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John Stettler Dissertation.pdf (5.07 MB)

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The Discrete Threshold Regression Model

Stettler, John
http://rave.ohiolink.edu/etdc/view?acc_num=osu1440369876

Abstract Details

2015, Doctor of Philosophy, Ohio State University, Statistics.
Threshold regression (TR) models have recently become a popular tool for survival analysis. A number of different stochastic processes have been considered as the underlying latent process used to construct threshold regression models, the most popular being Brownian motion with drift and the Ornstein-Uhlenbeck process. TR models have a number of advantages over competing models such as proportional hazards regression. For example, TR models can have proportional or nonproportional hazards. The effects of covariates on the hazard are not required to be multiplicative. Also, because threshold regression models use a latent stochastic process to model an unobserved mechanism that leads individuals to events of interest, the interpretation of the parameters can be very intuitive and insightful. The TR models that have received the most attention are based on continuous latent models. Continuous models offer much flexibility in terms of drift and the ability to adjust the time scale. However, it is very difficult to incorporate time-varying covariates into a continuous model in a way that is natural and intuitive. This is not the case for TR models based on a latent discrete-time Markov chain. Discrete latent Markovian models have a different level of flexibility compared to continuous models. Because quantities like hazard rates, first hitting times, and survival probabilities are calculated by matrix multiplication, the process can be allowed to change over time by changing the transition probability matrix in accordance with changes in the covariates over time. This adds little to the computational burden. In this dissertation, a discrete threshold regression model is presented that is based on a discrete-state, discrete-time Markov chain. This model simplifies the incorporation of time-varying coefficients while retaining a good deal of flexibility in fitting hazard functions with various shapes, estimating event probabilities when there are two events that depend on the same underlying process, and estimating hitting time distributions for two events of interest.
Mario Peruggia (Advisor)
181 p.
Statistics
Threshold regression; Markov chain; time-varying covariates; discrete-state; discrete-time

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Citations

  • Stettler, J. (2015). The Discrete Threshold Regression Model [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1440369876

    APA Style (7th edition)

  • Stettler, John. The Discrete Threshold Regression Model. 2015. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1440369876.

    MLA Style (8th edition)

  • Stettler, John. "The Discrete Threshold Regression Model." Doctoral dissertation, Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1440369876

    Chicago Manual of Style (17th edition)

osu1440369876
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© 2015, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.