Intraocular lens power in bilateral cataract surgery: Whether adjusting for error of predicted refraction in the first eye improves prediction in the second eye

J CATARACT REFRACT SURG - VOL 32, DECEMBER 2006

Intraocular lens power in bilateral cataract surgery: Whether adjusting for error of predicted refraction in the first eye improves prediction in the second eye James Jabbour, BSc(Med), MBBS, MPH (Hons), Les Irwig, MBBCh, PhD, FFPHM, Petra Macaskill, MAppStat, PhD, Michael Peter Hennessy, BMedSc, MB BS Qld, MBiomedE UNSW, FRANZCO

PURPOSE: To assess whether the retrospectively calculated intraocular lens (IOL) position value in the first eye reduces the error of predicted refraction in the second. SETTING: Prince of Wales Hospital, Sydney, Australia. METHODS: One hundred twenty-one consecutive patients who had bilateral cataract surgery with the same IOL (SI-30NB, Advanced Medical Optics) were identified. The case-derived A-constant in the first eye was calculated from the postoperative refraction. This value was used to calculate the adjusted error of predicted refraction in the second eye and compared against the unadjusted error in that eye (calculated using manufacturer’s A-constant). RESULTS: Axial length (r Z 0.97), corneal power (r Z 0.97), and IOL power (r Z 0.90) were strongly correlated between eyes with no statistically significant mean interocular difference. Although there was no significant interocular difference in the mean error of predicted refraction (SRK/T), there was only a moderate correlation between eyes (r Z 0.40). Using the axial length vergence formula, the mean adjusted error of predicted refraction in the second eye (0.66 diopter [D]) was significantly larger than the mean unadjusted error (0.47 D) (P Z .029). The standard deviation of the adjusted error of predicted refraction (SRK/T) in the second eye (0.85 D) was greater than the standard deviation of the unadjusted error (0.79). Similarly, the adjusted mean absolute error of predicted refraction (0.65 D) was greater than the unadjusted error (0.63 D). CONCLUSION: Adjusting the IOL power in the second eye by the amount of overprediction or underprediction in the first eye did not improve prediction accuracy because the error of predicted refraction varied independently between the 2 eyes of an individual. J Cataract Refract Surg 2006; 32:2091–2097 Q 2006 ASCRS and ESCRS

Refining theoretical and regression-derived intraocular lens (IOL) power formulas to minimize the error of predicted refraction has been the subject of much discussion and research.1–14 In the context of bilateral cataract surgery, it is unclear whether the retrospectively calculated IOL position value in the first eye improves formula prediction accuracy when calculating IOL power for the second eye. There is much evidence in the literature to suggest a high degree of optical symmetry between eyes.15 Of the variables in Fedorov et al.’s original vergence formula,16 corneal power (K) features most prominently. Myrowitz et al.17 discovered a high correlation between eyes for Q 2006 ASCRS and ESCRS Published by Elsevier Inc.

simulated keratometry (Pearson correlation coefficient r Z 0.90, P!.001) and central corneal thickness (r Z 0.95 P!.001). Chiang and Hersh18 report no significant difference in the error of predicted refraction between eyes having bilateral laser in situ keratomileusis. They extended this information to generate a theoretically derived postoperative manifest spherical equivalent (SE) refraction by adjusting for the amount of overcorrection or undercorrection in the first eye. Compared to the actual refraction in the second eye, this theoretically adjusted refraction was closer to emmetropia, particularly in the low myopia group (P!.006). Our study assessed whether the use of the refractive results 0886-3350/06/$-see front matter doi:10.1016/j.jcrs.2006.08.030

