**Purpose**:
To evaluate the accuracy of the optical coherence tomography–based (OCT formula) and Barrett True K (True K) intraocular lens (IOL) calculation formulas in eyes with previous radial keratotomy (RK).

**Methods**:
In 95 eyes of 65 patients, using the actual refraction following cataract surgery as target refraction, the predicted IOL power for each method was calculated. The IOL prediction error (PE) was obtained by subtracting the predicted IOL power from the implanted IOL power. The arithmetic IOL PE and median refractive PE were calculated and compared.

**Results**:
All formulas except the True K produced hyperopic IOL PEs at 1 month, which decreased at ≥4 months (all *P* < 0.05). For the double-K Holladay 1, OCT formula, True K, and average of these three formulas (Average), the median absolute refractive PEs were, respectively, 0.78 diopters (D), 0.74 D, 0.60 D, and 0.59 D at 1 month; 0.69 D, 0.77 D, 0.77 D, and 0.61 D at 2 to 3 months; and 0.34 D, 0.65 D, 0.69 D, and 0.46 D at ≥4 months. The Average produced significantly smaller refractive PE than did the double-K Holladay 1 at 1 month (*P* < 0.05). There were no significant differences in refractive PEs among formulas at 4 months.

**Conclusions**:
The OCT formula and True K were comparable to the double-K Holladay 1 method on the ASCRS (American Society of Cataract and Refractive Surgery) calculator. The Average IOL power on the ASCRS calculator may be considered when selecting the IOL power. Further improvements in the accuracy of IOL power calculation in RK eyes are desirable.

^{1}The treatment used 4 to 32 radial incisions to flatten the central cornea and correct myopia.

^{1,2}The challenges in intraocular lens (IOL) power calculations in eyes following RK include

^{2–4}(1) difficulties in determining true corneal refractive power due to the anterior and posterior corneal irregularities induced by the RK incisions, (2) inaccurate estimation of the effective lens position,

^{5}and (3) hyperopic shift over time.

^{6–8}Studies have reported accuracy of IOL power calculations in eyes with previous RK, using corneal powers obtained from various corneal topography/tomography, such as Orbscan,

^{9}EyeSys,

^{10}Tomey,

^{11}Atlas,

^{12}and Pentacam.

^{13}Unfortunately, the refractive outcomes after cataract surgery in these RK eyes are still very challenging to predict, and no single method has been reported to be superior to others in determining IOL powers.

^{14}uses data from the RTVue (Optovue, Inc., Fremont, CA, USA). For this formula, the OCT is used to measure anterior and posterior corneal power within the central 3 mm. Barrett

^{15,16}proposed a universal theoretical formula more than 20 years ago, and the True K formula was developed for eyes with previous corneal refractive surgery and was derived from the Barrett Universal II formula, which is a modified version of the original universal theoretical formula.

^{14,17–21}In this study, using data from two study centers, we evaluated the accuracy of the IOL power calculation methods on the ASCRS postrefractive calculator in eyes with previous RK.

*n*= 41; Fort Worth, TX, USA) and the Abbott Medical Optics lenses (ZCB00, ZA9003, and ZCT toric series,

*n*= 54; Santa Ana, CA, USA).

^{17}This method uses the anterior corneal power, posterior corneal power, and central corneal thickness obtained from the RTVue, and axial length (AL) and anterior chamber depth (ACD, defined as the distance from the corneal epithelium to the crystalline lens) obtained from the IOLMaster. The effective lens position was predicted by using a regression-derived formula based on ACD constant, AL of the eye, and a fixed posterior corneal power of −5.65 D, which was the mean posterior corneal power in a group of normal eyes with the OCT (data not published). For IOL power calculation, the net corneal power was converted to an effective corneal power based on linear regression analysis, and an eye model consisting of three optical surfaces (cornea, IOL, and retina) was used to calculate the OCT IOL power.

^{17}The detailed formulas have been described by Huang and colleagues.

