Logistic Regression for Dichotomized Counts

• Activity Number: 321
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): John Preisser*+ and Kalyan Das and John Stamm
• Companies: The University of North Carolina and University of Calcutta and The University of North Carolina
• Keywords: dentistry ; excess zeros ; marginal effects ; odds ratio ; zero-altered Poisson ; zero inflation

Abstract

Sometimes there is interest in a dichotomized outcome indicating whether a count variable is positive versus the count is zero. Under such a scenario, ordinary logistic regression results in efficiency loss, which is quantifiable under an assumed count data model. To prevent efficiency loss, a marginalized zero-inflated Poisson model for logistic regression modeling (MZIP-logist) of overall effects is introduced. Developed in a product zero-inflated Poisson distribution framework, the primary model part is a logistic regression for modeling the occurrence of a positive count, or, equivalently, the probability of a zero count irrespective of its source. The secondary part consists of an ancillary model for the mean of the `susceptible' population, the latter which is retained in the likelihood function from the standard ZIP model. An analogous modeling approach using hurdle models is also investigated. The proposed models, including shared-parameter versions of them, are applied to data from a clinical trial conducted in 1988-1992 in Scotland comparing toothpaste formulations for the presence of incident dental caries in children.