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in the first eye improved the accuracy of formula prediction in the second eye in bilateral cataract surgery. Our objectives were to (1) assess whether using the case-derived IOL position value in the first eye in the calculation of lens power for the second eye reduces the error of predicted refraction and (2) to describe the degree of symmetry between eyes for both biometric data (ie, axial length and corneal power) and the variables generated by the IOL power formulas (ie, IOL power to implant for emmetropia, predicted refraction for the IOL power implanted, error of predicted refraction, and the case IOL position; that is, the Sanders-Retzlaff-Kraff theoretical formula [SRK/T]1 A-constant and the axial length vergence formula4 effective lens position [ELP]). PATIENTS AND METHODS Two hundred and nine consecutive patients admitted under the same surgeon (M.P.H.) for bilateral cataract surgery with implantation of the same IOL model (SI-30NB, Advanced Medical Optics) between the February 1996 and March 2005 were identified through the Prince of Wales Hospital cataract surgery computerized database. Patients were excluded on the basis of either eye having 1 or more of the following characteristics: IOL inserted in the ciliary sulcus rather than the capsular bag (19 patients), stabilized postoperative best corrected visual acuity worse than 6/12 (29 patients), previous or concurrent ocular surgery such as a trabeculectomy (12 patients) or anterior vitrectomy (4 patients), no recorded measurement of the postoperative SE (24 patients), and preoperative corneal astigmatism greater than 3.00 diopters (D) (5 patients).1 The information gathered on the final study population of 121 patients (242 eyes) included demographic details (age and sex), time between operations, ultrasonic axial length, keratometric corneal power in 2 meridians, the power of the SI-30NB IOL implanted, and the postoperative SE. Two calibrated ultrasonic biometers (Quantel Cine AB Scanner, Quantel Medical; model 820 A-scanner, Allergan Humphrey) and 2 calibrated identical keratometers (Bausch & Lomb) were used during the study to measure axial length and corneal power, respectively. The measurements were always performed bilaterally with the same instrument and repeated by a different operator in the event of an ambiguous or extreme result. The postoperative SE was the optimally measured subjective spherocylindrical refraction.

The mean, standard deviation, and standard error were calculated in each eye and overall, for both the biometric and formularelated variables. The degree of association between eyes for each variable was assessed through a Pearson correlation. The mean in the first eye was compared to that in the second eye for each variable and the mean adjusted error of predicted refraction compared to the unadjusted error using the paired t test. The variability of the differences between eyes was assessed by examining the size of the standard deviation of the differences between eyes and the 95% confidence limits of agreement between eyes. These limits were the mean difference G 1.96  the standard deviation of the differences between eyes. Bland-Altman plots19–22 were generated to graphically assess whether the mean interocular difference and the standard deviation of the differences between eyes changed according to the magnitude of the variable. The relationship between the differences between the eyes and the mean between the eyes for each variable was assessed using simple linear regression. The predicted refraction in each eye was generated using both the SRK/T formula and the axial length vergence formula. The predicted refraction was subtracted from the postoperative SE to arrive at the error of predicted refraction in each eye. The case-derived A-constant (IOL position value) for the SRK/T formula in each eye was back-calculated using a stepwise numeric approach. That is, the A-constant was adjusted until the predicted refraction was equal to the postoperative SE, while the power of the IOL implanted, the axial length, and the corneal power remained constant. The ELP of the axial length vergence formula was calculated as published by Holladay.4 For the presentation of data in this study, this value was converted to the A-constant equivalent (axial length vergence).4 The predicted refraction (adjusted) in the second eye was recalculated using the case-derived A-constant in the first eye. The unadjusted predicted refraction in the first eye and second eye was calculated using the manufacturer’s A-constant. The unadjusted error of predicted refraction in the second eye was compared to the adjusted error in this eye and to the unadjusted error in the first eye. This analysis was repeated after restricting the data according to the screening guidelines advocated by Holladay et al.5 (Table 1) to assess whether removing biometrically extreme or asymmetric pairs of eyes from the data Table 1. Holladay et al.5 data-screening criteria.

Parameter Individual eye

Restriction Axial length !20.0 or O25.0 mm Corneal power !40.00 D or O47.00 D Emmetropic IOL power greater than 3.00 D from the calculated mean emmetropic IOL power*

Accepted for publication August 13, 2006. From the University of New South Wales at the Prince of Wales Hospital and the School of Public Health, University of Sydney, Sydney, Australia.

