IOL Formula Constants: Strategies for Optimization and Defining Standards for Presenting Data

Purpose: The aim of this study is to present strategies for optimization of lens power (IOLP) formula constants and to show options how to present the results adequately. Methods: A dataset of N = 1,601 preoperative biometric values, IOLP data and postoperative refraction data was split into a training set and a test set using a random sequence. Based on the training set, we calculated the formula constants for established lens calculation formulae with different methods. Based on the test set, we derived the formula prediction error (PE) as difference of the achieved refraction from the formula predicted refraction. Results: For formulae with 1 constant, it is possible to back-calculate the individual constant for each case using formula inversion. However, this is not possible for formulae with >1 constant. In these cases, more advanced concepts such as non-linear optimization strategies are necessary to derive the formula constants. During cross-validation, measures such as the mean absolute or the root mean squared PE or the ratio of cases within mean absolute PE (MAE) limits could be used as quality measures. Conclusions: Different constant optimization concepts yield different results. To test the performance of optimized formula constants, a cross-validation strategy is mandatory. We recommend performance curves, where the ratio of cases within absolute PE limits is plotted against the MAE.