This study was conducted retrospectively in a private practice setting. Nine formulas were compared for prediction error (postoperative spherical equivalent (SE) minus, predicted SE calculated by each formula), using two optical biometers (Lenstar – optical low coherence reflectometry (OLCR) and IOLMaster – partial coherence interferometry (PCI), in 1079 eyes. Each formula was ranked for accuracy by biometer and by axial length (AL). Inclusion criteria was in-the-bag placement of Acrysof SN60WF and exclusion criteria, any ocular pathology. Manifest refraction was carried out three weeks and three months postoperatively. Formulas included were 1) SRKT, 2) Haigis-L, 3) Hoffer Q, 4) Holladay I 5) Olsen OLCR and Olsen standalone 6) Holladay 2 with no pre-op refraction 7) Holladay 2 with presurgical refraction 9)T2 and 9) Superformula. Optimised constants were used, to achieve a predicted error as close to zero as possible, for the entire dataset. The Haigis constants were obtained by linear regression analysis as described by Haigis. Long eyes >26.0mm and short eyes less than 22.0mm were analysed separately. When OLCR values were used the Olsen formula outperformed other formulas in all categories except long eyes for which the difference was minimal.
The Olsenstandalone and OlsenOLCR had different predictions even though the same lens constants were used in both formulae. The OlsenOLCR predicts postoperative anterior chamber depth (ACD) using preoperative ACD and preoperative lens thickness. The Olsenstandalone in addition uses preoperative AL and preoperative K-values. When PCI measurements were used the Barrett Universal II was the best formula except in eyes longer than 26.0mm. It was only slightly worse than the Olsen when OLCR was used. The Olsenstandalone gave the worst prediction errors as lens thickness isn’t measured in IOLMaster pre-dating IOLMaster 700. The Olsen formula uses the C-constant which requires lens thickness data in order to calculate lens position. For extreme axial lengths both the Haigis and Olsen formulas performed with prediction errors closest to zero compared to all other formulas.
The authors report Olsen formula difficult to study as it is a proprietary formula and cumbersome because it requires six lens constants, five relating to IOL manufacturers’ specifications. The most difficult constants to obtain are the front and back curvature constants from manufacturers. When preoperative refraction was intentionally excluded the Holladay 2 formula performed better than when included.
In conclusion the Barrett Universal II formula performs the best in both the OLCR and PCI biometers. In addition Barrett II only requires one constant, i.e. the A-constant as used in SRKT therefore much easier to find optimised IOL constants. It is also available online where measurement data can be entered at no cost. Short eyes generally yielded myopic predictions and this has been widely reported by others. None of the formulas predict well for short eyes compared to normal length eyes and had prediction errors far from zero. Long eyes yielded hyperopic outcomes and the Haigis performed the best in terms of mean prediction errors, also previously reported. The reason Haigis is able to do this is because it is a two constant (one of three constants) associates effective lens position with axial length. It therefore has good results across the axial length spectrum. The study was limited because it only used Acrysof SN60WF between 6.0D and 30.0D with limited number of extreme length eyes. As we know different IOL models behave different in different sized eyes in terms of ELP as they are greatly affected by axial length and anterior chamber depth.