Between eye

Corneal power difference O1.00 D

No author has a proprietary or financial interest in any material or method mentioned. Corresponding author: Michael Hennessy, BMedSc, MBBS Qld, MBiomedE UNSW, FRANZCO, and James Jabbour, BSc(Med), MBBS UNSW, MPH (Hons), USyd, Department of Ophthalmology, Prince of Wales Hospital, Barker St, Randwick, New South Wales, 2031, Australia. E-mail: [email protected] and j.jab [email protected].

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Axial length difference O0.3 mm Emmetropic lens power difference O1.00 D

IOL Z intraocular lens *Holladay et al. recommend calculating this mean from the surgeon’s A-constant, a corneal power of 43.81 D, and an axial length of 23.5 mm. However, in this study, the sample mean was used to restrict the data according to these guidelines because it was markedly different from the value generated using Holladay et al’s recommendations.

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set would influence the relative standard deviation and size of the adjusted and unadjusted errors of predicted refraction. The analysis was also repeated for patients in whom the absolute error of predicted refraction in the first eye was greater than 0.50 D. RESULTS

The median time between surgery was 3 months (range 0.93 to 48 months). There were 44 men and 77 women. The number of left eyes that were operated on as first eyes (53) was roughly equivalent to the number of right eyes (68). Biometric Data and Formula-Derived Variables Between Eyes

Table 2 shows the overall mean and standard deviation in all eyes for the biometric and formula-related variables. The actual IOL power, calculated emmetropic IOL power, axial length, and corneal power were approximately normally distributed according to the normal probability plot. However, of these 4 variables, only corneal power had a statistically insignificant Shapiro-Wilk test statistic (w Z 0.99, P Z.14) consistent with a normal distribution. There was strong interocular correlation for axial length, corneal power, emmetropic and actual IOL powers (Table 2). There was no significant difference in these variables between the means in the first and second eyes or left and right eyes (Table 2). The standard deviation of the differences between eyes for axial length was 0.24 mm. Hence,

95% of the axial length interocular differences were between 0.46 mm and C0.46 mm (ie, mean G 1.96  standard deviation) (Table 2). These are the 95% confidence limits of agreement between eyes. This is equivalent to an IOL power difference between the eyes of 2.80 D using the SRK/T formula. The large standard deviation of the interocular axial length differences is reflected graphically by the wide distribution of the differences on the BlandAltman plot (Figure 1). This plot primarily shows that the mean axial length interocular difference and the variability of the differences between eyes (reflected in the size of the standard deviation) did not change as the axial length increased (Figure 1). Hence, the regression coefficient relating the difference between eyes to the mean between eyes for axial length was very small (r Z 0.038) and not statistically significant (Table 2). The standard deviation of the interocular differences and the 95% limits of agreement between eyes for corneal power, IOL power, and calculated emmetropic IOL power (Table 2) were also indicative of considerable variability between eyes. The Bland-Altman plots for these variables show that the mean difference between eyes and the standard deviation of the differences between eyes did not change as the variable increased. This was reflected in the small and statistically insignificant regression coefficients relating the difference between eyes to the mean between eyes. Table 2 also shows the mean and the standard deviation of the error of predicted refraction and of the

Table 2. Descriptive statistics.

Variable Axial length (mm) Corneal power (D) IOL power (D) Emmetropic IOL power (D) SRK/T ALV Error of predicted refraction SRK/T ALV A-constant SRK/T ALV*

Overall Mean G SD

Interocular Correlation (r)†

Regression Coefficients 95% CLs of Agreement (b) of Difference Between Eyes Against Mean Between Eyes Mean Difference Between Eyesx Between Eyes G SDz (MD G 1.96  SD_d)

