A semiparametric model for between‐subject attributes: Applications to beta‐diversity of microbiome data

Abstract

The human microbiome plays an important role in our health and identifying factors associated with microbiome composition provides insights into inherent disease mechanisms. By amplifying and sequencing the marker genes in high‐throughput sequencing, with highly similar sequences binned together, we obtain operational taxonomic units (OTUs) profiles for each subject. Due to the high‐dimensionality and nonnormality features of the OTUs, the measure of diversity is introduced as a summarization at the microbial community level, including the distance‐based beta‐diversity between individuals. Analyses of such between‐subject attributes are not amenable to the predominant within‐subject‐based statistical paradigm, such as t‐tests and linear regression. In this paper, we propose a new approach to model beta‐diversity as a response within a regression setting by utilizing the functional response models (FRMs), a class of semiparametric models for between‐ as well as within‐subject attributes. The new approach not only addresses limitations of current methods for beta‐diversity with cross‐sectional data, but also provides a premise for extending the approach to longitudinal and other clustered data in the future. The proposed approach is illustrated with both real and simulated data.

Effects of formic acid and glycerol monolaurate on weanling pig growth performance, fecal consistency, fecal microbiota, and serum immunity

“…The analysis of the Shannon Diversity indices, which accounts for species evenness in addition to species richness, only detected a significant difference within samples from pigs fed either GML or FORMI over time ( P < 0.05), which suggests that GML supplemented alone or with formic acid can alter the structure of the microbial community in piglet feces. Beyond evaluating differences in microbial populations within a given sample, comparison between samples is considered Beta diversity ( Liu et al, 2021 ). No evidence of differences in beta diversity was seen across dietary treatments ( P ≥ 0.25).…”

On Semiparametric Efficiency of an Emerging Class of Regression Models for Between-subject Attributes

“…The coefficients of the dummy variables now reveal the heterogeneity in f i among different subgroups defined by δ (X i ). Such a pairwise one-hot encode also facilitates disentangling different types of heterogeneity (e.g., "location" or "scale" difference) 18 , which is laborious or not even feasible using existing approaches such as PERMANOVA. We can also include either between-or within-subject attributes as covariates in (6).…”

“…But in the growing applications, of major interest are outcomes defined by a pair of subjects, or the "between-subject attributes." 18 The probability index P r(Y i 1 < Y i 2 ), (i 1 , i 2 ) ∈ C n 2 in the Mann-Whitney-Wilcoxon (MWW) rank-sum test is a classical example 7 . Fueled by innovative technologies such as high-throughput sequencing and wearable devices, the pairwise dissimilarity/distance metrics that summarize high-dimensional sequences also entail a between-subject nature 28 .…”

“…The FRM framework admits a wide range of applications. For instance, Liu et al (2021) 18 adopted the FRM to extend the predominant ANOVA-based approach to model microbiome Beta-diversity in a regression; Lin et al (2021) 17 implemented the MWW rank-sum test and FRM in survey data to address the restrictive test of equal distributions; Wu et al…”

A new paradigm for high‐dimensional data: Distance‐based semiparametric feature aggregation framework via between‐subject attributes

“…For example, the Mantel's test (Mantel, 1967) has long been established to evaluate the correlation between matrices formed by two outcomes, while the multiple regression on distance matrices (MRM) (Lichstein, 2007) extends it to allow for a regression-type analysis of multiple (dis)similarity matrices. Within content-specific research, the permutational multivariate analysis of variance (PERMANOVA) (Anderson, 2001) and its variations (Liu et al, 2021) compare the mean between-subject microbiome diversity across different groups. The multivariate distance matrix regression (Reiss et al, 2010) adopts a similar strategy and has been popularized in fMRI research to demystify convoluted brain connectivity.…”