JSM 2005 Online Program

Abstract #302953

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Activity Number:	447
Type:	Contributed
Date/Time:	Wednesday, August 10, 2005 : 2:00 PM to 3:50 PM
Sponsor:	General Methodology
Abstract - #302953
Title:	Regression Analysis of Mean Lifetime: Exploring Nonlinear Relationship with Heteroscedasticity
Author(s):	Linda Sun*+ and Wenxin Jiang
Companies:	Northwestern University and Northwestern University
Address:	820 Noyes st, Evanston, IL, 60201, United States
Keywords:	Accelerated failure time model ; Asymptotic normality ; Heteroscedasticity ; Kaplan-Meier estimate ; Mixtures of experts ; Nonlinear regression
Abstract:	As a generalization of the accelerated failure time models, we consider parametric models of lifetime $Y$, where the conditional mean $E(Y\|X;\beta)$ can depend nonlinearly on the covariates $X$ and some parameters $\beta$. The error distribution can be heteroscedastic and dependent on $X$. With observed data subject to right censoring, we propose regression analysis for $\beta$ based on Kaplan-Meier estimates of the means over several regions of $X$. Consistency and asymptotic distributional properties of the estimators are established under general conditions. A resulting estimator of $\gb$ is shown to be the sum of two possibly dependent asymptotic normal quantities based on which conservative confidence intervals and tests are derived. A simulation study is conducted to investigate the performance of the proposed method. To illustrate the methodology, we study an example with kidney transplant data where a nonlinear relationship called "mixtures-of-experts," proposed in the neural networks literature, is used to model the relationship between the survival time and the age of the patients.

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