Year of Publication

2010

Degree Name

Doctor of Philosophy (PhD)

Document Type

Dissertation

College

Arts and Sciences

Department

Statistics

First Advisor

Dr. Richard J. Kryscio

Abstract

The research on multi-state Markov transition model is motivated by the nature of the longitudinal data from the Nun Study (Snowdon, 1997), and similar information on the BRAiNS cohort (Salazar, 2004). Our goal is to develop a flexible methodology for handling the categorical longitudinal responses and competing risks time-to-event that characterizes the features of the data for research on dementia. To do so, we treat the survival from death as a continuous variable rather than defining death as a competing absorbing state to dementia. We assume that within each subject the survival component and the Markov process are linked by a shared latent random effect, and moreover, these two pieces are conditionally independent given the random effect and their corresponding predictor variables. The problem of the dependence among observations made on the same subject (repeated measurements) is addressed by assuming a first order Markovian dependence structure.

A closed-form expression for the individual and thus overall conditional marginal likelihood function is derived, which we can evaluate numerically to produce the maximum likelihood estimates for the unknown parameters. This method can be implemented using standard statistical software such as SAS Proc Nlmixed©. We present the results of simulation studies designed to show how the model’s ability to accurately estimate the parameters can be affected by the distributional form of the survival term.

Then we focus on addressing the problem by accommodating the residual life time of the subject’s confounding in the nonhomogeneous chain. The convergence status of the chain is examined and the formulation of the absorption statistics is derived. We propose using the Delta method to estimate the variance terms for construction of confidence intervals. The results are illustrated with applications to the Nun Study data in details.

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