The Precision of Estimation between ZINB for Count and ZINB for Rate in Dental Health Research

Abstract

Poisson regression is divided into two types which are Poisson for count and Poisson for rate; when
considering dental caries, susceptible tooth and host, substrate, and bacteria including exposure time are
the risk factors. Researcher should consider the impact of the exposure time before conclusion. However,
if the researcher does not have this information, age or number that can identify the association with
exposure time can be put instead of this variable. This study is a part of the study on “the Association
Between Daily Pocket Money and DMFT among children aged 12 years in a primary school at Khumuang
District, Buriram Province” which data had over-dispersion and 11.37% of zero outcomes, the researcher
considered the total number of teeth in the mouth as an offset and using the zero-inflated negative
binomial regression (ZINB) which is a part of Poison statistics for the research question. As a result, the
previous study researchers used ZINB to analyze the data but they did not identify that the analysis was
by count or rate then the objective of this study was to assess the precision of estimation between ZINB
for count and ZINB for rate and compared the standard error between the two methods in dental health
research. The results found that the parameters in the ZINB for rate model had more precisions than the
parameters in the ZINB for count model. Moreover, ZINB for rate could estimate standard errors less than
the ZINB for count. The prominent feature of the zero-inflated negative binomial regression (ZINB) is
that it is a “mixed effect model”, which estimates the parameters in both fixed effect and random effect
and thus reduces the standard error of estimation.