Estimation of Baseline Hazard with Time-Dependent Covariates

• Activity Number: 116
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2003 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Feng Gao*+
• Companies: Emory University
• Keywords: survival data ; CART ; baseline hazard

Abstract

Often, in many biomedical and epidemiologic studies, estimating hazard function is of interest. The Breslow's estimator (1974) is commonly used for estimating the integrated baseline hazard but this estimator requires the functional form of covariate effects to be correctly specified. It is generally difficult to identify the true functional form of covariate effects from data, particularly in the presence of time-dependent covariates. A tree-type model is proposed which enables simultaneously estimating both baseline hazard function and the effects of time-dependent covariates. The proposed method approximates the baseline hazard and covariate effects with step-functions. The jump points in time and in covariate space are searched via an algorithm based on the improvement of a full log-likelihood function. Since the determination of these jump points is totally data driven, the proposed method in principle takes a nonparametric approach. In contrast to most other estimating methods, the proposed method estimates the hazard function rather than integrated hazard. The performance of the proposed method is evaluated by several simulation studies.