Two-level lognormal frailty model and competing risks model with missing cause of failure TWO-LEVEL LOGNORMAL FRAILTY MODEL AND COMPETING RISKS MODEL WITH MISSING CAUSE OF FAILURE Title and Department Date Thesis Supervisor Title and Department Date TWO-LEVEL LOGNORMAL FRAILTY MODEL AND COMPETING RISKS MODEL WITH MISSING CAUSE OF FAILURE
Xiongwen Tang, Xiongwen Tang, Michael Jones, Ying Zhang, Xiongwen Tang, Ying Zhang, Kung-Sik Chan, Jiang Huang, Russell Lenth, Alyssa
2012
unpublished
Part of the Statistics and Probability Commons Recommended Citation Tang, Xiongwen. "Two-level lognormal frailty model and competing risks model with missing cause of failure." PhD (Doctor of Philosophy) thesis, University of Iowa, 2012. ABSTRACT In clustered survival data, unobservable cluster effects may exert powerful influences on the outcomes and thus induce correlation among subjects within the same cluster. The ordinary partial likelihood approach does not account for this dependence.
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... ilty models, as an extension to Cox regression, incorporate multiplicative random effects, called frailties, into the hazard model and have become a very popular way to account for the dependence within clusters. We particularly study the twolevel nested lognormal frailty model and propose an estimation approach based on the complete data likelihood with frailty terms integrated out. We adopt B-splines to model the baseline hazards and adaptive Gauss-Hermite quadrature to approximate the integrals efficiently. Furthermore, in finding the maximum likelihood estimators, instead of the Newton-Raphson iterative algorithm, Gauss-Seidel and BFGS methods are used to improve the stability and efficiency of the estimation procedure. We also study competing risks models with missing cause of failure in the context of Cox proportional hazards models. For competing risks data, there exists more than one cause of failure and each observed failure is exclusively linked to one cause. Conceptually, the causes are interpreted as competing risks before the failure is observed. Competing risks models are constructed based on the proportional hazards model specified for each cause of failure respectively, which can be estimated using partial likelihood approach. However, the ordinary partial likelihood is not applicable when the cause of failure could be missing for some reason. We propose a weighted 2 partial likelihood approach based on complete-case data, where weights are computed as the inverse of selection probability and the selection probability is estimated by a logistic regression model. The asymptotic properties of the regression coefficient estimators are investigated by applying counting process and martingale theory. We further develop a double robust approach based on the full data to improve the efficiency as well as the robustness. Abstract Approved: Thesis Supervisor ii ACKNOWLEDGEMENTS I owe my deepest gratitude to my advisors, Professor Michael P. Jones and Professor Ying Zhang, for their guidance throughout my dissertation work. I have been greatly impressed by their inspiration, enthusiasm and immense knowledge, which help me move forward. I have learned from them not only in academic research, but also in American culture, life experience and future career development. I extremely appreciate their time and patience with me. It is also my big pleasure to thank my committee members, Professors Kung-Sik Chan, Jiang Huang, and Russell V. Lenth, for sharing their insightful comments and suggestions on my research work. I shall give my immense thanks to my beloved wife Jing Pan for her continuous support and encouragement, and especially for the birth of our daughter Alyssa S. Tang. Though the baby's birth inevitably distracted me quite a bit, I have been really enjoying the new life. The happiness and fun from family is always bringing me more energy and motivation. I am also imdebted to my parents and my parents-in-law for their care and support. Moreover, I would like to thank the statistics department, every professors I took courses from, and the staff members Tammy, Margie and Dena for all help and convenience they provided. Last but not the least, I shall thank Eastern Cooperative Oncology Group (ECOG) for providing the data from study E1178. iii ABSTRACT In clustered survival data, unobservable cluster effects may exert powerful influences on the outcomes and thus induce correlation among subjects within the same cluster. The ordinary partial likelihood approach does not account for this dependence. Frailty models, as an extension to Cox regression, incorporate multiplicative random effects, called frailties, into the hazard model and have become a very popular way to account for the dependence within clusters. We particularly study the twolevel nested lognormal frailty model and propose an estimation approach based on the complete data likelihood with frailty terms integrated out. We adopt B-splines to model the baseline hazards and adaptive Gauss-Hermite quadrature to approximate the integrals efficiently. Furthermore, in finding the maximum likelihood estimators,
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