Semiparamertic dimension reduction model and applications
Open Access
- Author:
- Zhao, Ge
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 07, 2019
- Committee Members:
- Yanyuan Ma, Dissertation Advisor/Co-Advisor
Yanyuan Ma, Committee Chair/Co-Chair
Michael G Akritas, Committee Member
Bing Li, Committee Member
James Z Wang, Outside Member - Keywords:
- Survival Analysis
Sufficient Dimension Reduction
Semiparametric
Nonparametric - Abstract:
- In the robust nonparametric kernel regression context, we prescribe a data driven method to select the trimming parameter and the bandwidth robustly. The estimator is obtained through solving estimating equations, and it controls the effect from outlying observations through a combination of weighting and trimming. We show asymptotic consistency, establish the estimation bias, variance properties and derive the asymptotic distribution of the resulting estimator. The finite sample performance of the estimator is illustrated through both simulation studies and analysis on a problem related to wind power generation, which motivated this study at the first place. We propose a general index model for survival data, which generalizes many commonly used semiparametric survival models and belongs to the framework of dimension reduction. Using a combination of geometric approach in semiparametrics and martingale treatment in survival data analysis, we devise estimation procedures that are feasible and do not require covariate-independent censoring as assumed in many dimension reduction methods for censored survival data. We establish the root-$n$ consistency and asymptotic normality of the proposed estimators and derive the most efficient estimator in this class for the general index model. Numerical experiments are carried out to demonstrate the empirical performance of the proposed estimators and an application to an AIDS data further illustrates the usefulness of the work. Kidney transplantation is the most effective renal replacement therapy for renal failure patients. With the severe shortage of kidney supplies and for the clinical effectiveness of transplantation, it would be crucial to design objective measures, such as the Estimated Post-Transplant Survival (EPTS) score, to quantify the benefit that a renal failure patient would gain from a potential transplantation by comparing the expected residual lives of the same patient with and without transplant. However, in the current EPTS system, the most dominant predictors are severe comorbidity conditions (such as diabetes) and age, which might preclude old and sick patients for receiving transplants. To help design a more fair score system, we propose a flexible and general covariate-dependent mean residual life model to estimate EPTS. Our method is both efficient and robust as the covariate effect is estimated via a semiparametrically efficient estimator, while the mean residual life function is estimated nonparametrically. We further provide a formula to predict the residual life increment potential for any given patients. Our method would facilitate allocating kidneys to patients who would have the largest residual life increment among all the eligibles. Our analysis of the kidney transplant data from the U.S. Scientific Registry of Transplant Recipients indicated that the most important predictor is the waiting time for transplantation: a shorter waiting time may lead to larger potential gains. We also identified an index which could serve as an additional important predictor if the waiting time is approximately between 1.5 years and three years. As our framework is general, we envision that our analytical strategies can be adopted to other organ transplantation settings.