Application of the Taylor Diagram in Evaluating the Performance of IOL Formulas.

Purpose: To apply a new method, the Taylor Diagram, and a new concept, the centered root mean square error (cRMSE), in evaluating the performance of IOL formulas.

Methods: The preoperative biometrics were measured with the IOLMaster 700 (Carl Zeiss Meditec) and the postoperative spherical equivalent refraction (SER) was calculated in 888 anonymous patients. The Taylor Diagram was applied to visualize the centered root mean square error (cRMSE) and the correlation coefficient between the predictions and the observations (R). Ten formulas across generations were optimized by zeroing the mean predictive error, including SRK I, SRK II, SRK/T, Holladay I, Hoffer-Q, Haigis, Barrett Universal II, VRF, EVO 2.0, and Næser 2. The RMSE and cRMSE at a range of IOL constants around the optimized constant were calculated for SRK/T, Holladay I, Hoffer-Q, and Haigis.

Results: The Taylor Diagram showed improved performance of formulas across generations and the aggregations of the same-generation formulas. The SRK I performed worst with an RMSE of 0.819 and R of 0.659, and the EVO 2.0 performed best with an RMSE of 0.341 and R of 0.930. At a range of IOL constants, cRMSE is generally much closer to the optimized value than RMSE. At a relatively wide range of constant values, cRMSEs showed no significant discrepancy with the optimized value at the optimized constant.

Conclusions: The Taylor Diagram is a powerful tool for visualizing the performances of IOL formulas. Constant optimization is proved necessary. When the optimization is unavailable, cRMSE is a good approximation. .