Count Regression Modeling Applied to Caries Clinical Trial Data

In some child populations, caries experience and caries incidence have declined to an extent that statistical analysis based on assumptions of normality for continuous data are found to be incongruent with disease measures such as caries incidence. Early approaches to this problem relied on application of Poisson (PS) and Negative Binomial (NB) models. (Grainger and Reid, 1954; Hujoel et al, 1994). Recently, Böhning, Dietz and Schlattmann (1999) introduced Poisson count models for DMFT that incorporated accommodation for excess zeros. Objective: to investigate the application of PS, NB, zero-inflated Poisson (ZIP), and zero-inflated negative binomial (ZINB) models to incidence data from caries trials. Methods: the data were from a 3-year randomized caries trial involving 4,294 11-13 yr. olds to compare caries prevention efficacy of toothpastes containing NaF, Na+TMP, or SMFP at fluoride levels of 1000 and 1500 ppm F, (Stephens et al, 1995). The original study analyses used ANOVA. The current secondary analysis of 1-year decayed surfaces (DS) increment data applied PS, NB, ZIP, and ZINB models. Results: One, unlike ANOVA, all four count regression models ignore caries reversals (real or erroneous) which bears on the mean and variance estimates. A total of 15.8% of children had negative DS increments at the end of year 1; a further 49.5% had DS increments of zero. Two, PS models fit the DS increment data poorly, while NB, ZIP, and ZINB dramatically improved model fit. Three, even where model fit was good, ZINB models often did not converge, yielding unreliable parameter estimates. Conclusion: ZIP and ZINB models may be better suited for exploratory analyses than for assessing efficacy in a confirmatory clinical trial that requires a priori specification of the analysis plan.