Re-Visiting the Decay, Missing, Filled Teeth (DMFT) Index with a Mathematical Modeling Concept

Amar Hassan Khamis

doi:10.4236/ojepi.2016.61003

Abstract

Background: The well-established DMFT index has been used for over 75 years as a key for measuring dental caries in dentistry. DMFT is applied to permanent dentition and expressed as the total number of teeth decayed (D), missing (M), or filled (F), tooth (T) in an individual. Objectives: The objective of this study is to build a mathematical model for the existing DMFT index and compare its parameters by suggested new mathematical model. Mathematical Models: Fixed Model: Is a mathematical model for the existing DMFT index and will be considered as fixed model; in which all individuals under screening will have the same probability θ, 0 ≤ θ ≤1 of dental caries. In this fixed model the unit of the screening is the individual, and will be evaluated for caries as a dichotomous (0, 1) variable. Random Model: The new suggested model is a random model that suggests a mouth of an individual as an environment and the tooth is a unit of research. In this random model, only the teeth in one mouth have the same probability θ, 0 ≤ θi ≤ 1 where i =1, 2...,k ; number of screening individuals. Expected Outcome: Mathematically, the fixed model will highlight what the value 1 will hide as information and hence this may explain why the average of DMFT is may be overestimated for any sample studied using fixed model. The random model will yield a cumulative weighed probability on the function of the number of teeth screened per mouth θ, 0 ≤ θ ≤ 1, hence the average DMFT index will be weighed against the number of teeth screened per all subjects. Conclusion: The random model yields an average and more realistic expected value for the population studied. Furthermore, in such model, it is easy to estimate the variance and it is obvious that this model yields the smallest variance.

Highlights

Dental caries is a public oral health problem in Asia, Middle East and across the African Sub-Saharan regions [1] [2]
The DMFT index calculates different clusters per individual; the number one demonstrates the existence of caries from screening teeth, in a given environment that might be affected by other factors such as oral hygiene, public health awareness, genetic factors and the accessibility to the oral health services
The DMFT is a simple way of characterizing the status of the dental caries of an individual, the parametrization of the indices estimated by DMFT index using an individual through multiple subunits is not well integrated

Summary

Introduction

Dental caries is a public oral health problem in Asia, Middle East and across the African Sub-Saharan regions [1] [2]. The DMFT index calculates different clusters per individual; the number one demonstrates the existence of caries from screening teeth, in a given environment that might be affected by other factors such as oral hygiene, public health awareness, genetic factors and the accessibility to the oral health services. These contributing factors will lead us to consider how the individual will contribute to the cumulative variance in caries as part of a given population. The aim of the present study is to try to construct mathematical model of the existing DMFT index in order to more accurately estimate the prevalence, and the average, of the DMFT index

Mathematical Models

Fix Model

Random Model

Theoretical Scenarios

Discussion