Type of Document	Dissertation
Author	Ye, Gang
Author's Email Address	ye@stat.fsu.edu
URN	etd-03012005-181420
Title	Inference for Semiparametric Time-Varying Covariate Effect Relative Risk Regression Models
Degree	Doctor of Philosophy
Department	Statistics, Department of
Advisory Committee	Advisor Name Title Ian W. McKeague Committee Chair Fred W. Huffer Committee Member Kai-Sheng Song Committee Member Xiaoming Wang Committee Member
Keywords	Time-varying Hazard Function Regression Model Counting Process Method Cox Model
Date of Defense	2004-12-03
Availability	unrestricted
Abstract A major interest of survival analysis is to assess covariate effects on survival via appropriate conditional hazard function regression models. The Cox proportional hazards model, which assumes an exponential form for the relative risk, has been a popular choice. However, other regression forms such as Aalen¡¯s additive risk model may be more appropriate in some applications. In addition, covariate effects may depend on time, which can not be reflected by a Cox proportional hazards model. In this dissertation, we study a class of time-varying covariate effect regression models in which the link function (relative risk function) is a twice continuously differentiable and prespecified, but otherwise general given function. This is a natural extension of the Prentice¨CSelf model, in which the link function is general but covariate effects are modelled to be time invariant. In the first part of the dissertation, we focus on estimating the cumulative or integrated covariate effects. The standard martingale approach based on counting processes is utilized to derive a likelihood-based iterating equation. An estimator for the cumulative covariate effect that is generated from the iterating equation is shown to be ¡Ìn-consistent. Asymptotic normality of the estimator is also demonstrated. Another aspect of the dissertation is to investigate a new test for the above time-varying covariate effect regression model and study consistency of the test based on martingale residuals. For Aalen¡¯s additive risk model, we introduce a test statistic based on the Huffer¨CMcKeague weighted-least-squares estimator and show its consistency against some alternatives. An alternative way to construct a test statistic based on Bayesian Bootstrap simulation is introduced. An application to real lifetime data will be presented.
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