A Bayesian approach for analyzing zero-inflated clustered count data with dispersion

Stat Med. 2018 Feb 28;37(5):801-812. doi: 10.1002/sim.7541. Epub 2017 Nov 6.

Abstract

In practice, count data may exhibit varying dispersion patterns and excessive zero values; additionally, they may appear in groups or clusters sharing a common source of variation. We present a novel Bayesian approach for analyzing such data. To model these features, we combine the Conway-Maxwell-Poisson distribution, which allows both overdispersion and underdispersion, with a hurdle component for the zeros and random effects for clustering. We propose an efficient Markov chain Monte Carlo sampling scheme to obtain posterior inference from our model. Through simulation studies, we compare our hurdle Conway-Maxwell-Poisson model with a hurdle Poisson model to demonstrate the effectiveness of our Conway-Maxwell-Poisson approach. Furthermore, we apply our model to analyze an illustrative dataset containing information on the number and types of carious lesions on each tooth in a population of 9-year-olds from the Iowa Fluoride Study, which is an ongoing longitudinal study on a cohort of Iowa children that began in 1991.

Keywords: Bayesian modeling; Conway-Maxwell-Poisson distribution; clustering; count data; zero inflation.

Publication types

  • Research Support, N.I.H., Extramural

MeSH terms

  • Bayes Theorem*
  • Child
  • Cluster Analysis*
  • Computer Simulation
  • Data Interpretation, Statistical
  • Dental Caries / prevention & control
  • Fluorides / therapeutic use
  • Humans
  • Iowa
  • Longitudinal Studies
  • Markov Chains
  • Monte Carlo Method
  • Poisson Distribution*

Substances

  • Fluorides