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Regression Modeling of Time to Event Data Using the Ornstein-Uhlenbeck Process

Erich, Roger Alan
http://rave.ohiolink.edu/etdc/view?acc_num=osu1342796812

Abstract Details

2012, Doctor of Philosophy, Ohio State University, Biostatistics.
In this research, we develop innovative regression models for survival analysis that model time to event data using a latent health process which stabilizes around an equilibrium point; a characteristic often observed in biological systems. Regression modeling in survival analysis is typically accomplished using Cox regression, which requires the assumption of proportional hazards. An alternative model, which does not require proportional hazards, is the First Hitting Time (FHT) model where a subject's health is modeled using a latent stochastic process. In this modeling framework, an event occurs once the process hits a predetermined boundary. The parameters of the process are related to covariates through generalized link functions thereby providing regression coefficients with clinically meaningful interpretations. In this dissertation, we present an FHT model based on the Ornstein-Uhlenbeck (OU) process; a modified Wiener process which drifts from the starting value of the process toward a state of equilibrium or homeostasis present in many biological applications. We extend previous OU process models to allow the process to change according to covariate values. We also discuss extensions of our methodology to include random effects accounting for unmeasured covariates. In addition, we present a mixture model with a cure rate using the OU process to model the latent health status of those subjects susceptible to experiencing the event under study. We apply these methods to survival data collected on melanoma patients and to another survival data set pertaining to carcinoma of the oropharynx.
Michael Pennell, PhD (Advisor)
Thomas Santner, PhD (Committee Member)
Dennis Pearl, PhD (Committee Member)
142 p.
Biostatistics; Statistics
cancer clinical trial; cure rate model; first hitting time model; Gaussian process; mixture model; nonproportional hazards, survival analysis, Ornstein-Uhlenbeck process; random effects model

Recommended Citations

Citations

  • Erich, R. A. (2012). Regression Modeling of Time to Event Data Using the Ornstein-Uhlenbeck Process [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1342796812

    APA Style (7th edition)

  • Erich, Roger. Regression Modeling of Time to Event Data Using the Ornstein-Uhlenbeck Process. 2012. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1342796812.

    MLA Style (8th edition)

  • Erich, Roger. "Regression Modeling of Time to Event Data Using the Ornstein-Uhlenbeck Process." Doctoral dissertation, Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1342796812

    Chicago Manual of Style (17th edition)

osu1342796812
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© 2012, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.