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

Esthetic proportion rules such as the Recurring Esthetic Dental (RED) proportion and the Golden Proportion are frequently used in smile design, yet their population validity remains uncertain and may vary by ethnicity and dental arch form. This study estimated the population distribution and uncertainty of RED ratios and Golden Proportion conformity in the maxillary anterior dentition of young adult Pakistani participants using Bayesian models to support inference under small-sample conditions. A cross-sectional sample of 28 adults (13 male, 15 female; age 18 to 30 years) was recruited from Dental College of Riphah International University, Islamabad, Pakistan. Standardized frontal smile photographs were calibrated using a reference scale and measured digitally for mesiodistal widths and cervico-incisal heights of maxillary central incisors, lateral incisors, and canines. RED ratios (lateral incisor to central incisor; canine to lateral incisor) and Golden Proportion conformity (operationalized as being within a 10 percent tolerance of 0.618) were computed, then modeled using Bayesian regression and prevalence estimation. The posterior mean lateral incisor to central incisor RED ratio was 0.686 (95 percent credible interval: 0.65 to 0.72), with an essentially certain probability of lying within the conventional 0.60 to 0.80 RED band, while the canine to lateral incisor ratio was higher at 0.814 (95 percent credible interval: 0.77 to 0.87), indicating weaker conformity to the classic RED range. The Golden Proportion was observed in about 50 percent of lateral incisor to central incisor pairs (95 percent credible interval: 33 to 68 percent) and about 17 percent of canine to lateral incisor pairs (95 percent credible interval: 6 to 32 percent), with a negligible probability of a full anterior sextant meeting Golden Proportion criteria; gender effects were small and statistically uncertain. These findings suggest that the Golden Proportion should not be treated as a universal standard for this population, and that RED logic may be clinically useful for the central-to-lateral transition but likely requires adaptation for the lateral-to-canine transition. Limitations include the small, single-center sample, young age range, and reliance on two-dimensional photographs; future work should validate these Bayesian estimates in larger multicenter Pakistani cohorts using three-dimensional digital scans and broader age strata.