Calculation of proper intraocular lens (IOL) power after laser in situ keratomileusis (LASIK) and photorefractive keratectomy (PRK) has been one of the most challenging tasks for cataract surgeons over the past 20 years. Relying on standard formulas leads to inaccurate results for 3 reasons: the keratometric index (or index of refraction) error, the radius (or instrument) error, and the formula error.1 As a consequence, eyes with previous myopic correction may end up with a hyperopic refraction, and eyes with previous hyperopic correction may end up with a myopic refraction. More than 30 methods have been published to calculate IOL power. Choosing the best calculation value is difficult because large discrepancies may be found among the available solutions. Several studies have compared such methods.2–5 In 2010,5 our group published a paper reporting the results in 3 different groups of eyes: those in which all perioperative data were available (ie, preoperative corneal power and laser-induced refractive change), those with known preoperative corneal power and uncertain refractive change, and those with known refractive change but unknown preoperative corneal power. This approach was chosen to determine the best methods for each clinical situation because not all patients have complete perioperative data available to them, and many come to our attention with no data at all.
The purpose of the present study was to follow the same approach to determine the best methods in a larger group of eyes.
Patients and methods
All patients who were examined in a private practice between September 2005 and March 2014 were prospectively enrolled. Informed consent was obtained from each patient, and the study was approved by the local ethics committee. The study methods adhered to the tenets of the Declaration of Helsinki for the use of human participants in biomedical research.
The same methods described in a previous paper5 were adopted for the following procedures: exclusion criteria, corneal power and axial length (AL) measurement techniques, A-constant selection, IOL power calculation, back-calculation of the IOL for emmetropia, and the IOL power prediction error. The latter was computed as the difference between the predicted IOL power and the back-calculated IOL power for emmetropia, with positive values indicating an overpredicted IOL power and a subsequent myopic refractive outcome.
Four groups of eyes were defined on the basis of the available clinical data:
- Group 1: Preoperative corneal power available, preoperative and postoperative refraction (ie, the surgically induced refractive change) known and certain.
- Group 2: Preoperative corneal power available, surgically induced refractive change known but uncertain (in most cases because the postoperative refraction was unknown).
- Group 3: Preoperative corneal power unknown, surgically induced refractive change known, even if the refractive measurements were uncertain.
- Group 4: Both preoperative corneal power and surgically induced refractive change unknown.
Two categories of methods were evaluated. The former included simulated keratometry and methods adjusting the overestimation of corneal power (ie, the clinical history method), calculated at the corneal plane6,7; the Seitz/Speicher method8,9; the Seitz/Speicher/Savini method10; the no-history method by Shammas et al.11,12; the method described by Camellin and Calossi13; Savini et al.14; Awwad et al. (equation 2)15; Rosa et al.,16 with its later modification17; and Ferrara et al.18
The latter category included the methods that directly correct the calculated IOL power; that is, the formula and nomogram by Feiz et al.,19 the method described by Latkany et al.,20 the corneal bypass method,21,22 the method described by Masket and Masket,23 and the method described by Diehl and Miller et al.24 and later refined by Date et al.25
Methods relying on specific instruments such as partial coherence interferometry (PCI) (IOLMaster, Carl Zeiss Meditec AG) or Scheimpflug imaging (Pentacam, Oculus Optikgeräte GmbH) for which measurements were not available for all eyes were not included.26–31
The double-K formulas by Aramberri32 were used for the first category of methods as previously described.5,33 For eyes in Group 4, the average preoperative corneal power of Groups 1 and 2 (ie, 43.54 diopters [D]) was entered into the double-K SRK/T formula.
The median absolute error, mean absolute error (MAE), and mean arithmetic error in IOL power prediction were calculated for each method. The median absolute error, MAE, and mean arithmetic error in refraction prediction were calculated as the difference between the predicted and the postoperative refraction. In the case of methods requiring a modified corneal power to be entered into the single- or double-K formulas, the predicted refraction was calculated using the equations originally described for each formula,34–36 and the error in refraction prediction was obtained by subtracting the postoperative from the predicted refraction. As for the methods adjusting IOL power (Masket, Latkany, Feiz, corneal bypass, Diehl/Miller), the error in IOL power prediction was multiplied by 0.7 as previously done by others.2,19 Due to the different IOL models included in this study, constant optimization could not be carried out to obtain a zero mean arithmetic error, so the accuracy of these values cannot be considered optimal.
