  Quantifying the relation between gut microbiome and body weight can provide
insights into personalized strategies for improving digestive health. In this
paper, we present an algorithm that predicts weight fluctuations using gut
microbiome in a healthy cohort of newborns from a previously published dataset.
Microbial data has been known to present unique statistical challenges that
defy most conventional models. We propose a mixed effect Dirichlet-tree
multinomial (DTM) model to untangle these difficulties as well as incorporate
covariate information and account for species relatedness. The DTM setup allows
one to easily invoke empirical Bayes shrinkage on each node for enhanced
inference of microbial proportions. Using these estimates, we subsequently
apply random forest for weight prediction and obtain a microbiome-inferred
weight metric. Our result demonstrates that microbiome-inferred weight is
significantly associated with weight changes in the future and its non-trivial
effect size makes it a viable candidate to forecast weight progression.
