GEE-Type Inference for Clustered Zero-Inflated Negative Binomial Regression with Application to Dental Caries

• Activity Number: 645
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Maiying Kong*+ and Somnath Datta
• Companies: University of Louisville and University of Louisville
• Keywords: Zero-inflated models ; Generalized estimating equations ; Sandwich variance estimate ; Bootstrap

Abstract

Use of zero-inflated count data models is common in applications where the number of zero counts exceeds that predicted from a traditional count data model such as Poisson or negative binomial. When count data exhibiting inflated zero counts are correlated among subjects, a natural approach will be to fit a marginal model with the help of generalized estimating equations that can incorporate subject-to-subject correlations. An algorithmic approach to fitting such models, called expectation-solution, has been proposed in the literature. In this work, we successfully adapt the parameter estimation procedure to fit a zero-inflated negative binomial (ZINB) regression to clustered counts with excessive zeros. However, the corresponding sandwich variance estimator appears to underestimate the true variance. We explain the theoretical reasons for its failure and offer a correction under additional modeling assumptions. We then propose a clustered resampling (bootstrap) procedure to estimate the variance and show that it captures the correct variance under no additional model assumptions. Utility of this marginal ZINB model over two other competing models has been accessed using a thorough