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Biometrika. 2009;96(2):445-456.

Marginal analysis of panel counts through estimating functions.

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Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia V5A 1S6, Canada,


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 in Wellner & Zhang (2000), assuming a Poisson counting process, and gives a nondecreasing estimator, which is the same as the nonparametric maximum likelihood estimator of Wellner & Zhang and thus 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 via simulation, and illustrate them with the data from a bladder cancer study.

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