Accuracy of the Refractive Prediction Determined by Multiple Currently Available Intraocular Lens Power Calculation Formulas in Small Eyes


To observe the refractive outcomes of cataract surgery in small adult eyes, and to investigate the accuracy of different intraocular lens (IOL) power prediction formulas.


Retrospective interventional case series.


We included consecutive small eyes undergoing uneventful phacoemulsification cataract surgery with a single highly powerful IOL (Acrysof SA60AT) implanted in the capsular bag (range of powers +35.0 to +40.0 diopters [D]), at the Cataract Centre for Moorfields Eye Hospital. Exclusion criteria were combined or previous intraocular surgical procedures, and any type of intraoperative complications. Main outcome measures were mean prediction errors with Hoffer Q, Holladay 1, Holladay 2, Haigis, SRK-T, and SRK-II IOL power prediction formulas and proportions of eyes achieving absolute errors within the dioptric ranges of 0.5, 1.0, and 2.0 D of target and emmetropia, respectively. The ANOVA test was used to compare the refractive results among various formulas.


Twenty-eight eyes were studied; the mean numerical error was 0.22 ± 1.22 D and the mean absolute error was 0.95 ± 0.78 D with the adopted Hoffer Q formula; 39%, 61%, and 89% of the eyes had a final refraction within 0.5 D, 1.0 D, and 2.0 D of target, respectively. None of the latest-generation formulas significantly outperformed the others ( P = .245).


The Hoffer Q formula led to good or fair refractive outcomes in less than two thirds of the cases. With Holladay 1 and 2 and Haigis formulas, outcomes would have not been significantly different. The SRK formulas yielded less accurate predictions. Possible reasons are discussed.

Refinements in surgical instrumentation and techniques associated with improved intraocular lens (IOL) technology commonly allow surgeons to meet the constantly rising patient expectations in terms of clinical and refractive outcomes. The latter are regarded as a quality indicator in cataract surgery, and represent one of the most common reasons for litigation related to intraocular surgery.

Patients with small eyes more commonly have surgery early in life, when lens opacities might not be visually significant, in order to obtain a better intraocular pressure control or to correct significant degrees of hyperopia. Therefore, these patients are generally more demanding, and unfortunately poor refractive outcomes may be expected, as shown by previous case series where ultrasound biometry technology was employed.

The purpose of the current study was to investigate the accuracy of the Hoffer Q formula for standard cataract surgery in small adult eyes when the current gold-standard optical biometry is employed for axial length measurement and corneal power assessment, and to investigate whether the adoption of a different IOL power prediction formula would have yielded better outcomes.


Institutional review board approval (at Moorfields Eye Hospital in London, United Kingdom) was obtained for this retrospective study for the collection of preoperative, intraoperative, and postoperative data, and precautions were taken to protect the identity of the study patients. All research and data collection adhered to the tenets of the Declaration of Helsinki.

Small adult eyes that had undergone uneventful phacoemulsification cataract surgery with implantation of the Acrysof SA60AT (Alcon Labs, Fort Worth, Texas, USA) in the capsular bag were eligible for this study. Exclusion criteria were additional surgical procedures at the time of cataract surgery, previous intraocular surgery (including previous refractive corneal surgery), intraoperative complications, any corneal pathology, IOL power lower than 35 diopters (D), lack of accurate optical biometric data, marked lens opacities or poor fixation requiring ultrasound biometry, postoperative corrected distance visual acuity (CDVA) worse than 20/40 (logMAR 0.3), subjective refraction obtained less than 4 weeks after surgery, and incomplete datasets. Eyes with axial length shorter than 20.9 mm were included.

Data collection included preoperative examinations, operative details, postoperative findings, and refractive data. Additionally, age and sex, laterality, axial length, anterior chamber depth, average corneal power, IOL power, and surgeon grade were recorded ( Table 1 ). All the included eyes underwent optical biometry with partial coherence interferometry (IOLMaster; Carl Zeiss Meditec, Dublin, California, USA), and only biometric measurements with signal-to-noise ratio values above 2.0 (≥2.1) were accepted as accurate.

