Modeling Clustered Count Data with Excess Zeros in Health Care Outcomes Research

In health research, count outcomes are fairly common and often these counts have a large number of zeros. In order to adjust for these extra zero counts, various modifications of the Poisson regression model have been proposed. Lambert (Lambert, D., Technometrics 34, 1-14, 1992) described a zero-inflated Poisson (ZIP) model that is based on a mixture of a binary distribution (πi ) degenerated at zero with a Poisson distribution (λi ). Depending on the relationship between πi and λi , she described two variants: a ZIP and a ZIP (τ ) model. In this paper, we extend these models for the case of clustered data (e.g., patients observed within hospitals) and describe random-effects ZIP and ZIP (τ ) models. These models are appropriate for the analysis of clustered extra-zero Poisson count data. The distribution of the random effects is assumed to be normal and a maximum marginal likelihood estimation method is used to estimate the model parameters. We applied these models to data from patients who underwent colon operations from 123 Veterans Affairs Medical Centers in the National VA Surgical Quality Improvement Program.