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Gut microbiota in the human lower gastrointestinal tract can impact the health through human functions as well as triggering numerous diseases. The colonization of the microbiota occurs immediately after the birth of an infant. Early life factors can highly influence the composition of gut microbiome, which ultimately affects infant’s health. Therefore, the relationship between microbiome composition and clinical outcomes of preterm infants observed in Neonatal Intensive Care Units (NICUs) is of critical importance. To study this relationship, it is common to use longitudinal study designs. One of the major challenges in these designs is the huge percentage of missingness of the microbiome composition data, which needs to be appropriately accounted for during the study design. In this thesis, we propose a mixed-effects zero-inflated Beta regression model for longitudinal composition designs with missing at random data. This model captures the dependence of repeated measures for each subject by assuming a first-order autoregressive correlation structure. A Bayesian approach was employed for parameter estimations and inferences under this model. Performance of the model was investigated by a simulation study using different settings of missing data mechanisms. A sensitivity analysis was conducted to study the model misspecification issue. The developed model was further illustrated by a real data analysis on gut microbiome compositions of NICU preterm infants.

A MIXED-EFFECTS REGRESSION MODEL WITH APPLICATION TO LONGITUDINAL MISSING AT RANDOM MICROBIOME DATA