Date of Award
Open Access Dissertation
Survival analysis is a branch of statistics to analyze the time-to-event data or survival data. One important feature of survival data is censoring, which means that not all the subjects’ survival time are observed directly. Among all the survival data, right-censored data are the most common type and consist of some exactly observed survival times and some right-censored observations. In this dissertation, we focus on studying flexible regression models for complicated right-censored survival data when the classical proportional hazards (PH) assumption is not satisfied. Flexible semiparametric regression models can largely avoid misspecification of parametric distributions and thus provide more modeling flexibility.
Cure models are studied in this dissertation to analyze survival data, for which there is a cured group in the study population and this is evidenced by a level-off at the end of the nonparametric survival estimate. In addition, we also incorporate background mortality in the cure models to improve estimation accuracy in this research. Considering the background mortality is important based on the fact that patients dying from other causes also benefit from the treatment of the disease of interest as shown in the SEER cancer studies. In Chapter 2, a semiparametric estimation approach is proposed based on EM algorithm under the mixture cure proportional hazards model with background mortality (MCPH+BM). In Chapter 3, a promotion time cure proportional hazards model with background mortality (PTPH+BM) is proposed, and its extension to the semiparametric transformation model is under further exploration. Both models are validated via comprehensive simulation studies and real data analysis.
Another perspective on non-proportional hazards is to explore a more general model than the Cox PH model such as the generalized odds-rate (GOR) models (Dabrowska and Doksum, 1988). In Chapter 4, the identifiability problems and the estimation of parameters in the GOR models are discussed.
Gu, E.(2020). Flexible Regression Models for Survival Data. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/5833