Unless otherwise indicated, all data are expressed as the mean ± standard deviation. Linear regression was used to analyze relationships between variants. A P value less than 0.05 was considered statistically significant. Statistical tests were performed using Graphpad Instat software (version 3a for Macintosh, Graphpad Software, Inc.).
In the case of patients having cataract surgery in both eyes, only the first eye operated on was included in the analysis, unless the 2 eyes were classified as belonging to different groups.
Ninety-two patients were examined. Due to the above-mentioned criteria or the lack of post-cataract surgery refraction, 22 eyes were excluded. Hence, 70 eyes of 70 patients were analyzed. Of these, 19 eyes were directly examined by the same author (G.S.), and the data from the remaining 51 eyes were submitted via e-mail by other surgeons who sought an opinion as to the power of the IOL to be implanted. The mean patient age was 50.1 years ± 9.2 (SD). The mean interval of time between refractive surgery and cataract surgery was 7.3 ± 3.5 years.
Of the 70 eyes enrolled, 30 were placed in Group 1, 16 in Group 2, 18 in Group 3, and 6 in Group 4 (PRK = 44, LASIK = 26). Their clinical features, such as mean AL, preoperative corneal power, and surgically induced refractive surgery, are shown in Table 1.
Cataract extraction was uneventfully performed by phacoemulsification in all cases; the A-constant of the implanted IOL was 118.4 in 41 eyes, 118.7 in 15 eyes, 119 in 3 eyes, 118 in 4 eyes, 118.5 in 2 eyes, 118.2 in 2 eyes, 118.3 in 1 eye, 119.4 in 1 eye, and 119.6 in 1 eye.
Table 2 shows for each group the mean postoperative corneal power as calculated using the different methods. Simulated K provided the highest mean corneal power in all groups, and Ferrara’s variable refractive index method always resulted in the lowest one.
When the preoperative corneal power was available and the refractive change induced by the laser was considered certain (Group 1; Table 3), the lowest median absolute error in IOL power (0.39 D) and refraction (0.29 D) prediction was obtained with Savini’s method, for which the rate of eyes within ±0.50 D of the predicted refraction was 70% (21 of 30 eyes). Coincidentally, this method achieved a 0.01 D mean artithmetic error, which is the same result that would be expected with constant optimization. As a consequence, the resulting median absolute error can be compared to the corresponding values reported in studies investigating unoperated eyes, where constant optimization is performed. However, the highest rate of eyes within ±0.50 D of the predicted refraction was achieved by the Seitz/Speicher/Savini (76.7%) and Masket (73.3%) methods. Good results were also achieved with the methods described by Seitz and Speicher, Awwad, Camellin, and Latkany, for which the median absolute error in refraction prediction was lower than 0.50 D and more than 50% of eyes within ±0.50 D of the predicted refraction (18, 17, 16, and 18 eyes, respectively). Fair results were observed with the methods of Shammas and Diehl/Miller. The remaining methods produced poor outcomes, with the MAE in IOL power prediction of higher than 1.0 D. This was also the case with the clinical history method, for which no difference was found between the double-K Hoffer Q, Holladay 1, and SRK/T formulas (although the clinical history method with the double-K Hoffer Q yielded a higher rate of eyes within ±0.50 D of the back-calculated IOL for emmetropia).
In Group 2 (Table 4), in which the refractive change was uncertain, the method described by Seitz and Speicher, with and without Savini’s adjustment, produced the lowest median absolute error in IOL power (0.52 D) and refraction prediction (0.36 D and 0.37 D, respectively). It also resulted in the highest rate of eyes within ±0.50 D of the predicted refraction (75%). Results were good with the methods described by Masket and Camellin; fair with those of Savini, Shammas, and Awwad; and poor with the remaining ones.
In Group 3 (Table 5), Masket’s method achieved the lowest median absolute error in refraction prediction (0.24 D) and highest rate of eyes within ±0.50 D of the predicted refraction (13 of 18 eyes, 72.2%), notwithstanding the mean underestimation of IOL power (−0.58 ± 0.93 D). Excellent results were also obtained with the Shammas and Seitz/Speicher/Savini methods, which achieved 11 eyes (61.1%) within ±0.50 D of the target refraction, with a median absolute error in refraction prediction lower than 0.40 D. Good results were obtained by Savini’s and Camellin’s methods (9 eyes [ie, 50.0% of eyes ±0.50 D of the predicted refraction]), whereas Diehl/Miller’s, Latkany’s, and Rosa’s modified methods gave fair results. The remaining methods had poor results.
