A Bayesian Functional Concurrent Zero-Inflated Dirichlet-Multinomial Regression Model with Application to Infant Microbiome

2026-03-27

AI Summary

This study addresses the challenges posed by longitudinal infant microbiome data—namely repeated measurements, excess zeros, compositional constraints, and high dimensionality—by proposing a Bayesian functional concurrent zero-inflated Dirichlet-multinomial regression model (FunC-ZIDM). This approach uniquely integrates functional concurrent modeling, a zero-inflation mechanism, and Dirichlet-multinomial regression to characterize the time-varying effects of covariates on microbial taxa. By leveraging Bayesian inference, the method effectively accommodates longitudinal dependence, compositional structure, and an overabundance of zeros. Simulation studies demonstrate that the model accurately estimates time-varying effects and performs well with high-dimensional compositional data. In empirical analysis, the model reveals that α-diversity significantly increases with both gestational age and the proportion of breastfeeding.

Technology Category

Reasoning under Uncertainty: Relational Probabilistic ModelsMachine Learning: Bayesian LearningData Mining & Knowledge Management: Mining of Visual, Multimedia & Multimodal Data

Application Category

Web Mining and Content Analysis: Models for Web evolutionGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsUser Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems

Abstract

The infant microbiome undergoes rapid changes in composition over time and is associated with long-term risks of conditions such as immune strength, allergy, asthma, and other health outcomes. Modeling the associations between exposures or treatments and microbial composition over time is essential for understanding the factors that drive these changes. Estimating these temporal dynamics has several challenges including: repeated measures, overdispersion, compositionality, high-dimensional parameter spaces, and zero-inflation. Many longitudinal regression models used in human microbiome research assume constant effects over time that cannot capture time-varying or functional effects of exposures, ignore the compositional structure of the data by modeling each taxon separately, and are not equipped to handle potential zero-inflation. Dirichlet-multinomial (DM) regression models inherently accommodate overdispersion and the compositional structure of the data and have been extended to account for excess zeros. However, existing DM-based regression models are unable to additionally handle repeated measures designs. To fill this gap, we propose a functional concurrent zero-inflated Dirichlet-multinomial (FunC-ZIDM) regression model which is designed to model time-varying relations between observed covariates and microbial taxa while accounting for zero-inflation, compositionality, and repeated measures. Through simulation, we demonstrate that the model can accurately estimate the underlying functional relations and scale to large compositional spaces. We apply our model to investigate time-varying associations between infant microbiome composition and observed covariates during the 11-week postnatal period. We found that $α$-diversity (i.e., diversity of the microbiome within an individual) is positively associated with a higher gestational age and percentage of breast milk in the diet.

Problem

• microbiome
• longitudinal regression
• zero-inflation
• compositional data
• time-varying effects

Innovation

• functional concurrent regression
• zero-inflated Dirichlet-multinomial
• compositional data
• longitudinal microbiome analysis
• Bayesian modeling