nature. Existing methods for analysis of cell type abundance data suffer from several limitations for high-dimensional mass cytometry data, especially when the sample size is small. Results: We proposed a new multivariate statistical learning methodology, Compositional Data Analysis using Kernels (CODAK), based on the kernel distance covariance (KDC) framework to test the association of the cell type compositions with important predictors (categorical or continuous) such as disease status. CODAK scales well for high-dimensional data and provides satisfactory performance for small sample sizes (n<25). We conducted simulation studies to compare the performance of the method with existing methods of analyzing cell type abundance data from mass cytometry studies. The method is also applied to a high-dimensional dataset containing different subgroups of populations including Systemic Lupus Erythematosus (SLE) patients and healthy control subjects. Availability and Implementation: CODAK is implemented using R. The codes and the data used in this manuscript are available on the web at http://github.com/GhoshLab/CODAK/. Supplementary information: Supplementary Materials.pdf.

scholarly journals A field guide for the compositional analysis of any-omics data

2018 ◽  
Author(s):  
Thomas P. Quinn ◽  
Ionas Erb ◽  
Greg Gloor ◽  
Cedric Notredame ◽  
Mark F. Richardson ◽  
...  
Keyword(s):  
Data Analysis ◽  
General Solution ◽  
Compositional Data ◽  
Compositional Analysis ◽  
Compositional Data Analysis ◽  
Sequencing Data ◽  
Nucleotide Synthesis ◽  
Library Size ◽  
Concise Guide ◽  
Log Ratio

AbstractNext-generation sequencing (NGS) has made it possible to determine the sequence and relative abundance of all nucleotides in a biological or environmental sample. Today, NGS is routinely used to understand many important topics in biology from human disease to microorganism diversity. A cornerstone of NGS is the quantification of RNA or DNA presence as counts. However, these counts are not counts per se: the magnitude of the counts are determined arbitrarily by the sequencing depth, not by the input material. Consequently, counts must undergo normalization prior to use. Conventional normalization methods require a set of assumptions: they assume that the majority of features are unchanged, and that all environments under study have the same carrying capacity for nucleotide synthesis. These assumptions are often untestable and may not hold when comparing heterogeneous samples (e.g., samples collected across distinct cancers or tissues). Instead, methods developed within the field of compositional data analysis offer a general solution that is assumption-free and valid for all data. In this manuscript, we synthesize the extant literature to provide a concise guide on how to apply compositional data analysis to NGS count data. In doing so, we review zero replacement, differential abundance analysis, and within-group and between-group coordination analysis. We then discuss how this pipeline can accommodate complex study design, facilitate the analysis of vertically and horizontally integrated data, including multiomics data, and further extend to single-cell sequencing data. In highlighting the limitations of total library size, effective library size, and spike-in normalizations, we propose the log-ratio transformation as a general solution to answer the question, “Relative to some important activity of the cell, what is changing?”. Taken together, this manuscript establishes the first fully comprehensive analysis protocol that is suitable for any and all -omics data.

scholarly journals Zero problems with compositional data of physical behaviors: a comparison of three zero replacement methods

2020 ◽  
Vol 17 (1) ◽  
Author(s):  
Charlotte Lund Rasmussen ◽  
Javier Palarea-Albaladejo ◽  
Melker Staffan Johansson ◽  
Patrick Crowley ◽  
Matthew Leigh Stevens ◽  
...  
Keyword(s):  
Data Analysis ◽  
Time Use ◽  
Compositional Data ◽  
Real Data ◽  
Compositional Data Analysis ◽  
Accelerometer Data ◽  
Relative Variation ◽  
Physical Behavior ◽  
Complete Dataset ◽  
Log Ratio