23.15 G 0.91 43.48 G 1.51 21.54 G 2.06

0.97 0.97 0.90

0.0028 G 0.24 0.0470 G 0.36 0.10 G 0.93

0.46 to 0.46 0.75 to 0.65 1.73 to 1.93

0.038 0.021 0.034

21.24 G 2.24 21.73 G 2.85

0.95 0.95

0.065 G 0.74 0.098 G 0.97

1.39 to 1.52 1.80 to 2.00

0.033 0.042

0.090 G 0.79 0.430 G 0.92

0.40 0.52

0.062 G 0.86 0.085 G 0.64

 1.75 to 1.63  1.86 to 1.69

0.018 0.060

117.92 G 0.91 118.24 G 1.17

0.40 0.53

0.094 G 1.00 0.120 G 1.14

2.05 to 1.87 2.35 to 2.11

0.0078 0.0046

ALV Z axial length vergence formula; b Z regression coefficient; CL Z confidence limits; Emmetropic IOL power Z lens power calculated for emmetropia; IOLZintraocular lens; MD Z mean difference between eyes; r Z correlation coefficient; SD_d Z standard deviation of the difference between eyes; SRK/T Z Sanders-Retzlaff-Kraff theoretical *This A-constant was calculated from the axial length vergence formula ELP using the conversion method described by Holladay et al.4 † All interocular correlation coefficients were statistically significant. z There was no significant difference in the means between eyes for all variables. x None of the regression coefficients was statistically significant. The relationship between the difference between eyes and the mean between eyes was no longer statistically significant when 2 and 3 influential points were removed for axial length and IOL power, respectively.

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difference in error of predicted refraction

0.8

difference in axial length (mm)

0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 21

22

23

24

25

26

3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0 -2.0

-1.5

Figure 1. Bland-Altman plot of the difference in axial length between eyes against the mean axial length between eyes. Dotted lines represent the mean difference between eyes and the 95% confidence limits of agreement between eyes for axial length. Solid lines represent Holladay et al’s5 data-screening criteria (Table 1).

case-derived A-constant. Both variables were approximately normally distributed according to the normal probability plot and the Shapiro-Wilk test statistic. There was only moderate interocular correlation for the error of predicted refraction (r Z 0.40, SRK/T) and the customized A-constant (r Z 0.40, SRK/T) using both the SRK/T and the axial length vergence formulas. However, there was no significant interocular difference in the mean error of predicted refraction (P Z .43) or the case-derived A-constant (P Z.31) on the paired t test. The large standard deviation of the interocular difference in the error of predicted refraction (0.86 D) and the wide 95% confidence limits of agreement between eyes (1.75 to 1.63) were indicative of considerable variability in the error of predicted refraction between eyes. The Bland-Altman plot shows that the mean interocular difference in the error of predicted refraction and the standard deviation of the interocular differences did not change as the error of predicted refraction increased (Figure 2). The regression coefficient relating the difference between the eyes to the mean between the eyes for the error of predicted refraction was small (r Z 0.014) and not statistically significant (P Z.88). Similar findings were seen between eyes using the axial length vergence formula for calculating the error of predicted refraction and both formulas for generating the case-derived Aconstant (Table 2). Adjusted to Unadjusted Error of Predicted Refraction in the Second Eye

Table 3 shows the mean and standard deviation of the adjusted error and the unadjusted error of predicted

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-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

mean error of predicted refraction

mean axial length (mm)

Figure 2. Bland-Altman plot of the difference in the error of predicted refraction between eyes against the mean error of predicted refraction between eyes. Dotted lines represent the mean difference between the eyes and the 95% limits of agreement between eyes for the error of predicted refraction.

