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

Abstract

Purpose: To present strategies for optimization of lens power formula constants and to show options how to present the results adequately. Methods: A dataset of N=1601 preoperative biometric values, lens power 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 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 more than 1 constant. In these cases, more advanced concepts such as nonlinear optimization strategies are necessary to derive the formula constants. During cross-validation, measures such as the mean absolute or the root mean squared prediction error or the ratio of cases within mean absolute prediction error 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 prediction error limits is plotted against the mean absolute prediction error.

Strategies for formula constant optimisation for intraocular lens power calculation

“…Currently there are no generally accepted guidelines or recommendations for formula constant optimisation [ 15 , 20 , 29 ]. Where a formula is fully disclosed, and in the simple case of a formula with a single constant, it would be possible to reorganise the formula to solve for the formula constant (for each clinical case), and from the distribution of the formula constants the clinician could select statistical metrics such as the arithmetic or geometric mean or the median.…”

Update Biometrie und Linsenberechnung – ein Review zu Grundlagen und neuen Entwicklungen

“…Ein Wert, der den mittleren Fehler und die Standardabweichung gut abdeckt, ist die Wurzel der mittleren quadratischen Abweichung. Es bietet sich an, diesen Wert als Optimierungswert zu verwenden [24,25]. In Formeln mit einer Konstante sollten hierzu zumindest 80 Augen herangezogen werden [26].…”

“…A value that covers the mean error and stan-dard deviation well is the root of the mean square deviation. It is a good idea to use this value as the optimization value [24,25]. In formulae with a constant, the constant should be based on data from at least 80 eyes [26].…”

Intraokularlinsen

“…Um die Formeln nun also an verschiedene Kunstlinsendesigns anzupassen, gibt es in den Formeln spezifische Konstanten, die zumeist entweder in die Berechnung der ELP bzw. der Linsenstärke eingehen [24] und die Formel an die jeweiligen Umstände, z.B. die spezifische Linse und den spezifischen Operateur, anpassen sollen.…”

“…Dies kann jedoch an verschiedenen Werten orientiert werden: entweder bezogen auf den Mittelwert oder auf den Median oder auf den quadratischen Mittelwert des Vorhersagefehlers. Langenbucher et al schlagen hierzu beispielsweise einen Levenberg-Marquardt-Algorithmus vor [24]. Für welches Verfahren man sich auch entscheidet, man sollte seine optimierten Werte auf jeden Fall anhand zweier unterschiedlicher Kontrollgruppe kreuzvalidieren.…”