Table 1

Accuracy of Intraocular Lens Power Calculation Formulas in Small Adult Eyes: Preoperative Characteristics of the Studied Eyes

Mean (SD) Median (25th–75th Percentiles) Range
Age (y) 72 (10) 71 (63–79) 55–92
Sex (male/female) 11/17
AL (mm) 19.86 (0.55) 19.94 (19.61–20.17) 18.41–20.64
ACD (mm) 2.56 (0.42) 2.51 (2.17–2.99) 1.93–3.25
K-aver (D) 43.76 (2.07) 43.84 (42.76–44.74) 38.70–48.22
SE preOP (D) 8.53 (1.95) 8.50 (7.75–9.63) 3.00–11.88
Refractive target (D) −0.44 (0.49) −0.47 (−0.73/−0.08) −1.30/0.70
IOL power (D) 36 (35–37) 35–39

ACD = anterior chamber depth; AL = axial length; D = diopters; IOL = intraocular lens; K-aver = mean corneal power; SD = standard deviation; SE-preOP = preoperative spherical equivalent.

The IOLMaster software was used to calculate the required IOL power with the Hoffer Q formula, a third-generation IOL power prediction formula specifically suggested for calculations in short eyes. The recommended lens constant for optical biometry was used. The observed postoperative refraction was converted to spherical equivalent and the mean numeric error was calculated as the difference between refractive outcome and predicted spherical equivalent (Actual postoperative refraction–Predicted refraction). In this way, a negative prediction error value indicated a tendency toward overcorrection that would produce a more myopic result than intended, and vice versa. The mean absolute error and the median absolute error were calculated as the mean and median of the magnitude of the prediction error, regardless of sign.

The proportions of eyes achieving absolute errors within the dioptric ranges of 0.5, 1.0, and 2.0 D of target and 0.5 and 1.0 D of emmetropia were calculated.

To back-calculate the mean numerical error, mean absolute error, and median absolute error with other currently available IOL power prediction formulas, the IOLMaster software and the Holladay IOL Consultant Software (Holladay Consulting, Inc, Bellaire, Texas, USA) were used: the predicted target with the actual IOL power that was implanted in the studied eyes was noted for each of the tested formulas and used for the calculations.

Axial length, anterior chamber depth, horizontal corneal diameter, and average corneal power data were obtained with the IOLMaster (version 5.4). For the lens thickness measurement, A-scan ultrasonography with the Accutome A-scan Plus (Accutome Inc, Malvern, Pennsylvania, USA) was performed, and values accepted if at least 3 readings were available with a deviation inferior to 0.10 mm.

Preoperative and postoperative uncorrected distance visual acuity (UDVA) and CDVA and refraction (subjective and objective) data were available for all eyes; in all included cases the subjective refraction was performed at least 4 weeks after surgery.

All eyes had uneventful standard sutureless phacoemulsification cataract surgery with either a 3.2-mm or 2.75-mm clear corneal incision and endocapsular-fixated intraocular lens implantation at the Cataract Centre for Moorfields Eye Hospital. The procedures were performed by a number of surgeons; the standard pseudophakic endophthalmitis prophylaxis was employed in all cases.

Statistical Analysis

Continuous variables were described with the mean, standard deviation, and range of values. The normality assumption of the distribution was assessed and confirmed with the Shapiro-Wilk normality tests ( P = .236). The Fisher exact tests were used for odds ratio tests; paired t tests were used for means. A P value of less than .05 was considered statistically significant; all tests were 2-sided. For the analysis of the differences in mean numerical and absolute errors between formulas, the 1-way ANOVA (analysis of variance) test was employed. All analyses were performed using SPSS software (version 20.0, IBM Corp., Armonk, New York).