^{17}Briefly, both the cornea and the IOL were modeled as thin lenses. Light traveled through the first three surfaces and was focused on the retina.

^{15,16}was used to calculate the IOL power. This formula uses corneal power, AL, and ACD values obtained from the IOLMaster. Details regarding the design of the True K and Universal II formulas are not published.

^{22}with each formula for each eye, the refractive PE was calculated from the IOL PE. In this study, we calculated the absolute refractive PE both with and without adjusting the mean PE to zero. The median absolute refractive PEs were calculated. The percentage of eyes within refractive PE of ±0.50 D, ±1.00 D, ±1.50 D, and ±2.00 D were computed for each method.

- Comparison of methods in the whole group: Results using four methods were compared: DK-Holladay–IOLM, OCT formula, True K, and Average of these three formulas; and
- Comparison of methods in the subgroup: In eyes with Atlas corneal topography measurements, results using five methods were compared: DK-Holladay–Atlas, DK-Holladay–IOLM, OCT formula, True K, and Average of these four methods.

*t*-test or Wilcoxon one-sample signed rank test was used to assess if the mean arithmetic IOL PEs produced by various methods were significantly different from zero. A nonparametric method, Wilcoxon test, was performed to compare the absolute refractive PEs using different formulas. The McNemar test was used to compare percentages of eyes ±0.5 D, ±1.0 D, ±1.5 D, and ±2.0 D of refractive PEs. Bonferroni correction was applied to adjust for multiple comparisons. The Bonferroni correction is a multiple-comparison correction used when several dependent or independent statistical tests are being performed simultaneously, in order to avoid spurious positives. The SPSS 22.0 for Windows (SPSS, Inc., Chicago, IL, USA) was used for statistical analysis, and

*P*< 0.05 was considered statistically significant. For sample size, we wished to detect a difference of one-half of the standard deviation of differences between two formulas. With a significance level of 5% and a test power of 80%, 32 eyes were required in each group.

**Table 1**

*P*< 0.05). The True K formula had more myopic IOL PEs than did the DK-Holladay–IOLM, OCT formula, and Average at all visits (all

*P*< 0.05). The IOL PEs for all formulas shifted in a myopic direction at each subsequent visit after the surgery (all

*P*< 0.05) (Table 3).

**Table 2**

**Table 3**

*P*< 0.05). There were no significant differences among other formulas.

**Table 4**

**Table 5**

*P*< 0.05) (Table 6). The True K formula had significant smaller IOL PEs than did all other formulas at 1 month (all

*P*< 0.05). There were no significant differences among other formulas.

**Table 6**

**Table 7**

**Table 8**

^{4}have reported that, following cataract surgery, RK eyes experience an initial hyperopic shift caused by an early postoperative corneal flattening of greater than or equal to 1 D, which partially regresses. In this study, we separated all cases into subgroups with postoperative follow-up at 1 month, 2 to 3 months, and ≥4 months. At 1 month postoperatively, all formulas except the True K produced hyperopic IOL PEs. As anticipated, compared to IOL PEs at 1 month, IOL PEs shifted in a more myopic direction with all formulas over time. The RK incisions swell during cataract surgery, and the swelling can induce central corneal flattening, which results in excessive hyperopia immediately postoperatively.

^{4}As the swelling subsides over time, refraction may shift to less hyperopic or more myopic. These RK patients may experience fluctuations in their refractive state for many weeks after the cataract surgery.

^{12}have evaluated the ASCRS calculator for eyes with previous RK. Two formulas on the calculator were assessed: the average central power, using the equivalent keratometry reading at a 4.5-mm optical zone obtained from the Pentacam and the Atlas 1-4 mm. In 15 eyes with postcataract refraction at an average of 4.33 ± 3.70 months, the authors report that, with the Atlas 1-4 mm, the mean IOL PE is 1.07 D, and the percentages of eyes within 0.5 D and 1.0 D of refractive PEs are 0.0% and 46.67%, respectively. In our study, with the Atlas 4-mm zone (DK-Holladay–Atlas), we found slightly smaller (or less hyperopic) IOL PEs, and the percentages of eyes within ±0.5 D and ±1.0 D of refractive PEs ranged from 41% to 44% and 65% to 75%, respectively. In 10 eyes, Canto et al.

