Date of Award
Summer 2025
Document Type
Open Access Dissertation
Department
Statistics
First Advisor
Lianming Wang
Second Advisor
Joshua M. Tebbs
Abstract
This dissertation explores novel and efficient estimation methods for regression analyses of complex survival data, aiming to identify significant risk factors, estimate their effects on survival time, and examine survival patterns. The study focuses on (1) regression analysis of arbitrarily censored survival data, (2) regression analysis of group-tested current status data, and (3) regression analysis of group-tested current status data with retesting.
Chapter 2 explores regression analysis of arbitrarily censored data with the semiparametric Probit model. A sieve maximum likelihood approach is proposed with the unknown baseline function being approximated by monotone splines, and the implementation is carried out by a direct constrained optimization since there are only a finite number of parameters involved. The optimal number of knots and degree are chosen based on the Akaike Information Criteria. The proposed method also provides valid inference under the proportional odds model based on the resulting estimates from the probit model with slight modifications.
Chapter 3 investigates group-tested current status data, arising in disease screening studies with cost-effective group testing strategies. Focusing on the test results of master pools with imperfect tests, we develop two novel estimation approaches, from both frequentist’s and Bayesian perspectives, under a semiparametric Probit model. Both approaches have a good estimation performance in a simulation study and are illustrated by an application to chlamydia data from the Infertility Prevention Project.
Chapter 4 extends the work in Chapter 3 by studying group-tested current status data from studies with any group testing strategies. The proposed method is developed to incorporate both master pool results and individual testing results, allow any group testing strategies including master pooling, Dorfman’s testing, and array testing, and accommodate imperfect tests. Our approach is computationally efficient based on a Gibbs sampler, which allows to sample all unknowns easily from known distributions. The proposed approach has excellent estimation performance in an intensive simulation study and is applied to chlamydia data from the State Hygienic Laboratory at the University of Iowa.
Chapter 5 discusses regression analysis of bivariate group-tested current status data arising in group testing studies. The research goal is to model two correlated onset times of sexually transmitted infections, chlamydia and gonorrhea, and assess the covariate effects on these two onset times. A Bayesian estimation approach is developed based on a semiparametric frailty model. The proposed method also allows for potential test imperfections. Discussion of continued research effort is provided for completion.
Rights
© 2025, Jihyun Kim
Recommended Citation
Kim, J.(2025). Regression Analysis of Arbitrarily Censored Data and Group-Tested Current Status Data. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/8448