Generalized estimating equation based zero-inflated models with application to examining the relationship between dental caries and fluoride exposures.

Abstract

In the study of dental caries, the number of caries is frequently characterized by over-dispersion and excessive zeros. In addition, the numbers of caries from the same subject are correlated. Zero-Inflated (ZI) regression models, such as ZI-Poisson (ZIP), ZI-Negative Binomial (ZINB), have been developed to account for the excessive zeros in count data. However, the existing zero-inflated models assume that the counts are uncorrelated. On the other hand, Generalized Estimating Equations (GEE) have been developed in the literature to estimate the parameters while accounting for the correlations of observations from the same subject. However, the GEE models incorporating excessive zero counts are not widely available. In this paper, we developed GEE based zero inflated negative binomial model (GEE.ZINB) which account for over-dispersion, excessive zeroes as well as the correlations among the observations from the same subject. We have applied GEE.ZINB, the independent ZINB, and GEE without zero inflation models to examining the association between the dental caries and fluoride exposures using the Iowa fluoride study. We have carried out extensive simulations to examine and compare the performances of the three different methods.