^{23}report that the ASCRS calculator, using the IOLMaster data, produces 14% and 43% of eyes within ±0.5 D and ±1.0 D of IOL PE. In our study, the IOLMaster, using the ASCRS calculator, had 25% to 54% and 49% to 62% of eyes within ±0.5 D and ±1.0 D of IOL PEs at different visits.

^{19}nicely demonstrates the differences in outcomes between RK eyes and LASIK/PRK eyes. In that study, we compare the OCT formula, the True K formula, and the methods on the ASCRS calculator in eyes with previous myopic LASIK/PRK. The median absolute refractive PEs are 0.35 D, 0.42 D, and 0.35 D for the OCT formula, the True K formula, and the average of formulas on the ASCRS calculator, respectively; 58.7% to 68.3% of eyes are within 0.5 D of refractive PEs, and 90.4% to 94.2% of eyes are within 1.0 D of refractive PEs. In contrast, for the RK eyes in our current study, results were much poorer. We found that the median absolute refractive PEs were 0.65 to 0.77 D, 0.60 to 0.77 D, and 0.46 to 0.61 D for the OCT formula, the True K formula, and the average of formulas on the ASCRS calculator, respectively; and only 27% to 58% of eyes were within 0.5 D of refractive PEs and 62% to 77% of eyes within 1.0 D of refractive PEs.

^{22}Calculating IOL power PEs using the ASCRS calculator is a readily reproducible method for evaluating calculation errors using various formulas on the calculator in eyes with previous corneal refractive surgery. This method has been used by other authors who have evaluated outcomes with the ASCRS calculator.

^{12,19,23–25}Additionally, the IOL power PEs provide direct information for surgeons when they select IOL powers.

**J.X. Ma**, None;

**M. Tang**, Optovue, Inc. (F);

**L. Wang**, None;

**M.P. Weikert**, None;

**D. Huang**, Optovue, Inc. (F);

**D.D. Koch**, Alcon (C), Albott Medical Optics (C), Revision Optics (C)

*. 1982; 100: 578–580.*

*Arch Ophthalmol**. 1992; 110: 351–356.*

*Arch Ophthalmol**. 1992; 33: 3271–3282.*

*Invest Ophthalmol Vis Sci**. 1989; 108: 676–682.*

*Am J Ophthalmol**. 2003; 29: 2063–2068.*

*J Cataract Refract Surg**. 2015; 2015: 592495.*

*Case Rep Ophthalmol Med**. 1996; 12: 160–162.*

*J Refract Surg**. 1994; 112: 1298–1308.*

*Arch Ophthalmol**. 2009; 25: 1061–1074.*

*J Refract Surg**. 1999; 30: 155–159.*

*Ophthalmic Surg Lasers**. 2007; 33: 1045–1050.*

*J Cataract Refract Surg**. 2011; 5: 1243–1247.*

*Clin Ophthalmol**. 2013; 39: 358–365.*

*J Cataract Refract Surg**. 2010; 26: 430–437.*

*J Refract Surg**. 1993; 19: 713–720.*

*J Cataract Refract Surg**. 1987; 13: 389–396.*

*J Cataract Refract Surg**. 2013 ; 111: 34–45.*

*Trans Am Ophthalmol Soc**. 2012 ; 38: 589–594.*

*J Cataract Refract Surg**. 2015; 122: 2443–2449.*

*Ophthalmology**. 2015; 122: 1096–1101.*

*Ophthalmology**. In press.*

*J Cataract Refract Surg**. 2001; 20: 792–797.*

*Cornea**. 2013; 29: 484–489.*

*J Refract Surg**. 2010; 36: 1466–1473.*

*J Cataract Refract Surg**. 2013; 39: 1327–1335.*

*J Cataract Refract Surg*