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.