IOL Power Formula Prediction Accuracy at the Extremes of Axial Length: A Prospective Outcome Verification Study (FORMULEX-OV)

Modern IOL power formulas achieve high refractive predictability in average-length eyes but deteriorate at the extremes of axial length, where effective lens position modelling diverges most between formulas. A preceding retrospective study at this center quantified the formula-dependent variability of IOL power recommendations at the axial length extremes using fully standardized biometric inputs; however, planning discrepancy alone does not indicate which formula's recommendation yields the better clinical outcome. This prospective outcome verification study closes that gap by linking a standardized postoperative assessment to the pre-existing, pseudonymized preoperative planning dataset.

Design: single-center, prospective, cross-sectional, observational (paired within-eye) study. From the retrospective source cohort (approximately 927 short and 769 long eyes; approximately 1,000-1,200 patients; index surgeries January 2022-December 2025), a stratified random sample of 200 patients is drawn (110 short stratum, 90 long stratum; 55:45 ratio) and invited to a single outcome visit. Each eligible eye contributes up to eight paired, formula-specific prediction errors that differ only by the calculation formula, while the postoperative reference (manifest refraction) and all preoperative inputs are held constant. Eyes are stratified a priori into a short (AL < 22.0 mm) and a long (AL > 26.0 mm) stratum and analyzed separately.

Formulas evaluated: Barrett Universal II, Cooke K6, EVO 2.0, Hill-RBF 3.0, Hoffer QST, Kane and PEARL-DGS (via the ESCRS IOL calculator), and the stand-alone Ladas Super Formula 2.0.

Outcome visit (single visit, all non-invasive standard ophthalmic techniques, no study-mandated therapy, medication or surgery): uncorrected and best-corrected distance visual acuity, IOLMaster 700 optical biometry, CASIA2 and Pentacam AXL corneal tomography, autorefraction and standardized subjective manifest refraction (primary outcome measure), slit-lamp examination with posterior capsule opacification grading, and macular OCT (obligatory in the long stratum, recommended in the short stratum).

Primary analysis: for each formula, the spherical equivalent prediction error (SE-PE = measured postoperative spherical equivalent minus the residual spherical equivalent predicted for the actually implanted IOL power step) is computed and the absolute error (|SE-PE|) compared globally across the eight formulas using the Friedman test, with post-hoc pairwise Wilcoxon signed-rank tests (Holm-corrected, 28 formula pairs), separately in each axial length stratum. The primary accuracy metric per formula is the median absolute prediction error.

All data are processed in pseudonymized form and linked via a study ID and laterality, in accordance with the Declaration of Helsinki (2024), ICH-GCP, and the GDPR. The study is reported per STROBE and is registered on ClinicalTrials.gov prior to the start of recruitment.