Chasing the objective upper eyelid symmetry formula; R², RMSE, POC, MAE, and MSE

Area of Science:

• Ophthalmology and Oculoplastic Surgery
• Biomedical Engineering
• Medical Imaging Analysis

Background:

• Assessing upper eyelid contour symmetry is crucial in oculoplastic surgery.
• Subjective grading by surgeons can be inconsistent.
• Objective mathematical methods are needed for reliable symmetry evaluation.

Purpose of the Study:

• To identify the most appropriate mathematical formula for objectively quantifying upper eyelid contour symmetry.
• To compare objective mathematical assessments with subjective grading by oculoplastic surgeons.

Main Methods:

• Bézier curves were generated from upper eyelid contours of 62 eyes from 31 patients.
• Objective symmetry metrics including R² (Coefficient of determination), RMSE (Root-mean-square error), MSE (Mean squared error), POC (Percentage of co-efficiency), and MAE (Mean absolute error) were calculated.
• Spearman's rho correlation was used to compare objective metrics with subjective symmetry grades from three oculoplastic surgeons (senior, expert, junior).

Main Results:

• All tested mathematical formulas showed correlation with subjective surgeon grading.
• The Coefficient of determination (R²) demonstrated the strongest correlation with subjective assessments across all surgeon experience levels.
• Correlation strength decreased with increasing surgeon experience, with the senior surgeon showing the highest correlation with R².

Conclusions:

• Mathematical formulas, particularly R², can objectively and reliably express upper eyelid contour symmetry.
• These objective measures are comparable to oculoplastic surgeon assessments.
• R² shows the highest concordance with expert clinical judgment for evaluating eyelid symmetry.