Testing hypotheses about the microbiome using the linear decomposition model (LDM)

Abstract

Motivation Methods for analyzing microbiome data generally fall into one of two groups: tests of the global hypothesis of any microbiome effect, which do not provide any information on the contribution of individual operational taxonomic units (OTUs); and tests for individual OTUs, which do not typically provide a global test of microbiome effect. Without a unified approach, the findings of a global test may be hard to resolve with the findings at the individual OTU level. Further, many tests of individual OTU effects do not preserve the false discovery rate (FDR). Results We introduce the linear decomposition model (LDM), that provides a single analysis path that includes global tests of any effect of the microbiome, tests of the effects of individual OTUs while accounting for multiple testing by controlling the FDR, and a connection to distance-based ordination. The LDM accommodates both continuous and discrete variables (e.g. clinical outcomes, environmental factors) as well as interaction terms to be tested either singly or in combination, allows for adjustment of confounding covariates, and uses permutation-based P-values that can control for sample correlation. The LDM can also be applied to transformed data, and an ‘omnibus’ test can easily combine results from analyses conducted on different transformation scales. We also provide a new implementation of PERMANOVA based on our approach. For global testing, our simulations indicate the LDM provided correct type I error and can have comparable power to existing distance-based methods. For testing individual OTUs, our simulations indicate the LDM controlled the FDR well. In contrast, DESeq2 often had inflated FDR; MetagenomeSeq generally had the lowest sensitivity. The flexibility of the LDM for a variety of microbiome studies is illustrated by the analysis of data from two microbiome studies. We also show that our implementation of PERMANOVA can outperform existing implementations. Availability and implementation The R package LDM is available on GitHub at https://github.com/yijuanhu/LDM in formats appropriate for Macintosh or Windows. Supplementary information Supplementary data are available at Bioinformatics online.

Analyzing matched sets of microbiome data using the LDM and PERMANOVA

“…As we have assumed the samples in each set are exchangeable, we propose to perform restricted permutation among samples from the same set. As permuting residuals of Y in the Freedman and Lane scheme [6] is typically equivalent to permuting X k s [5], the restricted permutation refers to permuting the (orthonormalized) traits of interest within samples from the same set. The same permutation scheme can be used for testing the interactions between traits of interest or between traits and set-level covariates; the latter allows us to detect whether the associations between the microbiome and the traits of interest are homogeneous across study groups (which can be defined by the set-level covariates).…”

“…To generate our simulation data, we used the same motivating dataset as Hu and Satten [5], i.e., data on 856 OTUs of the upper-respiratory-tract microbiome first described by Charlson et al [8]. In most simulations we considered a binary trait such as case-control status, but we also considered matched sets with a continuous trait.…”

“…The manual for the DESeq2 software package [3] stated that the set indicators should be included as a term in the design formula, but DESeq2 does not account for within-set correlations. The documentation of both implementations of PERMANOVA [4], adonis2 (R package vegan) and permanovaFL (R package ldm [5]), suggest that restricted permutation within each set should be performed. (Note that the two implementations differ slightly in their permutation schemes; in particular, permanovaFL was based on the Freedman-Lane scheme [6]).…”

“…We previously introduced the linear decomposition model (LDM) [5] primarily for analyzing independent data. The LDM provides tests at the community level and also tests of the contribution of individual operational taxonomic units (OTUs; here we use "OTU" generically to refer to any feature such as amplicon sequence variants or taxonomic/functional grouping of bacterial sequences).…”

“…Both PERMANOVA and the LDM are regression-and permutation-based, making them readily extendable to analyzing matched-set data while accounting for the aforementioned data complexities. Although we considered within-cluster permutation in the LDM paper [5], that was in a context in which variables of interest could be below the cluster level. We did not explicitly consider the matched set data we describe here from either a theoretical or numerical point of view.…”