A group penalization framework for detecting time-lagged microbiota-host associations.

There is rising interest in using longitudinal microbiome data to understand how the past status of the microbiome impacts the current state of the host, referred to as "time-lagged" effects, as these effects may take time to occur. While existing works used previous states of the microbiome in their analysis, they did not use methods that identify both the time-lagged associations and their corresponding time lags. In this article, we present a framework to identify time-lagged associations between abundances of longitudinally sampled microbiota and a stationary response (final health outcome, disease status, etc.). We start with a definition of the time-lagged effect by imposing a particular structure on the association pattern of longitudinal microbial measurements. Using group penalization methods, we identify these time-lagged associations including their strengths, signs, and timespans. Through simulation studies, we demonstrate accurate identification of time lags and estimation of signal strengths by our approach. We further apply our approach to find specific gut microbial taxa and their time-lagged effects on increased parasite worm burden in zebrafish.