Statistical Contributions to Order Restricted Inference for Survival Data Analysis Public Deposited

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  • March 20, 2019
Creator
  • Chung, Yunro
    • Affiliation: Gillings School of Global Public Health, Department of Biostatistics
Abstract
  • This dissertation aims to study order restricted inference for survival data analysis where a hazard function is assumed to have a shape restriction with respect to continuous covariates. In the first chapter, we consider estimation of the semiparametric proportional hazards model with a completely unspecified baseline hazard function where the effect of a continuous covariate is assumed isotonic (or monotone) but otherwise unspecified. The pseudo iterative convex minorant algorithm is proposed to compute the isotonic estimator by optimizing a sequence of pseudo partial likelihood functions. A local consistency is established for a one-step update of the estimator when an initial value is in a shrinking neighborhood of the true value. Analysis of data from a recent HIV prevention study illustrates the practical utility of the methodology in estimating monotonic covariate effects that are nonlinear. In the second chapter, we consider additive hazards model with a unimodal hazard function in a continuous covariate with unknown mode. A quadratic loss function is defined, which allows efficient computations to estimate the mode and unimodal covariate effects. The methodology is applied to analyze the data from a recent randomized clinical trial of cardiovascular disease in kidney transplant patients. In the third chapter, we focus on multiple continuous covariates for a shape restricted hazard function. By assuming an additive isotonic structure of the multiple covariates under the proportional hazards model, the hazard function is defined as isotonic with respect to the partial order on the covariates. An efficient computation is proposed by combining the pseudo iterative convex minorant algorithm and the cycling algorithm. We use the proposed method to analyze the data from a recent clinical trial with cardiovascular outcome.
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Rights statement
  • In Copyright
Advisor
  • Peddada, Shyamal Das
  • Fine, Jason
  • Hudgens, Michael
  • Richardson, David
  • Ivanova, Anastasia
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2016
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