Zero-inflated Bayesian factor analysis model with skew-normal priors for modeling microbiome data

Abstract

Background: Advancements in next-generation sequencing have transformed our understanding of host-microbe interactions, revealing links between microbial composition and chronic conditions such as diabetes, Crohn's disease, and others. However, the analysis of microbiome data is complex due to its high-dimensionality as well as additional statistical characteristics. One primary objective is to achieve effective dimensionality reduction while simultaneously accounting for the data's compositional nature and zero inflation. Existing probabilistic models are often based on the assumption that the log-ratio-transformed compositions are normally distributed. This assumption is problematic because it can fail to capture the significant skewness inherent in these transformed compositions. Results: We propose a new model called the Zero-Inflated Factor Analysis Logistic Skew-Normal Multinomial (ZIFA-LSNM) model. ZIFA-LSNM integrates a zero-inflation component to handle excess zeros, employs factor analysis for dimensionality reduction, and, critically, utilizes skew-normal priors on the latent factors to explicitly model data asymmetry. Posterior inference is performed using an efficient variational inference algorithm. Through simulation studies and real data analysis, the ZIFA-LSNM model is shown to have improved performance in parameter recovery and composition estimation compared to its Gaussian-based counterpart. Conclusion: The ZIFA-LSNM model demonstrates that explicitly accounting for skewness in the latent factor structure improves inference in microbiome data. The proposed model, therefore, offers a flexible and scalable framework allowing for the improved analysis of the complex relationships between microbial communities and human health.