Most methods with poor outcomes were highly sensitive to the surgically induced refractive change as their results were worse in eyes with higher corrections. For example, after Groups 1 and 2 were merged, a statistically significant correlation was found between the refractive change and the corneal bypass method (R2 = 0.2418, P = .001), which overestimated IOL power in eyes with a higher refractive change. A similar result was observed for the Feiz formula (R2 = 0.2971, P < .001) and nomogram (R2 = 0.6405, P < .001) and, after Groups 1, 2, and 3 were merged, for Diehl/Miller’s method (R2 = 0.3657, P < .001).
In Group 4 (Table 6), the best performance was shown by Shammas’s no-history method, which achieved 5 of 6 eyes (83.3%) within ±0.50 D of the predicted refraction with a low median absolute error in IOL power prediction (0.45 D) and refraction prediction (0.31 D). Good results were achieved also with the Seitz/Speicher/Savini method, with 4 of 6 eyes (66.7%) within ±0.50 D of the target refraction.
In all groups, entering the simulated K into the double-K SRK/T led to IOL power underestimation by about 1.0 D on average.
This study shows that accurate IOL power calculation after myopic LASIK and PRK is possible. In each group of eyes, the best methods provided a percentage of eyes within ±0.50 D of the predicted refraction similar to that achieved in normal unoperated eyes and higher than the 55% value established as the benchmark standard by the National Health Service of the United Kingdom.37 Several studies have shown that in eyes with no previous corneal refractive surgery, a refraction within ±0.50 D of the target is achieved in 70% to 80% of cases.38–40 The best methods in Group 1 (ie, Savini, Seitz/Speicher/Savini, and Masket) enabled us to achieve such a result in 70.0%, 76.7%, and 73.3% of cases, respectively. The median absolute error (0.29 D, 0.35 D, and 0.34 D) and MAE (0.39 D, 0.49 D, and 0.48 D) in refraction prediction with these methods were also similar to those reported for unoperated eyes. These formulas do not completely eliminate the risk for refractive surprises as the prediction error in refraction ranged from about −1.0 D to about +1.0 D, but this finding is also expected in unoperated eyes. In addition to the above-mentioned methods, others gave good results and should be considered when choosing the IOL power (ie, those described by Awwad, Seitz/Speicher, Latkany, Camellin, Shammas, and Diehl/Miller). In Group 1 we also tested the Masket formula as modified by Wang et al.2 and currently available on the ASCRS calculator,A and we did not find any significant advantage over the original formula as the median absolute error in IOL power prediction was 0.53 D (0.48 D with the original formula).
Even when the refractive change induced by the excimer laser was uncertain, as in Group 2, good results could be achieved. In this case, the best methods were the ones described by Seitz and Speicher, which achieved a 75% rate of eyes within ±0.50 D of the predicted refraction (this rate did not change with or without Savini’s adjustment). This result is not surprising as the method of Seitz and Speicher does not rely on the refractive change but only on topographic data. Good results also were observed with the Masket, Camellin, and Savini methods, although they depend on the refractive change and thus had lower accuracy than Seitz and Speicher’s method.
When preoperative corneal power was unknown (Group 3), Masket’s method23 provided the best solution, with 72.2% of eyes within ±0.50 D of the target refraction and a median absolute error in refraction prediction as low as 0.24 D. Good results also were obtained by means of the Shammas, Seitz/Speicher/Savini, and to a lesser extent, Camellin and Savini methods. The good performance of the Masket and Shammas methods was foreseeable as the former does not require knowledge of the preoperative corneal power and the latter is a no-history method. With the Seitz/Speicher/Savini, Camellin, and Savini methods, it should be highlighted that they require the double-K formulas, and thus the preoperative corneal power has to be known or estimated. The approach we followed seems to be quite accurate in this respect.
Eyes with no perioperative data at all were the minority (ie, only 6 of 70), which represents an unexpected finding. In such cases, the most accurate solution was provided by the Shammas no-history method (83.3% of eyes within ±0.50 D of the target refraction). Of course, this result has to be considered with caution due to the small sample. Nevertheless, it is interesting to know that a reliable method can be used even when no data are available. Using a mean estimated preoperative corneal power (43.54 D) is another useful option for these eyes when using the Seitz/Speicher/Savini method.
Figure 1 illustrates a decision tree to assist ophthalmologists in choosing the best method for their patients in each group of eyes.
The results in this study confirm those in our previous paper,5 in which we reported that the most accurate methods were those proposed by Seitz and Speicher, Savini, Masket, and Shammas. They also confirm the results in other studies showing that that the methods by Seitz/Speicher/Savini,41 Savini,3 Masket,2–4 and Shammas12 can provide good results in these eyes.
