Exact variance component tests for longitudinal microbiome studies

Abstract

In metagenomic studies, testing the association between microbiome composition and clinical outcomes translates to testing the nullity of variance components. Motivated by a lung human immunodeficiency virus (HIV) microbiome project, we study longitudinal microbiome data by using variance component models with more than two variance components. Current testing strategies only apply to models with exactly two variance components and when sample sizes are large. Therefore, they are not applicable to longitudinal microbiome studies. In this paper, we propose exact tests (score test, likelihood ratio test, and restricted likelihood ratio test) to (a) test the association of the overall microbiome composition in a longitudinal design and (b) detect the association of one specific microbiome cluster while adjusting for the effects from related clusters. Our approach combines the exact tests for null hypothesis with a single variance component with a strategy of reducing multiple variance components to a single one. Simulation studies demonstrate that our method has a correct type I error rate and superior power compared to existing methods at small sample sizes and weak signals. Finally, we apply our method to a longitudinal pulmonary microbiome study of HIV‐infected patients and reveal two interesting genera Prevotella and Veillonella associated with forced vital capacity. Our findings shed light on the impact of the lung microbiome on HIV complexities. The method is implemented in the open‐source, high‐performance computing language Julia and is freely available at https://github.com/JingZhai63/VCmicrobiome.

FiMAP: A fast identity-by-descent mapping test for biobank-scale cohorts

“…Although under regularity conditions, and are consistent estimators for variance component parameters and under the null hypothesis , the classical score-type variance component test above treats them as fixed numbers and ignores the variability in their estimation, which could result in not well-calibrated p values in finite samples. This is a known issue for score-type variance component tests in microbiome association studies with small sample sizes [ 48 – 50 ]. Despite large sample sizes in biobank-scale cohorts, the local IBD matrix Ψ l for genetic locus l is often sparse, which could invalidate asymptotic inference on the quadratic form .…”

FiMAP: A Fast Identity-by-Descent Mapping Test for Biobank-scale Cohorts

“…This is a known issue for scoretype variance component tests in microbiome association studies with small sample sizes. [43][44][45] Despite large sample sizes in biobank-scale cohorts, the local IBD matrix 𝛹 𝑙 for genetic locus 𝑙 is often sparse, which could invalidate asymptotic inference on the quadratic form 𝑄 𝑙 =…”

Empirical Likelihood Inference of Variance Components in Linear Mixed-Effects Models

“…However, inference on Statistica Sinica: Newly accepted Paper (accepted author-version subject to English editing) the variance components is less studied and often requires strong distributional assumptions on the random effects and the error terms. When the underlying distributions are assumed to be multivariate normal, classical inference methods, such as the likelihood ratio test, the restricted likelihood ratio test, and the score test (Self and Liang, 1987;Zhang and Lin, 2003;Koh et al, 2019;Zhai et al, 2019), can be applied. However, these parametric methods are often restrictive and not robust if the model assumptions are violated.…”

“…The linear structure holds when each components of D(θ * ) is a linear function of θ * (Lin, 1997). This encompasses both nested, crossed and clustered designs (Michalski and Zmyślony, 1996;Zhai et al, 2019;Chen et al, 2019;Li et al, 2021). See Section 5.1 for a specific example of such a random-effect model for modeling the family data that includes additive genetic effect, common environment and unique subject-specific We first introduce some notation.…”