Strategies for formula constant optimisation for intraocular lens power calculation

Abstract

Background To investigate modern nonlinear iterative strategies for formula constant optimisation and show the application and results from a large dataset using a set of disclosed theoretical-optical lens power calculation concepts. Methods Nonlinear iterative optimisation algorithms were implemented for optimising the root mean squared (SoSPE), the mean absolute (SoAPE), the mean (MPE), the standard deviation (SDPE), the median (MEDPE), as well as the 90% confidence interval (CLPE) of the prediction error (PE), defined as the difference between postoperative achieved and formula predicted spherical equivalent power of refraction. Optimisation was performed using the Levenberg-Marquardt algorithm (SoSPE and SoAPE) or the interior point method (MPE, SDPE, MEDPE, CLPE) for the SRKT, Hoffer Q, Holladay 1, Haigis, and Castrop formulae. The results were based on a dataset of measurements made on 888 eyes after implantation of an aspherical hydrophobic monofocal intraocular lens (Vivinex, Hoya). Results For all formulae and all optimisation metrics, the iterative algorithms showed a fast and stable convergence after a couple of iterations. The results prove that with optimisation for SoSPE, SoAPE, MPE, SDPE, MEDPE, and CLPE the root mean squared PE, mean absolute PE, mean PE, standard deviation of PE, median PE, and confidence interval of PE could be minimised in all situations. The results in terms of cumulative distribution function are quite coherent with optimisation for SoSPE, SoAPE, MPE and MEDPE, whereas with optimisation for SDPE and CLPE the standard deviation and confidence interval of the PE distribution could only be minimised at the cost of a systematic offset in mean and median PE. Conclusion Nonlinear iterative techniques are capable of minimising any statistical metrics (e.g. root mean squared or mean absolute error) of any target parameter (e.g. PE). These optimisation strategies are an important step towards optimising for the target parameters which are used for evaluating the performance of lens power calculation formulae.

Biometry and Intraocular Lens Power Calculation in Eyes with Prior Laser Vision Correction (LVC) – A Review

“…Adjusting IOL constants specifically for eyes after LVC does not seem intuitive, as these constants must depend on the ablation profile/amount of correction and ablation zone and require sufficient case numbers. Unless the surgical site has unusually large numbers of eyes with prior LVC, constants from eyes without prior LVC (e.g., from IOLCON [platform for characteristics of intraocular lenses and the optimization of lens constant], previously the ULIB [user group for laser interference biometry] site) should be used 16 , 17 , 18 . Additionally, interpretation of IOL power prediction accuracy studies on eyes after LVC is often difficult.…”

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].…”

“…Formeln mit mehreren Konstanten benötigen höhere Fallzahlen und andere Optimierungsstrategien, z. B. den Levenberg-Marquard-Algorithmus oder die Interior-Point-Methode [24]. Haigis verwendete eine einfache multiple lineare Regression mit 2 Variablen.…”

“…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].…”

“…In formulae with a constant, the constant should be based on data from at least 80 eyes [26]. Formulae with multiple constants require higher numbers of cases and other optimization strategies, e.g., the Levenberg-Marquard algorithm, or the interior-point method [24]. Haigis used a simple multiple linear regression with two variables.…”