GEE type inference for clustered zero-inflated negative binomial regression with application to dental caries

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Modeling

Background:

• Count data with excessive zeros are common in various fields.
• Traditional models like Poisson or negative binomial may not adequately handle inflated zero counts.
• Correlated count data with excess zeros require specialized modeling approaches.

Purpose of the Study:

• To propose a marginal generalized estimating equation (GEE) based zero-inflated negative binomial (ZINB) model for clustered count data with excessive zeros.
• To address the underestimation issue of the sandwich variance estimator in GEE-based ZINB models.
• To introduce and validate a clustered resampling (bootstrap) procedure for accurate variance estimation.

Main Methods:

• Development of a GEE-based ZINB model for clustered, zero-inflated count data.
• Theoretical analysis of the sandwich variance estimator's failure.
• Proposal and evaluation of a clustered bootstrap procedure for variance estimation.
• Simulation studies to compare the proposed model with competing methods.
• Application to real-world data from the Iowa Fluoride Study.

Main Results:

• The standard sandwich variance estimator in GEE-based ZINB models underestimates true variance.
• A correction for the sandwich variance is proposed under specific modeling assumptions.
• The clustered bootstrap procedure provides accurate variance estimates without additional assumptions.
• The proposed GEE-based ZINB model demonstrates utility over competing models in simulations.
• Significant risk factors for dental caries associated with fluoride exposure were identified.

Conclusions:

• The GEE-based ZINB model with bootstrap variance estimation is a reliable tool for analyzing correlated, zero-inflated count data.
• The bootstrap procedure offers a robust alternative for variance estimation when traditional methods fail.
• The model successfully identified key risk factors in the association between dental caries and fluoride exposure.