LOG-CONTRAST REGRESSION WITH FUNCTIONAL COMPOSITIONAL PREDICTORS: LINKING PRETERM INFANT'S GUT MICROBIOME TRAJECTORIES TO NEUROBEHAVIORAL OUTCOME.

The neonatal intensive care unit (NICU) experience is known to be one of the most crucial factors that drive preterm infant's neurodevelopmental and health outcome. It is hypothesized that stressful early life experience of very preterm neonate is imprinting gut microbiome by the regulation of the so-called brain-gut axis, and consequently, certain microbiome markers are predictive of later infant neurodevelopment. To investigate, a preterm infant study was conducted; infant fecal samples were collected during the infants' first month of postnatal age, resulting in functional compositional microbiome data, and neurobehavioral outcomes were measured when infants reached 36-38 weeks of post-menstrual age. To identify potential microbiome markers and estimate how the trajectories of gut microbiome compositions during early postnatal stage impact later neurobehavioral outcomes of the preterm infants, we innovate a sparse log-contrast regression with functional compositional predictors. The functional simplex structure is strictly preserved, and the functional compositional predictors are allowed to have sparse, smoothly varying, and accumulating effects on the outcome through time. Through a pragmatic basis expansion step, the problem boils down to a linearly constrained sparse group regression, for which we develop an efficient algorithm and obtain theoretical performance guarantees. Our approach yields insightful results in the preterm infant study. The identified microbiome markers and the estimated time dynamics of their impact on the neurobehavioral outcome shed lights on the linkage between stress accumulation in early postnatal stage and neurodevelpomental process of infants.