Biometrika Advance Access originally published online on April 24, 2009
Biometrika 2009 96(2):445-456; doi:10.1093/biomet/asp010
Article |
Marginal analysis of panel counts through estimating functions
Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada V5A 1S6 joanh{at}stat.sfu.ca
Department of Biostatistics, Harvard School of Public Health, 655 Huntington Avenue, Boston, Massachusetts 02115, U.S.A. lagakos{at}biostat.harvard.edu
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.
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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