Marginalized zero-inflated Poisson models with missing covariates.

Unlike zero-inflated Poisson regression, marginalized zero-inflated Poisson (MZIP) models for counts with excess zeros provide estimates with direct interpretations for the overall effects of covariates on the marginal mean. In the presence of missing covariates, MZIP and many other count data models are ordinarily fitted using complete case analysis methods due to lack of appropriate statistical methods and software. This article presents an estimation method for MZIP models with missing covariates. The method, which is applicable to other missing data problems, is illustrated and compared with complete case analysis by using simulations and dental data on the caries preventive effects of a school-based fluoride mouthrinse program.

Marginalized mixture models for count data from multiple source populations.

Mixture distributions provide flexibility in modeling data collected from populations having unexplained heterogeneity. While interpretations of regression parameters from traditional finite mixture models are specific to unobserved subpopulations or latent classes, investigators are often interested in making inferences about the marginal mean of a count variable in the overall population. Recently, marginal mean regression modeling procedures for zero-inflated count outcomes have been introduced within the framework of maximum likelihood estimation of zero-inflated Poisson and negative binomial regression models. In this article, we propose marginalized mixture regression models based on two-component mixtures of non-degenerate count data distributions that provide directly interpretable estimates of exposure effects on the overall population mean of a count outcome. The models are examined using simulations and applied to two datasets, one from a double-blind dental caries incidence trial, and the other from a horticultural experiment. The finite sample performance of the proposed models are compared with each other and with marginalized zero-inflated count models, as well as ordinary Poisson and negative binomial regression.

Modelling changes in clinical attachment loss to classify periodontal disease progression.

AIM: The goal of this study was to identify progressing periodontal sites by applying linear mixed models (LMM) to longitudinal measurements of clinical attachment loss (CAL). METHODS: Ninety-three periodontally healthy and 236 periodontitis subjects had their CAL measured bi-monthly for 12 months. The proportions of sites demonstrating increases in CAL from baseline above specified thresholds were calculated for each visit. The proportions of sites reversing from the progressing state were also computed. LMM were fitted for each tooth site and the predicted CAL levels used to categorize sites regarding progression or regression. The threshold for progression was established based on the model-estimated error in predictions. RESULTS: Over 12 months, 21.2%, 2.8% and 0.3% of sites progressed, according to thresholds of 1, 2 and 3 mm of CAL increase. However, on average, 42.0%, 64.4% and 77.7% of progressing sites for the different thresholds reversed in subsequent visits. Conversely, 97.1%, 76.9% and 23.1% of sites classified as progressing using LMM had observed CAL increases above 1, 2 and 3 mm after 12 months, whereas mean rates of reversal were 10.6%, 30.2% and 53.0% respectively. CONCLUSION: LMM accounted for several sources of error in longitudinal CAL measurement, providing an improved method for classifying progressing sites.