Date of Award

Spring 5-2020

Degree Name

Doctor of Philosophy (PhD)



Second Advisor


Third Advisor



Longitudinal studies have been critical in understanding the characteristics of chronic diseases or interventions. Since many processes have natural multi-categorical responses over time, multi-state stochastic models have been used to estimate the transition rates between stages. Some multi-state models applied in practice assume the Markov property. The Markov property constrains the sojourn distribution to be exponentially distributed. While useful theoretical properties arise by the Markov assumption, we will consider a more flexible framework by allowing arbitrarily distributed waiting times. This describes a semi-Markov process which has already been applied to various fields in Public Health. Similar to Markov model developments, semi-Markov models have been extended to add covariate e↵ects on each transition intensity for better estimation. Statistical inference methods for semi-Markov chains are still being developed for unique problems for ecient estimation and computational feasibility. Particularly, in this dissertation, we have developed a partial likelihood based approach under a semi-Markov framework. First, we will consider estimating parameters for a three to four stage process by a partial likelihood approach and examining the sensitives of the transition intensity estimates with models that have a gamma or Weibull sojourn time. This approach will estimate the hazard rates between discrete stages. Secondly, we will extend the semiMarkov model to include covariate e↵ects on the transition rates and again, analyze its results with models assuming the gamma or Weibull sojourn time. Two applications will be considered to illustrate our method: A caregiver stress-level study from the Baylor’s Alzhemier’s Disease and Memory Disorders Center and a depression severity level study from the Hispanic Established Population for the Epidemiological Study of the Elderly (HEPESE).