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Flexible Modeling Method Based on Bayesian Regression Using Multivariate Piecewise Linear Splines

Huang, Rui
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1721398235655928

Abstract Details

2024, PhD, University of Cincinnati, Arts and Sciences: Statistics.
In this dissertation, we develop a flexible methodology using a multivariate piecewise linear spline (MPLS) regression model to address challenges in large clinical trials and observational studies. Our approach is characterized by several key contributions. Firstly, we introduce a novel method to model heteroscedastic data, ensuring robust estimation of the mean regression surface E(Y|X), and demonstrating strong predictive performance using piecewise basis functions. Secondly, our methodology is tailored to causal inference settings, where we incorporate treatment effects into our model and employ a Markov chain Monte Carlo method for simultaneous estimation of both mean and treatment surfaces. Thirdly, we extend our model to accommodate multivariate outcomes, enhancing its applicability to complex clinical studies where multiple endpoints are of interest. Lastly, to address the challenge of censored data, particularly in survival analysis, we integrate the truncated normal method with our spline model under a log-normal regression framework. This approach enables accurate estimation in the presence of truncated outcomes, enhancing the model's applicability to studies where survival data is critical. By comparing our model fitting with the BART method, we demonstrate the flexibility and accuracy of our approach using both simulated data and real data obtained from a secondary data core. This methodology provides valuable insights for examining treatment outcomes and heterogeneity in response across diverse patient populations, thereby contributing significantly to the field of medical research.
Siva Sivaganesan, Ph.D. (Committee Chair)
Emily Kang, Ph.D. (Committee Member)
Bin Huang, Ph.D. (Committee Member)
Hang Joon Kim, Ph.D. (Committee Member)
Seongho Song, Ph.D. (Committee Member)
114 p.
Statistics

Recommended Citations

Citations

  • Huang, R. (2024). Flexible Modeling Method Based on Bayesian Regression Using Multivariate Piecewise Linear Splines [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1721398235655928

    APA Style (7th edition)

  • Huang, Rui. Flexible Modeling Method Based on Bayesian Regression Using Multivariate Piecewise Linear Splines. 2024. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1721398235655928.

    MLA Style (8th edition)

  • Huang, Rui. "Flexible Modeling Method Based on Bayesian Regression Using Multivariate Piecewise Linear Splines." Doctoral dissertation, University of Cincinnati, 2024. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1721398235655928

    Chicago Manual of Style (17th edition)

ucin1721398235655928
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© 2024, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.