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October 2007 Two likelihood-based semiparametric estimation methods for panel count data with covariates
Jon A. Wellner, Ying Zhang
Ann. Statist. 35(5): 2106-2142 (October 2007). DOI: 10.1214/009053607000000181

Abstract

We consider estimation in a particular semiparametric regression model for the mean of a counting process with “panel count” data. The basic model assumption is that the conditional mean function of the counting process is of the form E{ℕ(t)|Z}=exp(β0TZ0(t) where Z is a vector of covariates and Λ0 is the baseline mean function. The “panel count” observation scheme involves observation of the counting process ℕ for an individual at a random number K of random time points; both the number and the locations of these time points may differ across individuals.

We study semiparametric maximum pseudo-likelihood and maximum likelihood estimators of the unknown parameters (β0, Λ0) derived on the basis of a nonhomogeneous Poisson process assumption. The pseudo-likelihood estimator is fairly easy to compute, while the maximum likelihood estimator poses more challenges from the computational perspective. We study asymptotic properties of both estimators assuming that the proportional mean model holds, but dropping the Poisson process assumption used to derive the estimators. In particular we establish asymptotic normality for the estimators of the regression parameter β0 under appropriate hypotheses. The results show that our estimation procedures are robust in the sense that the estimators converge to the truth regardless of the underlying counting process.

Citation

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Jon A. Wellner. Ying Zhang. "Two likelihood-based semiparametric estimation methods for panel count data with covariates." Ann. Statist. 35 (5) 2106 - 2142, October 2007. https://doi.org/10.1214/009053607000000181

Information

Published: October 2007
First available in Project Euclid: 7 November 2007

zbMATH: 1126.62084
MathSciNet: MR2363965
Digital Object Identifier: 10.1214/009053607000000181

Subjects:
Primary: 60F05, 60F17
Secondary: 60J65, 60J70

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 5 • October 2007
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