  The human microbiome plays critical roles in human health and has been linked
to many diseases. While advanced sequencing technologies can characterize the
composition of the microbiome in unprecedented detail, it remains challenging
to disentangle the complex interplay between human microbiome and disease risk
factors due to the complicated nature of microbiome data. Excessive numbers of
zero values, high dimensionality, the hierarchical phylogenetic tree and
compositional structure are compounded and consequently make existing methods
inadequate to appropriately address these issues. We propose a multivariate
two-part zero-inflated logistic normal (MZILN) model to analyze the association
of disease risk factors with individual microbial taxa and overall microbial
community composition. This approach can naturally handle excessive numbers of
zeros and the compositional data structure with the discrete part and the
logistic-normal part of the model. For parameter estimation, an estimating
equations approach is employed that enables us to address the complex
inter-taxa correlation structure induced by the hierarchical phylogenetic tree
structure and the compositional data structure. This model is able to
incorporate standard regularization approaches to deal with high
dimensionality. Simulation shows that our model outperforms existing methods.
Our approach is also compared to others using the analysis of real microbiome
data.
