Comparison of the accuracy of six intraocular lens power calculation formulas for eyes of axial length exceeding 25.0 mm

Summary

Purpose

To compare intraocular lens power calculation formulas for eyes longer than 25.0 mm in terms of absolute error and the percentages of postoperative emmetropia and hyperopia.

Methods

The data for myopic patients who underwent uneventful phacoemulsification between October 2015 and June 2019 were reviewed. Intraocular lens power was calculated using Holladay 1, SRK/T, Hoffer Q, Holladay 2, Haigis, and Barrett Universal II formulas. The power of the lens implanted was based on Holladay 2. Three months after phacoemulsification, the refraction was measured, and the mean absolute error was calculated. The percentage of patients with good uncorrected visual acuity and percentage of hyperopic patients for each formula was established. ROC curves with a cut-off point of axial length were drawn for each formula and the area under the curve was evaluated.

Results

Seventy patients (81 eyes) whose ocular axial length ranged between 25.01 mm and 28.57 mm were included. The Barrett Universal II formula achieved the lowest mean absolute error of 0.08 ± 0.08 D. Additionally, with the Barrett Universal II, the percentage of patients with good uncorrected visual acuity (81.5%) was the highest, and the percentage of hyperopic patients (4.9%) was the lowest. The Barrett Universal II and Holladay 1 formulas had the largest area under curve (0.764 and 0.718, respectively).

Conclusion

1. The Barrett Universal II formula is recommended for intraocular lens power calculation for eyes with axial length greater than 25.0 mm. 2. Considering the ROC curve method, the Barrett Universal II and Holladay 1 formulas appear to be the most appropriate.

Résumé

Objectifs

Comparaison des formules pour le calcul de la puissance des lentilles intraoculaires pour les yeux de longueur supérieure à 25,0 mm en fonction de l’erreur absolue, du pourcentage d’emmétropie et d’hypermétropie postopératoire.

Méthodes

Les données des patients myopes ayant subi une phacoémulsification sans incident entre octobre 2015 et juin 2019 ont été étudiées. La puissance de la lentille intraoculaire a été calculée à l’aide des formules Holladay 1, SRK/T, Hoffer Q, Holladay 2, Haigis, Barrett Universal II. La puissance de l’implant était établie sur la base de Holladay 2. Trois mois après la phacoémulsification, la réfraction a été mesurée et l’erreur absolue moyenne a ainsi été calculée. Le pourcentage de patients ayant une bonne acuité visuelle sans aucune correction, et le pourcentage de patients hypermétropes, pour chaque formule, ont été déterminés. En fonction de la longueur axiale, des courbes ROC ont été tracées pour chaque formule et la surface sous la courbe a été évaluée.

Résultats

Soixante-dix patients (81 yeux), dont la longueur axiale oculaire variait entre 25,01 mm et 28,57 mm, ont été inclus. La formule Barrett Universal II a obtenu l’erreur absolue moyenne la plus basse, soit 0,08 ± 0,08 D. De même, avec la formule Barrett Universal II, le taux de patients ayant une bonne acuité visuelle sans aucune correction (81,5 %) était le plus élevé, et le nombre de patients hypermétropes (4,9 %) était le plus faible. Les formules Barrett Universal II et Holladay 1 avaient les surfaces les plus importantes sous les courbes (0,764 et 0,718, respectivement).

Conclusions

1. On recommande d’utiliser la formule Barrett Universal II pour calculer la puissance des lentilles intraoculaires pour les globes oculaires dont la longueur axiale est supérieure à 25,0 mm. 2. En tenant compte des courbes ROC, les formules de Barrett Universal II et Holladay 1 se sont avérées les mieux adaptées.

Introduction

Most intraocular lens (IOL) power calculation formulas are accurate for eye globes with axial length (AL) ranging between 22.0 mm and 25.0 mm [1]. With AL shorter than 22.0 mm or longer than 25.0 mm, only some formulas would produce reliable results [2], [3].

According to the literature, the most accurate IOL power calculation formula for myopic eyes would be Barrett Universal II [2], [4], [5], [6], [7], [8], [9], followed by Haigis [1], [7], [9], [10], [11], Holladay 1 [7], [9], [11], [12], [13], SRK/T [1], [10], [11], [14], [15]. However, there is still no agreement among cataract surgeons regarding the choice of the formula.

The Barrett Universal II is a formula based on gaussian principle or ray tracing. It differs therefore from conventional formulae in that it takes into account the change from principal planes that occur with different intraocular lens powers. It also changes the calculations depending whether the optic configuration alters from a plano-convex to meniscus lens. And finally, it recognises the change in vergence that occurs when the lens changes from a positive lens to a minus lens and as such it doesn’t require additional correction factors such as transformation or unusual constance for patients with high myopia and very long axial lens. In addition, it has a unique theoretical model to predict the effective lens position (ELP) and this differs quite significantly from what has been used previously [16]. However, this theoretical formula uses traditional mathematics for IOL power calculation based on obligatory data (lens factor or A-constant, AL, keratometric readings, optical anterior chamber depth (ACD), planned postoperative refraction value) and optional data such lens thickness (LT) and white-to-white (WTW) distance [17].

Also, many different tools could be employed to assess the accuracy of the chosen formula.

Most research in this area would be based on observation of mean absolute error (AE) only [2], [4], [5], [6], [7], [8], [10], [14]. Only a few authors have considered the percentage of patients with postoperative full visual acuity (VA) without any correction, as well as the percentage of postoperative hyperopia after phacoemulsification [4], [12], [18]. Moreover, the receiver operating characteristic (ROC) curves method, widely used to present results in various other medical studies, has not been used so far to assess the accuracy of IOL power calculation formulas.

This study aimed to compare the IOL power calculation formulas for eyes longer than 25.0 mm in terms of AE and the percentage of patients with full VA without any correction and percentage of hyperopic patients after cataract surgery. The study is pioneering due to its research method. Using the concept of sensitivity and specificity of the test and ROC curves, the study shows the superiority of some formulas over others.