PPubMed5 May 2022Cited 25×

Strategies for formula constant optimisation for intraocular lens power calculation Strategies for formula constant optimisation

Achim Langenbucher, Nóra Szentmáry, Alan Cayless, Jascha Wendelstein, Peter Hoffmann, Asaf Achiron

Abstract

For each formula under test, formula constant(s) were optimised to minimise the sum of squared prediction errors, the sum of absolute prediction errors, the mean prediction error, standard deviation (SD) of prediction error, a combination of mean and standard deviation of prediction error (SD & mean), median prediction error, the 90% confidence interval (CL) of prediction error, and a combination of median and 90% confidence interval of prediction error (90% CL & median). From the first graph (SRKT) we see that the CDFs for the prediction error are almost consistent except for the constant opt

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Nonlinear iterative optimisation can efficiently minimise various statistical error metrics for intraocular lens power calculation formulas across a large clinical dataset.

What’s new

i.Implemented nonlinear iterative optimisation algorithms (Levenberg‑Marquardt and interior‑point) for multiple error metrics across five IOL formulas.
ii.Applied the algorithms to a retrospective dataset of 888 eyes with biometric and postoperative refraction data.
iii.Demonstrated fast, stable convergence and minimisation of RMS, MAE, mean, median, SD, and confidence interval errors.
iv.Identified that optimisation for SD or confidence interval can introduce systematic offsets in mean/median prediction error.

How they did it

Nonlinear iterative optimisation algorithms were coded in MATLAB (Levenberg‑Marquardt for sum‑of‑squared and sum‑of‑absolute errors; interior‑point for mean, median, SD and confidence‑interval metrics) and applied to 888 eyes’ pre‑operative biometry and postoperative refraction to optimise constants of SRKT, Hoffer Q, Holladay 1, Haigis (two versions) and Castrop formulas; performance was assessed using prediction‑error statistics.

What they found

Convergence achieved in all optimisations, requiring up to 26 iterations (152 function evaluations) for SoSPE, up to 30 (148) for MPE, up to 32 (177) for MEDPE, up to 48 (255) for SoAPE, up to 50 (311) for SDPE, up to 48 (198) for CLPE, and up to 77 (510) for combined metrics.
Optimisation reduced root‑mean‑squared, mean absolute, mean, median, SD and 90 % confidence‑interval prediction errors for all formulas.
When optimising solely for SD or CL, a systematic offset of up to 0.4 dpt in mean and 0.14 dpt in median prediction error was observed.
The dataset comprised 888 eyes (490 right, 398 left; mean age 71.2 ± 9.1 years).

Caveats

✕Optimising for standard deviation or confidence interval alone can cause systematic offsets in mean or median prediction error.
✕The approach is limited to disclosed formulas that allow constant re‑organisation; undisclosed formulas cannot be batch‑optimised.
✕The study used data from a single centre and a single IOL model (Vivinex), limiting generalisability to other settings.

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