Compositional data analysis of the microbiome: fundamentals, tools, and challenges

Abstract

Purpose

Human microbiome studies are within the realm of compositional data with the absolute abundances of microbes not recoverable from sequence data alone. In compositional data analysis, each sample consists of proportions of various organisms with a sum constrained to a constant. This simple feature can lead traditional statistical treatments when naively applied to produce errant results and spurious correlations.

Methods

We review the origins of compositionality in microbiome data, the theory and usage of compositional data analysis in this setting and some recent attempts at solutions to these problems.

Results

Microbiome sequence data sets are typically high dimensional, with the number of taxa much greater than the number of samples, and sparse as most taxa are only observed in a small number of samples. These features of microbiome sequence data interact with compositionality to produce additional challenges in analysis.

Conclusions

Despite sophisticated approaches to statistical transformation, the analysis of compositional data may remain a partially intractable problem, limiting inference. We suggest that current research needs include better generation of simulated data and further study of how the severity of compositional effects changes when sampling microbial communities of widely differing diversity.

Introduction

Compositional data are vectors of nonnegative elements constrained to sum to a constant. This simple feature of compositional data can have surprisingly adverse effects when traditional methods of multivariate statistics are naively used [1]. The dangers of ignoring the effects of compositionality were noted by Pearson, who recognized more than a century ago, that “spurious correlations” would result, should values constructed as proportions be compared haphazardly [2]. Compositional data is subject to the “closure problem” that occurs when components necessarily compete to make up the constant sum constraint [3]. This can cause large changes in the absolute abundance of one component to drive apparent changes in the measured abundance of others, violating the assumption of sample independence and creating inevitable errors in covariance estimates that can lead to bias and flawed inference. Diverse academic disciplines have begun to appreciate the complexity of the analysis of compositional data, ranging from forensics [4], [5] and psychology [6] to the assessment of antibiotic use [7] and nutritional epidemiology [8].

In the case of the microbiome sequencing surveys, the compositional nature of the data comes from the fact that a correction must be made for different samples having different numbers of sequences while the total absolute abundance of all bacteria in each sample is unknown. These complications arise from sample collection, polymerase chain reaction (PCR) amplification, and the sequencing technology itself from which the absolute abundances of bacteria are not recoverable from sequence counts, but the proportions of different taxa are still relevant. Numerous schemes are used in the literature to convert the number of sequences for each taxon within each sample to relative abundance with popular techniques, including proportional abundance and rarefying, the latter being the default choice in the popular Quantitative Insights Into Microbial Ecology pipeline [9], [10]. Neither of these approaches corrects for compositionality and it has been argued that this lack of correction has led to erroneous analyses that fail to discriminate between true and spurious correlations between taxa [11], [12]. However, it remains unclear whether these sorts of normalization schemes routinely produce spurious correlations in the study of complex microbial communities, like the gut, or whether errors due to compositionality are instead restricted to analysis of microbial communities where only a few taxa dominate, such as the vaginal microbiome.

In this review, we examine the historical literature on the compositionality problem and some modern approaches to its solution that have been proposed for the analysis of next-generation sequencing data sets. We track recent progress and indicate where we think more research is needed. We also emphasize that the analysis of compositional data will always be at least a partially intractable problem despite the development of sophisticated statistical transformations as the absolute abundances of microbes before sequencing can never be recovered from sequence data alone, and this will inevitably color inference based on compositional samples.