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Register a new userA Phylogeny-based Test of Mediation Effect in Microbiome
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Zheng-Zheng Tang
Publication date
2021
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Mathematical Statistics
and research's language is
English
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Recent studies suggest that the microbiome can be an important mediator in the effect of a treatment on an outcome. Microbiome data generated from sequencing experiments contain the relative abundance of a large number of microbial taxa with their evolutionary relationships represented by a phylogenetic tree. The compositional and high-dimensional nature of the microbiome mediator invalidates standard mediation analyses. We propose a phylogeny-based mediation analysis method (PhyloMed) for the microbiome mediator. PhyloMed models the microbiome mediation effect through a cascade of independent local mediation models on the internal nodes of the phylogenetic tree. Each local model captures the mediation effect of a subcomposition at a given taxonomic resolution. The method improves the power of the mediation test by enriching weak and sparse signals across mediating taxa that tend to cluster on the tree. In each local model, we further empower PhyloMed by using a mixture distribution to obtain the subcomposition mediation test p-value, which takes into account the composite nature of the null hypothesis. PhyloMed enables us to test the overall mediation effect of the entire microbial community and pinpoint internal nodes with significant subcomposition mediation effects. Our extensive simulations demonstrate the validity of PhyloMed and its substantial power gain over existing methods. An application to a real study further showcases the advantages of our method.
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This paper proposes a new two-stage network mediation method based on the use of a latent network approach -- model-based eigenvalue decomposition -- for analyzing social network data with nodal covariates. In the decomposition stage of the observed network, no assumption on the metric of the latent space structure is required. In the mediation stage, the most important eigenvectors of a network are used as mediators. This method further offers an innovative way for controlling for the conditional covariates and it only considers the information left in the network. We demonstrate this approach in a detailed tutorial R code provided for four separate cases -- unconditional and conditional model-based eigenvalue decompositions for either a continuous outcome or a binary outcome -- to show its applicability to empirical network data.
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In microbiome studies, one of the ways of studying bacterial abundances is to estimate bacterial composition based on the sequencing read counts. Various transformations are then applied to such compositional data for downstream statistical analysis, among which the centered log-ratio (clr) transformation is most commonly used. Due to limited sequencing depth and DNA dropouts, many rare bacterial taxa might not be captured in the final sequencing reads, which results in many zero counts. Naive composition estimation using count normalization leads to many zero proportions, which makes clr transformation infeasible. This paper proposes a multi-sample approach to estimation of the clr matrix directly in order to borrow information across samples and across species. Empirical results from real datasets suggest that the clr matrix over multiple samples is approximately low rank, which motivates a regularized maximum likelihood estimation with a nuclear norm penalty. An efficient optimization algorithm using the generalized accelerated proximal gradient is developed. Theoretical upper bounds of the estimation errors and of its corresponding singular subspace errors are established. Simulation studies demonstrate that the proposed estimator outperforms the naive estimators. The method is analyzed on Gut Microbiome dataset and the American Gut project.
The natural indirect effect (NIE) and mediation proportion (MP) are two measures of primary interest in mediation analysis. The standard approach for estimating NIE and MP is through the product method, which involves a model for the outcome conditional on the mediator and exposure and another model describing the exposure-mediator relationship. The purpose of this article is to comprehensively develop and investigate the finite-sample performance of NIE and MP estimators via the product method. With four common data types, we propose closed-form interval estimators via the theory of estimating equations and multivariate delta method, and evaluate its empirical performance relative to the bootstrap approach. In addition, we have observed that the rare outcome assumption is frequently invoked to approximate the NIE and MP with a binary outcome, although this approximation may lead to non-negligible bias when the outcome is common. We therefore introduce the exact expressions for NIE and MP with a binary outcome without the rare outcome assumption and compare its performance with the approximate estimators. Based upon these theoretical developments and empirical studies, we offer several practical recommendations to inform practice. An R package mediateP is developed to implement the methods for point and variance estimation discussed in this paper.
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