Abstract Background Researchers applying compositional data analysis to time-use data (e.g., time spent in physical behaviors) often face the problem of zeros, that is, recordings of zero time spent in any of the studied behaviors. Zeros hinder the application of compositional data analysis because the analysis is based on log-ratios. One way to overcome this challenge is to replace the zeros with sensible small values. The aim of this study was to compare the performance of three existing replacement methods used within physical behavior time-use epidemiology: simple replacement, multiplicative replacement, and log-ratio expectation-maximization (lrEM) algorithm. Moreover, we assessed the consequence of choosing replacement values higher than the lowest observed value for a given behavior. Method Using a complete dataset based on accelerometer data from 1310 Danish adults as reference, multiple datasets were simulated across six scenarios of zeros (5–30% zeros in 5% increments). Moreover, four examples were produced based on real data, in which, 10 and 20% zeros were imposed and replaced using a replacement value of 0.5 min, 65% of the observation threshold, or an estimated value below the observation threshold. For the simulation study and the examples, the zeros were replaced using the three replacement methods and the degree of distortion introduced was assessed by comparison with the complete dataset. Results The lrEM method outperformed the other replacement methods as it had the smallest influence on the structure of relative variation of the datasets. Both the simple and multiplicative replacements introduced higher distortion, particularly in scenarios with more than 10% zeros; although the latter, like the lrEM, does preserve the ratios between behaviors with no zeros. The examples revealed that replacing zeros with a value higher than the observation threshold severely affected the structure of relative variation. Conclusions Given our findings, we encourage the use of replacement methods that preserve the relative structure of physical behavior data, as achieved by the multiplicative and lrEM replacements, and to avoid simple replacement. Moreover, we do not recommend replacing zeros with values higher than the lowest observed value for a behavior.

scholarly journals Compositional data analysis of microbiome and any-omics datasets: a revalidation of the additive logratio transformation

2021 ◽  
Author(s):  
Michael Greenacre ◽  
Marina Martinez-Alvaro ◽  
Agustin Blasco
Keyword(s):  
Data Analysis ◽  
Compositional Data ◽  
High Dimensional ◽  
Compositional Data Analysis ◽  
Rna Transcripts ◽  
Operational Taxonomic Units ◽  
Logratio Transformation ◽  
Large Numbers ◽  
Fixed Reference ◽  
Reference Component

Background: 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 are 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 in the sense of reproducing 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. Finally, it is preferable that the reference component not be a rare component but well populated, and substantive biological reasons might also guide the choice if several reference candidates are identified. Results: On each of three high-dimensional 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, 0.9977 and 0.9997, respectively. In the third case, where the objective was to distinguish between three groups of samples, the approximation was made to the restricted logratio space of the between-group variance. Conclusions: We show that for high-dimensional compositional data additive logratios can provide a valid choice as transformed variables that are (1) subcompositionally coherent, (2) explaining 100% of the total logratio variance and (3) coming measurably very close to being isometric, that is approximating almost perfectly the exact logratio geometry. The interpretation of additive logratios is simple and, when the variance of the log-transformed reference is very low, it is made even simpler since each additive logratio can be identified with a corresponding compositional component.

scholarly journals Visualizing balances of compositional data: A new alternative to balance dendrograms

F1000Research ◽  
2018 ◽  
Vol 7 ◽  
pp. 1278 ◽  
Author(s):  
Thomas P. Quinn
Keyword(s):  
Data Analysis ◽  
Compositional Data ◽  
High Dimensional Data ◽  
Large Data ◽  
High Dimensional ◽  
Compositional Data Analysis ◽  
Data Set ◽  
R Programming Language ◽  
Common Scale ◽  
R Programming

Balances have become a cornerstone of compositional data analysis. However, conceptualizing balances is difficult, especially for high-dimensional data. Most often, investigators visualize balances with the balance dendrogram, but this technique is not necessarily intuitive and does not scale well for large data. This manuscript introduces the 'balance' package for the R programming language. This package visualizes balances of compositional data using an alternative to the balance dendrogram. This alternative contains the same information coded by the balance dendrogram, but projects data on a common scale that facilitates direct comparisons and accommodates high-dimensional data. By stripping the branches from the tree, 'balance' can cleanly visualize any subset of balances without disrupting the interpretation of the remaining balances. As an example, this package is applied to a publicly available meta-genomics data set measuring the relative abundance of 500 microbe taxa.

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