Cluster Analysis Of Microbiome Data Via Mixtures Of Dirichlet-Multinomial Regression Models

CLUSTER ANALYSIS OF MICROBIOME DATA VIA MIXTURES OF DIRICHLET-MULTINOMIAL REGRESSION MODELS Drew Neish Advisors: University of Guelph, 2015 Dr. S. Dang (Subedi) Dr. Z. Feng The human gut microbiome is a source of genetic and metabolic diversity, and exploring the relationship between biological/environmental covariates and the resulting taxonomic composition of the gut microbial community is an active area of research. Previously, a Dirichlet-multinomial regression framework has been suggested to model this relationship, but it did not account for any latent group structure which has been observed across microbiome samples which share similar biota compositions (known as enterotypes). Here, a finite mixture of Dirichlet-multinomial regression models is proposed and illustrated in order to account for the enterotype structure and allow for a probabilistic investigation of the relationship between bacterial abundance and biological/environmental covariates within each inferred enterotype. Furthermore, finite mixtures of regression models which incorporate the concomitant effect of the covariates on the resulting mixing proportions are also proposed and examined within the Dirichlet-multinomial framework. iii Acknowledgements I would first and foremost like to thank my advisors Dr. Sanjeena Dang and Dr. Zeny Feng for their continuous guidance, expertise, and patience throughout the course of my research. Their mentorship has broadened my academic horizons and it has been a great pleasure to work with them. My masters experience has been booth productive and enriching, and without their support this work could not have been accomplished. I would also like to thank all the faculty in the Department of Mathematics and Statistics for their instruction, assistance, and contagious enthusiasm for their research which I hope to carry with me in my future. Finally, I would like to express my sincere gratitude to my friends and family for keeping me sane with their love and encouragement every step of the way.