Marginalizable mixed effect models for clustered binary, categorical and survival data
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In this thesis, I propose new models for clustered data, design estimators of covariate effects, implement model inference algorithms, and show asymptotic properties of my estimators, including consistency and asymptotic normality. I also present Monte Carlo simulations and real dataset analyses for demonstration. In this thesis three inherently related marginalizable mixed effects models for datasets with clustered binary, ordinal and right-censored, i.e. survival outcomes are proposed. These models can evaluate population-level covariate effects, and model a diverse variety of cluster correlation structures. The marginalizable property of the models is obtained via a pair of conjugate distributions. Chapter I contains literature review of various models designed for clustered datasets, focusing on binary, ordinal and survival data. Chapter II discusses and compares different inference methods for models in Part I. In Chapter III, I first give the motivation of the new marginalizable mixed effects model. Then I introduce the multivariate exponential random variables, which serve as random effects in the new models. I formally present the new model formulation for binary data, the inference procedure followed by a brief discussion, as well as relevant asymptotic theorems of my estimators. Chapter IV and Chapter V discuss clustered ordinal data and survival data, and are organized similarly. In Chapter VI I present some Monte Carlo simulation results along with real dataset applications: the Madras longitudinal schizophrenia study, the British Social Attitudes Panel Survey have clustered binary outcomes; the Arthritis data and the Television, the School and Family Smoking Prevention and Cessation Project have clustered ordinal outcomes; the Rats and Lung datasets for have clustered survival data.
- Biostatistics