refraction in the second eye for the SRK/T and axial length vergence formulas. The adjusted error of predicted refraction was approximately normally distributed according to the normal probability plot using both formulas. Using the SRK/T formula, the intraocular correlation between the adjusted error and unadjusted error of predicted refraction in the second eye was only 0.53. The intraocular difference between the adjusted mean error and unadjusted mean error of predicted refraction was not statistically significant (P Z .53, paired t test) and closely approximated zero (0.045 D). The mean absolute adjusted error of the predicted refraction (0.65 D) was greater than the unadjusted error (0.63 D) (Table 3). In 62 of the 121 patients, the absolute unadjusted error of predicted refraction was greater than the adjusted, and vice versa for the remaining 59 patients. Because this was very close to 50%, there was little difference in the frequency with which the casederived A-constant in the first eye performed better in the second eye than the manufacturer’s A-constant. The standard deviation of the adjusted error of predicted refraction (0.85 D) was larger than the unadjusted (0.79 D), irrespective of whether the data was restricted by the Holladay et al.5 screening criteria (Table 1) or limited to patients with an absolute error of predicted refraction greater than 0.50 D in the first eye. The proportion of patients within and around the ideal range for the unadjusted error of predicted refraction (R0.30 and %0.30) was 32.2%, which was slightly greater than the 30.6% for the adjusted error. There was less than 0.90 D hyperopic error in the predicted refraction in the second eye in 12.4% of patients with the adjusted formula (ie, using the

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Table 3. Comparison of the adjusted error of predicted refraction in the second eye (case-derived A-constant from the first eye) and the unadjusted (manufacturer’s A-constant) using the SRK/T and the axial length vergence formulas. Represents all data (N Z 121).

Formula SRK/T 2nd eye unadjusted 2nd eye adjusted 2nd eye adjusted  2nd eye unadjusted ALV 2nd eye unadjusted 2nd eye adjusted 2nd eye adjusted  2nd eye unadjusted

Mean G SD

Mean Absolute Error

0.12 G 0.79 0.076 G 0.85 0.045 G 0.79

0.63 0.65 d

0.47 G 0.90 0.66 G 0.89 0.19 G 0.92*

0.83 0.91 d

ALVZ axial length vergence; SRK/T Z Sanders-Retzlaff-Kraff theoretical *Paired t test: P Z .029 (all data); P Z .0009 (Holladay et al.5 data restricted)

case-derived A-constant in the first eye) compared to 8.3% with the unadjusted formula (ie, using the manufacturer’s A-constant). The standard deviation of the differences between the adjusted error and unadjusted error of predicted refraction was large (0.79 D), and the 95% limits of agreement between the adjusted and unadjusted errors were wide (1.51 to 1.60). This is represented graphically on the Bland-Altman plot by the wide distribution of the differences between the adjusted error and unadjusted error of predicted refraction about the mean difference. The Bland-Altman plot also demonstrates that the mean difference between the adjusted error and unadjusted error of predicted refraction did not significantly change as the error of predicted refraction rose (P Z.31) (Figure 3).

(adjusted - unadjusted) error of predicted refraction

2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5

A similar pattern was observed when comparing the adjusted error and unadjusted error of predicted refraction using the axial length vergence formula. The intraocular correlation between the adjusted error and unadjusted error predicted refraction was 0.47. Table 3 shows the mean and standard deviation of the adjusted error and unadjusted error of predicted refraction. There was a myopic shift using this formula. The mean adjusted error of predicted refraction was significantly more myopic than the mean unadjusted error (P Z.029, paired t test). The standard deviation was marginally less for the adjusted error (0.89 versus 0.90); however, this reversed after the data were restricted according the screening criteria suggested by Holladay et al.5 As with the SRK/T formula, there was considerable intraocular variability in the differences between the adjusted error and the unadjusted error of predicted refraction. The standard deviation of the differences between the adjusted error and unadjusted error of predicted refraction was 0.92 D, and the 95% confidence limits of agreement on the Bland-Altman plot were 0.19 D (the mean difference) G 1.84 D. The mean difference between the adjusted error and unadjusted error of predicted refraction and the standard deviation of the differences did not change significantly as the error of predicted refraction rose (0.022) (P Z.81). DISCUSSION

-3.0 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0

mean of adjusted and unadjusted error of predicted refraction Figure 3. Bland-Altman plot of the differences between the adjusted and unadjusted error of predicted refraction in the second eye against the mean of the adjusted and unadjusted error of predicted refraction. Dotted lines represent the mean difference between the adjusted error and the unadjusted error of predicted refraction in the second eye and the 95% confidence limits of agreement between the adjusted error and unadjusted error of predicted refraction.