On the other hand, even the most accurate methods showed different results in the various subgroups. The median absolute error of Savini’s method ranged from 0.29 D (Group 1) to 0.57 D (Groups 2 and 3). This discrepancy can be ascribed to the high dependency of this method on the refractive change, which was uncertain in Groups 2 and 3. The median absolute error of Masket’s method ranged from 0.24 D (Group 3) to 0.34 D (Group 1) and 0.50 (Group 2). Also in this case, the relatively worse result in Group 2 is likely to depend on the uncertain refractive change information. Conversely, the method by Seitz/Speicher revealed more constant results as the median absolute error ranged from 0.37 D (Group 2) to 0.42 D (Group 1); this is likely related to the fact that this method is not based on any refractive change data. Finally, the median absolute error of the method by Shammas ranged from 0.31 D (Group 4) to 0.63 D (Group 2). In this case, the variable results may depend on the lack of correlation with the amount of attempted correction and the small sample in Group 4.
An important consideration arising from our findings is that no expensive technology is required as all the methods are based on standard biometry equipment. More sophisticated technologies are available today, but their cost is considerably higher. Exact ray tracing can be computed to calculate IOL power; however, to maximize accuracy the posterior corneal curvature has to be measured, which can be done with Scheimpflug cameras or optical coherence tomography (OCT). Our group recently reported good results (median absolute error 0.25 D; 71.4% of eyes within ±0.50 D of the predicted refraction) with the ray-tracing software included in a rotating Scheimpflug camera combined with Placido topography (Sirius, Costruzione Strumenti Oftalmici).42 Tang et al.43 reported a 0.50 D MAE in refraction prediction using corneal power measurements by OCT and calculating IOL power by ray tracing. Similar results have been achieved with intraoperative refractive biometry (Optiwave Refractive Analysis, Wavetec Vision). Ianchulev et al.44 reported a median absolute error of 0.35 D and 67% of eyes within ±0.50 D of the predicted refraction when this technology was used. Overall, these systems are more user-friendly as they do not need complicated files and formulas and are likely to undergo further refinement that will lead to even better results. However, to date, they do not show any real refractive advantage over the best methods investigated in the present study.
The present study has limitations. First, we did not enter optimized constants into the IOL power formulas, but this would have been impossible given the great number of IOL models and instruments used by several ophthalmologists for this study. Second, we calculated IOL power using the double-K versions of the SRK/T formula and, in selected cases, the Holladay 1 and Hoffer Q formulas; different results might have been obtained with the Haigis formula,45 which calculates the effective lens position without being influenced by the postoperative corneal power. Third, when calculating the post-refractive surgery corneal power, we did not include many methods requiring specific instrumentation, such as the equivalent K reading, the modified double-K method, and the BESSt formula used with the Pentacam,27,30,31 the Haigis-L formula of the IOLMaster,29 the Galilei Total Corneal Power, the Orbscan Total Axial and Optical Power,28 or the methods described by Wang, Maloney28 and Awwad (equation 1).15 Nor did we investigate the accuracy of the C-concept developed by Olsen.46
In conclusion, we demonstrated that currently available methods to calculate IOL power after myopic excimer laser surgery can achieve results with accuracy equivalent to that obtained in unoperated eyes without relying on sophisticated technology.
What Was Known
- Previous data from a small sample of eyes (n = 28) showed that when the preoperative corneal power and refractive change are known, the Seitz/Speicher/Savini, Seitz/Speicher, Savini, Masket, and Shammas methods provide the best results in IOL power calculation.
- When preoperative corneal power is unknown, the lowest MAEs are obtained with the methods by Masket, Savini, and Seitz/Speicher/Savini. No results were available for eyes with no perioperative data. The percentage of eyes whose refraction was within ±0.50 D of the predicted value was not calculated.
What This Paper Adds
- Data on a larger sample (n = 70) revealed that in patients having cataract surgery after myopic excimer laser, a refraction within ±0.50 D of the predicted value can be obtained in more than 70% of eyes in all study groups.
- The methods by Savini, Seitz/Speicher, and Masket are the most accurate when the preoperative corneal power and refractive change are known.
- The method by Seitz/Speicher is the most accurate when the preoperative corneal power is known and the refractive change is uncertain.
- The method by Masket is the most accurate when the preoperative corneal power is unavailable and the refractive change is known.
- The method by Shammas is the most accurate when neither the preoperative corneal power not the refractive change are known.
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