Multi-state models are often used to evaluate the effect of death as a competing event to the development of dementia in a longitudinal study of the cognitive status of elderly subjects. In this dissertation, both multi-state Markov model and semi-Markov model are used to characterize the flow of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient, cognitive states and death as a competing risk.
Firstly, a multi-state Markov model with three transient states: intact cognition, mild cognitive impairment (M.C.I.) and global impairment (G.I.) and one absorbing state: dementia is used to model the cognitive panel data. A Weibull model and a Cox proportional hazards (Cox PH) model are used to fit the time to death based on age at entry and the APOE4 status. A shared random effect correlates this survival time with the transition model.
Secondly, we further apply a Semi-Markov process in which we assume that the wait- ing times are Weibull distributed except for transitions from the baseline state, which are exponentially distributed and we assume no additional changes in cognition occur between two assessments. We implement a quasi-Monte Carlo (QMC) method to calculate the higher order integration needed for the likelihood based estimation.
At the end of this dissertation we extend a non-parametric “local EM algorithm” to obtain a smooth estimator of the cause-specific hazard function (CSH) in the presence of competing risk.
All the proposed methods are justified by simulation studies and applications to the Nun Study data, a longitudinal study of late life cognition in a cohort of 461 subjects.
| Identifer | oai:union.ndltd.org:uky.edu/oai:uknowledge.uky.edu:statistics_etds-1013 |
| Date | 01 January 2015 |
| Creators | Wei, Shaoceng |
| Publisher | UKnowledge |
| Source Sets | University of Kentucky |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Theses and Dissertations--Statistics |
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