Marginal analysis of panel counts through estimating functions

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.