Simplification of a Three-Constant Intraocular Lens Calculation Formula to a Single-Constant Approach: The Haigis Formula

Abstract

Background/Objectives: To derive and validate a simplified modification of the Haigis intraocular lens (IOL) power calculation formula by reducing the three-constant effective lens position (ELP) model to a single constant while introducing an optimized keratometer index and axial length correction. Methods: In this retrospective study, a large multicentric dataset (Dataset 1; 22,466 eyes, 113 IOL models) was used to optimize the Haigis constant triplet and keratometer index using nonlinear programming with Cooke’s axial length correction. A second independent dataset (Dataset 2; 3181 eyes, six IOL models) was used for cross-validation. Three approaches were compared: classical Haigis, modified triplet, and two single-constant models acting on IOL power (H1) or ELP (H2). Results: The optimized keratometer index (1.3296 ± 0.0003) was significantly lower than the classical value, indicating systematic overestimation of corneal power. Modified triplet and single-constant approaches achieved comparable or slightly lower prediction errors than the classical formula. The H1 approach showed marginally superior performance. Bootstrapping confirmed parameter stability. Conclusions: A single-constant modification of the Haigis formula incorporating an optimized keratometer index and axial length correction maintains prediction accuracy while simplifying clinical implementation.