Title page for ETD etd-07222010-123652


Type of Document Dissertation
Author Wang, Lu
Author's Email Address luwang@vt.edu
URN etd-07222010-123652
Title Cure Rate Model with Spline Estimated Components
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Pang Du Committee Chair
George R. Terrell Committee Co-Chair
Chuanhai Liu Committee Member
Eric P. Smith Committee Member
Scotland C. Leman Committee Member
Keywords
  • Nonparametric Function Estimation; Smoothing Splin
Date of Defense 2010-07-13
Availability unrestricted
Abstract
In some survival analysis of medical studies, there are often long term survivors who can be considered as permanently cured. The goals in these studies are to estimate the cure probability of the whole population and the hazard rate of the noncured subpopulation. The existing methods for cure rate models have been limited to parametric and semiparametric models. More specifically, the hazard function part is estimated by parametric or semiparametric model where the effect of covariate takes a parametric form. And the cure rate part is often estimated by a parametric logistic regression model. We introduce a non-parametric model employing smoothing splines. It provides non-parametric smooth estimates for both hazard function and cure rate. By introducing a latent cure status variable, we implement the method using a smooth EM algorithm. Louis’ formula for covariance estimation in an EM algorithm is generalized to yield point-wise confidence intervals for both functions. A simple model selection procedure based on the Kullback-Leibler geometry is derived for the proposed cure rate model. Numerical studies demonstrate excellent performance of the proposed method in estimation, inference and model selection. The application of the method is illustrated by the analysis of a melanoma study.
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