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

Clinical Outcomes of Formula-dependent IOL Power Selection at the Extremes of Axial Length: a Cross-sectional Outcome Verification of Seven ESCRS-hosted Formulas and the Ladas Super Formula 2.0 in Short (<22.0 mm) and Long (>26.0 mm) Eyes Using Refractive, Biometric, and Tomographic Assessment

This single-center, prospective, cross-sectional study evaluates how accurately eight modern intraocular lens (IOL) power calculation formulas predicted the postoperative refractive result in eyes with extreme axial length after cataract surgery. Patients previously operated at the study center who had a very short (axial length < 22.0 mm) or very long (> 26.0 mm) eye and received a spherical monofocal IOL are invited to a single, non-invasive outcome visit. At this visit, standardized manifest refraction, optical biometry, corneal tomography, slit-lamp examination and, in long eyes, macular OCT are performed. The measured postoperative spherical equivalent is compared with the residual refraction that each of the eight formulas had predicted for the actually implanted IOL power, separately in short and long eyes. The study aims to identify which formula predicts the postoperative outcome most accurately at the extremes of axial length, where formula choice is most consequential and least well studied.

Study Overview

• Status: Not yet recruiting
• Conditions: Refractive Error; Pseudophakia
• Intervention / Treatment: Diagnostic test: Standardized postoperative outcome visit

Detailed Description

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.

• Study Type: Observational
• Enrollment (Estimated): 200

Contacts and Locations

• Study Contact: Name: Michal Klimek, MD; Phone Number: +436504607496; Email: klimek.michael@gmx.at

Study Locations

• Austria
  • State of Vienna
    • Vienna, State of Vienna, Austria, 1130
      • Klinik Hietzing, Augenabteilung
      • Contact: Michal Klimek, MD; Phone Number: 06504607496; Email: michak485@gmail.com

Participation Criteria

Eligibility Criteria

• Ages Eligible for Study: Child; Adult; Older Adult
• Accepts Healthy Volunteers: No

• Sampling Method: Non-Probability Sample

Study Population

Adults previously enrolled in the retrospective IOL power formula comparison study at the extremes of axial length at the study center, who underwent cataract surgery with a spherical (non-toric) monofocal IOL (HOYA Vivinex XY1, HOYA Vivinex Impress XY1-EM, or Johnson & Johnson Tecnis 1-Piece DIB00) between January 2022 and December 2025, and whose preoperative axial length was below 22.0 mm or above 26.0 mm. A stratified random sample of 200 patients (110 short-eye, 90 long-eye) is drawn from this source cohort and invited to a single outcome visit.

Description

Inclusion Criteria:

• - Participation in the retrospective IOL power formula comparison study at the extremes of axial length (pseudonymized study ID assigned; complete preoperative biometry and archived formula outputs for all eight formula pathways)
• Cataract surgery with a spherical (non-toric) IOL of one of the three reference models (HOYA Vivinex XY1, HOYA Vivinex Impress XY1-EM, or Johnson & Johnson Tecnis 1-Piece DIB00) at the study center between January 2022 and December 2025
• Preoperative axial length below 22.0 mm (short stratum) or above 26.0 mm (long stratum), measured on IOLMaster 700
• Documented implanted IOL model and power available from the operative record
• At least 3 months since cataract surgery at the time of the outcome visit
• Written informed consent for the outcome visit, including linkage of newly acquired postoperative data with the previously collected, pseudonymized preoperative planning data

Exclusion Criteria:

• - Interval ocular surgery on the study eye since the original cataract surgery that may affect refraction or IOL position (e.g., corneal refractive surgery, IOL exchange or repositioning, secondary IOL implantation, or any intraocular surgery). Uncomplicated YAG laser capsulotomy without IOL repositioning is not an exclusion criterion
• Implanted IOL not matching one of the three reference platforms (e.g., toric, multifocal or EDOF IOL, a different monofocal platform, or a sulcus-fixated IOL)
• Toric IOL implantation
• Acute ocular pathology preventing reliable refraction or biometric measurement
• Cognitive or physical limitations precluding standardized subjective manifest refraction
• Documented intraoperative complication with confirmed or suspected IOL malpositioning (e.g., posterior capsule rupture with vitreous loss, zonular dialysis requiring a capsular tension ring, sulcus placement)
• Withdrawal of informed consent

Note: macular pathology is not an exclusion criterion; macular status is documented on OCT and analyzed as a covariate.

