Microbiome studies offer important potential to identify organisms associated with human disease. Longitudinal measures may further reveal the dynamics of the microbiome and its accumulating effects on health outcomes. However, microbiome data are complex in nature, involving high dimensionality, compositionality, zero inflation and taxonomic hierarchy. This complexity cannot be adequately addressed using existing statistical methods, leaving the power of microbiome data relatively unharnessed. We recently developed novel statistical methods for associating (longitudinal) microbiome data with health outcomes, motivated by a study of neurodevelopment in preterm infants. The methods also have wide utility in other microbiome studies. In the first part of the talk, I will introduce a functional data approach to identify smoothly varying and accumulating effects of longitudinal microbiome data on the outcome. In the second part, I will introduce a novel regression paradigm for compositional data that can adequately accommodate extrinsic taxonomic tree structure. The application to the preterm infants study identifies important organisms that are related to neurodevelopment and provides critical insights into the linkage between gut and brain.
