Abstract
We extend the family of Poisson and negative binomial models to derive the joint distribution of clustered count outcomes with extra zeros. Two random effects models are formulated. The first model assumes a shared random effects term between the conditional probability of perfect zeros and the conditional mean of the imperfect state. The second formulation relaxes the shared random effects assumption by relating the conditional probability of perfect zeros and the conditional mean of the imperfect state to two different but correlated random effects variables. Under the conditional independence and the missing data at random assumption, a direct optimization of the marginal likelihood and an EM algorithm are proposed to fit the proposed models. Our proposed models are fitted to dental caries counts of children under the age of six in the city of Detroit.
Acknowledgements
This study was supported with funding from the National Institute on Dental and Craniofacial Research (NIDCR) grant # U-54 DE 14261-01, the Delta Dental Fund of Michigan, and the University of Michigan's Office of Vice President for Research. The authors thank the staff of the project for their diligence and commitment. Additional funding was provided by the NIDCR small grant mechanism #1R03 DE 016618.