Twenty-eight small eyes of 28 adult patients were recruited for this study; the operating surgeon was at consultant or fellow grade in the vast majority of cases (27/28), and the sex ratio was 1:1.5 male to female. The mean preoperative spherical equivalent was +8.53 ± 1.95 D (range +3.00 to +11.88 D), with a mean axial length of 19.86 ± 0.55 mm (range 18.41–20.64 mm) and a mean anterior chamber depth of 2.56 ± 0.42 mm (range 1.93–3.25 mm). The mean refractive target was −0.44 ± 0.49 D (range −1.30 to +0.70 D) ( Table 1 ).

The Hoffer Q formula was employed in all our patients and led to a mild overcorrection, resulting, therefore, in slightly more myopic outcomes than intended ( Table 2 ). The mean postoperative refraction was −0.66 ± 1.22 D spherical equivalent. Eleven eyes (39%) had a final refraction within 0.5 D of target, with 61% (17 eyes) being within 1.0 D of target. Twelve eyes (43%) and 18 eyes (64%) had a postoperative spherical equivalent within 0.5 D and 1 D of emmetropia, respectively.

Table 2

Accuracy of Intraocular Lens Power Calculation Formulas in Small Adult Eyes: Refractive Outcomes Obtained With the Adopted Hoffer Q Formula

Mean numerical error −0.22 1.22
Mean absolute error 0.95 0.78
Median absolute error 0.76
N %
±0.50 D a 12 43
±1.00 D a 18 64
±0.50 D b 11 39
±1.00 D b 17 61
±2.00 D b 25 89

D = diopters.

a Of emmetropia.

b Of target refraction.

The results of the back-calculation are presented in the predicted vs achieved refraction graphs ( Figure ). The ANOVA test showed no statistically significant difference among all the studied third- and fourth-generation formulas (F = 1.378, P = .245), whereas the results showed a statistically significant difference among studied subgroups when the obsolete SRK-II (Sanders-Retzlaff-Kraft) formula was included (F = 5.979, P < .0001). Although not statistically significant, a trend toward less accuracy of the prediction was observed with the SRK-T and the Holladay1 in this series, with only 21% (6/28) and 29% (8/28) of eyes obtaining a final refraction within 0.50 D of target, respectively ( Table 3 ).


Accuracy of different intraocular lens formulas for the prediction of postoperative refraction after cataract surgery in small adult eyes. The graphical representation of the predicted vs achieved refraction with the different studied formulas is shown. (Top left) Results with the Hoffer Q formula adopted in the study; (Top middle) back-calculated results with the Haigis formula; (Top right) back-calculated results with the Holladay 1 formula; (Bottom left) back-calculated results with the Holladay 2 formula; (Bottom middle) back-calculated results with the SRK-T formula; (Bottom right) back-calculated results with the SRK-II formula.

Table 3

Accuracy of Intraocular Lens Power Prediction Formulas in Small Adult Eyes: Prediction Errors Obtained by Back-Calculation

Hoffer Q Haigis Holladay 1 Holladay 2 SRK-T SRK II
D SD P Value b D SD P Value b D SD P Value b D SD D SD P Value b D SD P Value b
MNE −0.22 1.22 0.28 1.33 0.61 1.22 0.05 1.13 1.19 1.21 1.98 1.32
MAE 0.95 0.78 .3941 1.03 0.87 .4886 1.07 0.84 .0804 0.82 0.77 1.34 1.04 .0006 2.02 1.25 <.0001
MedAE 0.76 1.01 0.89 0.8 1.2 1.97
N % N % N % N % N % N %
±0.50 D a 11 39 12 43 8 29 12 43 6 21 3 0
±1.00 D a 17 61 13 46 16 57 18 64 12 43 6 0
±2.00 D a 25 89 24 86 25 89 26 93 22 79 15 0

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Jan 7, 2017 | Posted by in OPHTHALMOLOGY | Comments Off on Accuracy of the Refractive Prediction Determined by Multiple Currently Available Intraocular Lens Power Calculation Formulas in Small Eyes

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