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October, 1995 Semiparametric Analysis of General Additive-Multiplicative Hazard Models for Counting Processes
D. Y. Lin, Zhiliang Ying
Ann. Statist. 23(5): 1712-1734 (October, 1995). DOI: 10.1214/aos/1176324320


The additive-multiplicative hazard model specifies that the hazard function for the counting process associated with a multidimensional covariate process $Z = (W^T, X^T)^T$ takes the form of $\lambda(t\mid Z) = g\{\beta^T_0 W(t)\} + \lambda_0(t)h\{\gamma^T_0X(t)\}$, where $\theta_0 = (\beta^T_0, \gamma^T_0)^T$ is a vector of unknown regression parameters, $g$ and $h$ are known link functions and $\lambda_0$ is an unspecified "baseline hazard function." In this paper, we develop a class of simple estimating functions for $\theta_0$, which contains the partial likelihood score function in the special case of proportional hazards models. The resulting estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions. Weak convergence of the Aalen-Breslow type estimators for the cumulative baseline hazard function $\Lambda_0(t) = \int^t_0\lambda_0(u) du$ is also established. Furthermore, we construct adaptive estimators for $\theta_0$ and $\Lambda_0$ that achieve the (semiparametric) information bounds. Finally, a real example is provided along with some simulation results.


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D. Y. Lin. Zhiliang Ying. "Semiparametric Analysis of General Additive-Multiplicative Hazard Models for Counting Processes." Ann. Statist. 23 (5) 1712 - 1734, October, 1995.


Published: October, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0844.62082
MathSciNet: MR1370304
Digital Object Identifier: 10.1214/aos/1176324320

Primary: 62J99
Secondary: 62P10

Keywords: Aalen-Breslow estimator , adaptive estimation , Asymptotic efficiency , Censoring , Cox regression , Estimating equation , failure time , information bound , martingale , partial likelihood , proportional hazards , survival data , time-dependent covariate

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 5 • October, 1995
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