Abstract #300750


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JSM 2002 Abstract #300750
Activity Number: 108
Type: Contributed
Date/Time: Monday, August 12, 2002 : 10:30 AM to 12:20 PM
Sponsor: ENAR
Abstract - #300750
Title: Robust Inference for Proportional Hazards Frailty Regression Models
Author(s): Michael Kosorok*+ and Bee Leng Lee and Jason Fine
Affiliation(s): University of Wisconsin, Madison and National University of Singapore and University of Wisconsin, Madison
Address: K6/428 Clinical Science Center, 600 Highland Ave., Madison, Wisconsin, 53792, U.S.A.
Keywords: Survival Analysis ; Frailty ; Misspecification ; Empirical Process ; Semiparametric Efficiency ; Bootstrap
Abstract:

We consider a class of semiparametric regression models which are one parameter extensions of the Cox model for independent observations. These models assume that the hazard given the covariates, and a random frailty unique to each individual, have the proportional hazards form multiplied by the frailty. The frailty is assumed to be mean one within a known one-parameter family of distributions. Inference is based on a nonparametric likelihood. The behavior of the likelihood maximizer is studied under general conditions where the fitted model may be misspecified. The estimator is shown to be uniformly consistent for the pseudo-value maximizing the asymptotic limit of the likelihood. Appropriately standardized, the estimator converges weakly to a Gaussian process. When the model is correctly specified, the procedure is semiparametric efficient. It is also proved that the bootstrap gives valid inferences for all parameters, including the cumulative hazard, even under misspecification. We demonstrate, analytically, the importance of the robust inference in several examples. The practical utility of the procedure is illustrated on a non-Hodgkin's lymphoma dataset.


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