I wish to thank my thesis committee for their invaluable contributions and guidance on this research. In particular, my sincere appreciation goes to Dr. Myunghee Paik for initiating and directing this project, for encouraging me and providing support over years, and for mentoring me in Biostatistics. I would also like to express my gratitude to Dr. Wei-Yann Tsai for his statistical advice and many helps during these years. I thank Dr. Daniel Rabinowitz for his insightful comments in Statistics. I am deeply grateful to Dr. Frederica Perera and Dr. LaVerne Mooney for their valuable suggestions to the applied aspects of this research, for supply of the study dataset, and for lots of helps during my years with the Molecular Epidemiology Program.

Many thanks also go to other faculties and friends in the Division of Biostatistics and the Molecular Epidemiology Program at Columbia University for numerous helps and support, especially to Dr. Bruce Levin, Ms. Gerda Cordova, Dr. Deliang Tang, Dr. Chris Dickey, Dr. Robin Whyatt and Dr. Andrew Rundle. I would also like to thank Drs. Ora-Simcha Fagan and Stuart Fagan for their encouragement and help.

Finally, I dedicate this volume to my parents Mr. Zhaolian Xu and Mrs. Hanzhen Liu, and to my wife Jing Chi, with great appreciation for their consistent support, extraordinary patience and understanding.