Supplementary Material for: Discrete Distribution Based on Compound Sum to Model Dental Caries Count Data

Methods for analysing dental caries and associated risk indicators
have evolved considerably in recent decades. The use of zero-inflated or
hurdle models is increasing so as to take account of the decayed,
missing, and filled teeth (DMFT) distribution, which is positively
skewed and has a high proportion of zero scores. However, there is a
need to develop new statistical models that involve pragmatic biological
considerations on dental caries in epidemiological surveys. In this
paper, we show that the zero-inflated and the hurdle models can both be
expressed as a compound sum. Using the same compound sum, we then
present the generalized negative binomial (GNB) distribution for dental
caries count data, and provide a numerical application using the data of
the EPIPAP study. The GNB model generates the best score functions
while handling the lifetime dental caries disease process better. In
conclusion, the GNB model suits the nature of some count data, in
particular when structural zeros are unlikely to occur and when several
latent spells can lead to new countable events. For these reasons, the
use of the GNB distribution appears to be relevant for the modelling of
dental caries count data.