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Stochastic modeling of the sleep process

Gibellato, Marilisa Gail
http://rave.ohiolink.edu/etdc/view?acc_num=osu1110318321

Abstract Details

2005, Doctor of Philosophy, Ohio State University, Biostatistics.
The structure of sleep varies with perturbing factors such as age, pathological processes, and pharmacological agents. This can be appreciated by simple observation of the sleep patterns of individuals and electroencephalogram data. Statistical models have been proposed to track these changes, but there remains a need for a comprehensive and informative description of the sleep process. In this dissertation, I describe the sleep process in two manners using data collected from groups of younger (20-25 years of age) and older (70-79 years of age) subjects. The first model of sleep is comprised of the two stages “sleep” and “wake”. I model the times spent asleep between wakeful periods as independent observations from a generalized gamma distribution (GGD) using a maximum likelihood estimation (MLE) procedure and justify usage of a reparameterization of the GGD and the observed information to estimate the variance of the MLE’s. I next develop strategies for estimating and comparing underlying demographic group mean GGD parameters. The resulting analysis detects differences in the parameters of age and gender groups that serve as impetus to develop a “Sleep Index” based on the mean of the GGD fit to the data. The successive times of wakefulness are found to have a first order dependence structure. Although distributional fitting is limited due to censoring, I fit a GGD to the wake times greater than 2.5 minutes combined across all subjects. The wake and sleep processes are found to be independent of one another. The second model is a semi-Markov process including sleep stages 1, 2, 3, 4, wakefulness, and rapid eye movement (REM) sleep. The embedded Markov chains (MC) are characterized and shown to be non-stationary across a subject's night of sleep. I then compare the embedded MC's for the various age and gender groups across nights using general linear models to detect differences in transition probabilities. This investigation provides a comprehensive picture of the sleep process from two perspectives and yields concrete information that can be used in clinical applications. These characterizations will likely produce other meaningful measures of sleep process perturbation.
Haikady Nagaraja (Advisor)
188 p.
Statistics
Sleep and aging; Generalized Gamma Distribution; Maximum likelihood estimation; Semi-Markov process

Recommended Citations

Citations

  • Gibellato, M. G. (2005). Stochastic modeling of the sleep process [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1110318321

    APA Style (7th edition)

  • Gibellato, Marilisa. Stochastic modeling of the sleep process. 2005. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1110318321.

    MLA Style (8th edition)

  • Gibellato, Marilisa. "Stochastic modeling of the sleep process." Doctoral dissertation, Ohio State University, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=osu1110318321

    Chicago Manual of Style (17th edition)

osu1110318321
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© 2005, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.