The feasibility analysis of calculating proptosis by simple Heron’s formula

Purpose: We propose a new method to calculate proptosis by using the simple Heron’s formula and analyze its feasibility. Method: It was a none-inferiority trial. The registration number was ChiCTR1900026490. The absolute value of proptosis in 120 eyes, 60 patients without eye injury or diseases, was measured by computed tomography (CT) and simple Heron’s formula. We did regression analysis and analyzed the differences between the two methods with Medcalc software version 19.0.4. The result was showed by Passing–Bablok regression analysis diagram and Bland and Altman plot. Results: The Passing-Bablok showed that the result of proptosis measured by CT and simple Heron’s formula showed good positive correlation. A 95% limit of agreement in proptosis between CT and Heron’s formula method was -0.46 to 0.54 mm in right eye and -0.45 to 0.46 mm in left eye. 1.66% (1/60) point was outside 95% LoA in both eyes. Moreover, a 95% limit of agreement between CT and Heron’s formula method was -0.42 to 0.56 mm in difference of both eyes. 3.33% (2/60) points were outside 95% LoA. The points in all Bland and Altman plots were lower than 5%. It means that the results of comparison between the two methods had a good consistency in the measurement of proptosis. Conclusions: Heron’s formula could be applied to calculate proptosis and has a good consistency compared with computed tomography (CT). This method is practical in proptosis assessment because of its accuracy, reliability and simplicity.