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The zero‐inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology
Author(s) -
Böhning D.,
Dietz E.,
Schlattmann P.,
Mendonça L.,
Kirchner U.
Publication year - 1999
Publication title -
journal of the royal statistical society: series a (statistics in society)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.103
H-Index - 84
eISSN - 1467-985X
pISSN - 0964-1998
DOI - 10.1111/1467-985x.00130
Subject(s) - poisson regression , poisson distribution , statistics , covariate , count data , zero inflated model , mathematics , regression analysis , epidemiology , regression , dentistry , econometrics , medicine , environmental health , population
For frequency counts, the situation of extra zeros often arises in biomedical applications. This is demonstrated with count data from a dental epidemiological study in Belo Horizonte (the Belo Horizonte caries prevention study) which evaluated various programmes for reducing caries. Extra zeros, however, violate the variance–mean relationship of the Poisson error structure. This extra‐Poisson variation can easily be explained by a special mixture model, the zero‐inflated Poisson (ZIP) model. On the basis of the ZIP model, a graphical device is presented which not only summarizes the mixing distribution but also provides visual information about the overall mean. This device can be exploited to evaluate and compare various groups. Ways are discussed to include covariates and to develop an extension of the conventional Poisson regression. Finally, a method to evaluate intervention effects on the basis of the ZIP regression model is described and applied to the data of the Belo Horizonte caries prevention study.