The strong interocular correlation for axial length, corneal power, and implanted and emmetropic IOL powers in our study and elsewhere suggests a high degree of optical symmetry between eyes.15,7,23 Despite the strong biometric interocular correlation and the insignificant mean difference between eyes, there was considerable variability in individual patient interocular differences in each biometric variable. For example, the differences between eyes in axial length had a large standard deviation (0.24 mm). Because differences in axial length between eyes varied

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considerably in our study and even small differences in axial length result in a meaningful change in refraction,15,24–28 the axial length in the first eye unreliably estimated the value in the second eye. Because there was poor interocular correlation and considerable variability in the differences between eyes for the error of predicted refraction, the value in the first eye poorly estimated the value in the second eye. Hence, the standard deviation of the error of predicted refraction (and the mean absolute error) in the second eye using the case-derived A-constant in the first eye was greater than when the manufacturer’s A-constant was used. The mean adjusted error of predicted refraction was significantly larger than the unadjusted error using the axial length vergence formula, probably because there was no adjustment of the IOL position value for axial length and corneal power. The weak intraocular correlation and the large standard deviation of the differences between the adjusted error and unadjusted error of predicted refraction are also a reflection of the variability in the differences between eyes for the error of predicted refraction. These findings suggest that when using the SRK/T or axial length vergence formula, surgeons should not correct the IOL power in the second eye by the amount of overprediction or underprediction in the first eye because in most cases, this leads to a greater error of predicted refraction. Instead, surgeons should continue to use the surgeon’s or manufacturer’s A-constant in the second eye (instead of the case-derived A-constant in the first eye) to calculate IOL power. The poor interocular correlation in the error of predicted refraction may be attributed to measurement error.29 In a study based on the preoperative and postoperative biometry in 584 patients, Olsen30 found that 54% (0.76 D) of the error of predicted refraction was attributable to axial length errors, 8% (0.29 D) to corneal power errors, and 38% (0.43 D) to the estimation of postoperative anterior chamber depth. Interocular asymmetry in the error of predicted refraction in each pair of eyes probably represents asymmetry in the degree of measurement error for axial length and corneal power. In 7 ophthalmic practices across Europe and the United States, Norrby31 found the repeatability of axial length and corneal power measurements to be 0.30 mm (0.75 D) and 0.06 mm (0.36 D), respectively. We found similar repeatability results.25 The contribution of errors peculiar to the surgical environment (IOL style, IOL position, wound closure and suturing, capsulorhexis configuration, technician, surgeon, postoperative steroids5), which may have changed between the 2 admissions for cataract surgery, may also partly explain why the error of predicted refraction differed between eyes in our study. Maintaining a constant surgical environment and minimizing biometric measurement error will reduce the error of predicted refraction and possibly reveal a greater degree

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of correlation between eyes that may be exploited to enhance the precision of the predicted refraction in the second eye. Our hypothesis should be retested using other techniques to measure axial length such as partial coherence interferometry,32 other new calculation formulas to calculate IOL power, and other methods of determining IOL power such as intraoperative aphakic autorefractive retinoscopy.33 When using the SRK/T and axial length vergence formulas, we propose that surgeons continue to calculate IOL power using the manufacturer’s or the surgeon’s A-constant. Because the case-derived A-constants in our study were moderately correlated between eyes (Table 2), surgeons retrospectively calculating their personalized A-constant from a series of their own patients should adjust for interocular correlation using a random effects model.34–36 This enhances the power and the precision of the surgeon’s A-constant and avoids selection bias related to the exclusion of one eye over the other.34 In conclusion, when axial length was measured by ultrasound, there was no justification for clinically or theoretically adjusting the formula-derived IOL power in the second eye by the amount of overprediction or underprediction in the first, even when this was very large. Surgeons should take into account the refraction in first eye when planning the targeted refraction for the second eye.

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