Bayesian Morphometric Analysis of Recurring Esthetic Dental (RED) and Golden Proportions in the Maxillary Anterior Dentition using AutoCAD software

Objective The purpose of the study was to approximate the population distribution of Recurring Esthetic Dental (RED) and Golden proportions in the maxillary anterior teeth of Pakistan adults by use of Bayesian statistical statistics. Precisely, the objectives of the study were the estimation of population mean of the ratio of the RED, the uncertainty of RED ratios, the ability to compare the ratios with the estimated range suggested by Ward, the prevalence of the Golden Ratio, and sexual dimorphism in the esthetic parameters. Materials and Methods The study involved a descriptive cross-sectional research design and was carried out on 28 young adult Pakistani respondents (13 males and 15 females; age 18–30 years) with naturally matched dentitions. Standardized frontal smile photographs were acquired and calibrated using an L-shaped scale. Mesiodistal widths and cervico-incisal heights of maxillary central incisors (CI), lateral incisors (LI), and canines (Ca) were measured digitally using AutoCAD linear dimension tool. RED ratios (LI/CI, Ca/LI) and Golden Proportion conformity (ratios within 0.618 ± 10%) were calculated. Bayesian logistic regression models were used to estimate population parameters. Informative priors based on the existing morphometric literature were used to strongly address the small sample size. Results The Bayesian posterior mean for the LI/CI RED ratio was 0.69 (95% Credible Interval [CrI]: 0.65–0.72), with a probability of around1.00 (translating to 100%) falling within the classic 0.60–0.80 RED range. Conversely, the Ca/LI ratio mean was 0.81 (95% CrI: 0.77–0.87), significantly exceeding the standard RED limit. The Golden Proportion was observed in 50% (95% CrI: 33–68%) of LI/CI pairs but only 17% (95% CrI: 6–32%) of Ca/LI pairs. While females in this specific cohort exhibited larger absolute central incisor widths than males (mean difference + 1.46 mm), the esthetic ratios showed no statistically significant sexual diversity. Conclusions The Golden Proportion is not a universal standard for the Pakistani anterior dentition. The RED proportion concept is valid on the central-to-lateral incisor transition but needs to be adapted to the lateral-to-canine transition that is generally broader in this population irrespective of gender.