Marginal analysis of panel counts through estimating functions

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 pro...

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Bibliographic Details
Published in:Biometrika 2009-06, Vol.96 (2), p.445-456
Main Authors: HU, X. JOAN, LAGAKOS, STEPHEN W., LOCKHART, RICHARD A.
Format: Article
Language:English
Subjects:
Actuarial science
Algorithms
Analytical estimating
Applications
Biology, psychology, social sciences
Censorship
Consistent estimators
Counting process
Distribution theory
Estimators
Exact sciences and technology
General topics
Interval censoring
Interval estimators
Marginal analysis
Marginal mean function
Mathematical functions
Mathematics
Maximum likelihood estimation
Maximum likelihood estimators
Nonparametric estimation
Nonparametric inference
Placebos
Poisson process
Probability and statistics
Quasi-score function
Sciences and techniques of general use
Statistics
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Summary: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.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/asp010