Type of Document Dissertation Author Ye, Gang Author's Email Address firstname.lastname@example.org 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 AbstractA 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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