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Biometrika Advance Access originally published online on April 24, 2009
Biometrika 2009 96(2):445-456; doi:10.1093/biomet/asp010
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© 2009 Biometrika Trust

Article

Marginal analysis of panel counts through estimating functions

X. Joan Hu

Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada V5A 1S6 joanh{at}stat.sfu.ca

Stephen W. Lagakos

Department of Biostatistics, Harvard School of Public Health, 655 Huntington Avenue, Boston, Massachusetts 02115, U.S.A. lagakos{at}biostat.harvard.edu

Richard A. Lockhart

Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada V5A 1S6 lockhart{at}stat.sfu.ca

Received for publication 1 April 2007. Revision received 1 August 2008.
  Abstract

We develop nonparametric estimation procedures for the marginal mean function of a counting process based on periodic observations, using two types of self-consistent estimating equations. The first is derived from the likelihood studied by Wellner & Zhang (2000), assuming a Poisson counting process. It gives a nondecreasing estimator, which equals the nonparametric maximum likelihood estimator of Wellner & Zhang and is consistent without the Poisson assumption. Motivated by the construction of parametric generalized estimating equations, the second type is a set of data-adaptive quasi-score functions, which are likelihood estimating functions under a mixed-Poisson assumption. We evaluate the procedures using simulation, and illustrate them with the data from a bladder cancer study.

Key Words: Counting process • Interval censoring • Marginal mean function • Nonparametric estimation • Quasi-score function


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