Study Plan

How is the study designed?

Number of groups / cohorts

2

Cohorts and Interventions

Group / Cohort	Intervention / Treatment
Short axial length stratum (AL < 22.0 mm); Pseudophakic eyes with a preoperative axial length below 22.0 mm that received a spherical monofocal IOL. These eyes undergo the standardized postoperative outcome visit; the measured spherical equivalent is compared with each formula's prediction for the implanted IOL power.	Diagnostic test: Standardized postoperative outcome visit; A single, non-invasive multimodal assessment: uncorrected and best-corrected distance visual acuity, IOLMaster 700 optical biometry, CASIA2 and Pentacam AXL corneal tomography, autorefraction and subjective manifest refraction, slit-lamp examination with posterior capsule opacification grading, and macular OCT. No therapeutic intervention, medication or surgery is performed.
Long axial length stratum (AL > 26.0 mm); Pseudophakic eyes with a preoperative axial length above 26.0 mm that received a spherical monofocal IOL. These eyes undergo the standardized postoperative outcome visit (including obligatory macular OCT); the measured spherical equivalent is compared with each formula's prediction for the implanted IOL power.	Diagnostic test: Standardized postoperative outcome visit; A single, non-invasive multimodal assessment: uncorrected and best-corrected distance visual acuity, IOLMaster 700 optical biometry, CASIA2 and Pentacam AXL corneal tomography, autorefraction and subjective manifest refraction, slit-lamp examination with posterior capsule opacification grading, and macular OCT. No therapeutic intervention, medication or surgery is performed.

What is the study measuring?

Primary Outcome Measures

Outcome Measure	Measure Description	Time Frame
Spherical equivalent prediction error (SE-PE) across eight IOL power formulas, compared within each axial length stratum	For each eye, SE-PE is calculated as the measured postoperative spherical equivalent (standardized manifest refraction) minus the residual spherical equivalent predicted by each formula for the actually implanted IOL power step. The absolute prediction error (|SE-PE|) is compared globally across the eight formulas (Barrett Universal II, Cooke K6, EVO 2.0, Hill-RBF 3.0, Hoffer QST, Kane, PEARL-DGS, Ladas Super Formula 2.0) using the Friedman test, with post-hoc pairwise Wilcoxon signed-rank tests (Holm-corrected, 28 formula pairs), performed separately in the short (AL < 22.0 mm) and long (AL > 26.0 mm) strata. The primary accuracy metric per formula is the median absolute prediction error (MedAE).	Single study visit, at least 3 months after cataract surgery

Collaborators and Investigators

• Sponsor: Vienna Hospital Association

Study record dates

Study Major Dates

• Study Start (Estimated): August 1, 2026
• Primary Completion (Estimated): June 1, 2027
• Study Completion (Estimated): July 1, 2027

Study Registration Dates

• First Submitted: July 14, 2026
• First Submitted That Met QC Criteria: July 21, 2026
• First Posted (Actual): July 24, 2026

Study Record Updates

• Last Update Posted (Actual): July 24, 2026
• Last Update Submitted That Met QC Criteria: July 21, 2026
• Last Verified: July 1, 2026

More Information

Terms related to this study

• Keywords: Axial length; IOL formula; Intraocular lens power calculation; Short eye; Long eye
• Additional Relevant MeSH Terms: Eye Diseases; Pathological Conditions, Signs and Symptoms; Signs and Symptoms; Refractive Errors; Pseudophakia
• Other Study ID Numbers: MA_15_EK_26_128_VK

Plan for Individual participant data (IPD)

• Plan to Share Individual Participant Data (IPD)?: NO

Drug and device information, study documents

• Studies a U.S. FDA-regulated drug product: No
• Studies a U.S. FDA-regulated device product: No