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

Investigate the most appropriate mathematical formula to objectively express upper eyelid contour symmetry.

62 eyes of 31 patients were included in the study. The upper eyelid contour symmetry of the patients was classified subjectively (independent of MRD1) as poor, acceptable, and good by three oculoplastic specialists (senior, expert, and junior surgeon). Bézier curves of the upper lid contour were drawn with ImageJ software (NIH, Bethesda, MA, USA). Using the algorithms created by Author SKC in Spyder (Python 3.7.9.), the symmetry of the Bézier curves of the left eyelids were obtained according to the y-axis, and the mid-pupils of both eyes were superimposed. The lower curve moved vertically to the equal height of the other curve to equalize MRD1's. 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. We evaluated the correlation between these objective formulas and the subjective grading of three surgeons using Spearman's rho (ρ).

The correlation coefficient of RMSE and MSE were the same for all surgeons grading. There was a strong correlation between the senior surgeon's subjective scoring (N; poor = 8, acceptable = 16, good = 8) and R², RMSE, POC, MAE (ρ = 0.643, p < 0.001, ρ = -0.607, p < 0.001, ρ = 0.562, p < 0.001, ρ = -0.517, p < 0.001, respectively). We found a strong relationship between the expert surgeon's subjective scoring (N; poor = 9, acceptable = 13, good:10) and R² (ρ = 0.611, p < 0.001), RMSE (ρ = -0.549, p < 0.001), POC (ρ = 0.511, p < 0.001), and MAE (ρ = -0.450, p < 0.05). We found a strong correlation between junior surgeon's subjective scoring (N; poor = 6, acceptable = 18, good = 8) and R², RMSE, and POC (ρ: -0.517, p < 0.001; ρ: -0.470, p < 0.001; ρ: 0.521, p < 0.001; respectively) and moderate correlation between MAE (ρ:-0.394, p < 0.05). The highest correlation is observed with R².

RMSE, MSE, POC, MAE, and especially R², may quantitatively express upper eyelid contour symmetry, comparable with the oculoplastic surgeon. The highest correlation was observed between the senior surgeon and R², and decreases with the experience of the surgeon.