Considerations on the Haigis formula: Are better outcomes possible with tuning?

To design a vergence-based lens power formula based on the classical Haigis formula for better outcomes while retaining the original formula architecture.

Four new formula variants (A-D) incorporating a sum of segments correction for axial length, harmonic mean of corneal radii instead of arithmetic mean (all variants), and differing combinations of lower keratometer index (C, D) and an additional term (a3) representing the lens thickness in the effective lens position (B, D) were assessed in an analysis based on four datasets of IOLMaster 700 biometric data for eyes treated with the Hoya Vivinex lens (dataset 1), Alcon SA60AT lens (2), Johnson & Johnson ZCB00 lens (3), and the Bausch & Lomb MX60 lens (4). All parameters (formula constants and keratometer index) were calculated by nonlinear iterative optimisation techniques for minimising the root mean squared prediction error (RMSPE). Performance was assessed in terms of the final RMSPE.

All four variants showed reductions in RMSPE ranging from 2.8% to 12.6% over the original Haigis formula. For each of the four datasets, variants B and D (with the additional a3 constant) performed better in this respect than variants A and C. In all four cases, variants C and D (with the adjusted keratometer index) performed slightly better than A and B, respectively.

Although not amenable to statistical analysis, the % improvements in RMSPE would appear to be clinically relevant. However, the benefit has to be proven in a prospective multicentric study with a large sample size.