**3. Results**

A total of 11 eyes of 7 patients [1 (14%) female] were included with a mean follow up after SMILE of 2 ± 1 months (range of 1 to 4 months) and a mean follow up after cataract surgery of 8 ± 11 months (range of 1 to 38 months). The mean period of time between SMILE and cataract procedures were 31 ± 16 months (range 12 to 54 months). Subjects' baseline characteristics are summarized in Table 2. The mean pre- and post-SMILE manifest refraction spherical equivalent (SE) was −5.15 ± 1.31 diopters (D; range: −7.00 to −3.00 D) and −0.48 ± 0.57 D (range: −1.63 to +0.38 D), respectively. The mean preoperative SE before cataract surgery was −2.44 ± 2.48 D (range: −7.63 to +0.63 D). One patient developed a nuclear cataract, which lead to an index myopia of −7.63 D of SE. After cataract surgery, the mean SE amounted to −0.68 ± 0.65 D (range: −2.00 to 0.00 D).


**Table 2.** Subjects' characteristics.

SD, standard deviation; D, diopter; SMILE, small incision lenticle extraction; BCVA, best corrected visual acuity.

The performance of the investigated IOL power calculation formulae in reference to physical ray tracing is summarized in Table 3 and visualized by boxplots (Figure 1). On average, the formulae concordantly overestimated the required IOL power. Of all investigated traditional formulae, the Potvin–Hill formula yielded the smallest ME (−0.06 ± 0.86 D, range −1.67 to 1.22) and the Shammas formula resulted in the largest IOL power overestimation with a ME of −0.96 ± 1.14 D (range −2.32 to 1.07). Ray tracing was the only method resulting in a hyperopic ME of 0.18 D ± 0.48 D (range −0.43 to 1.22), even though in absolute terms the ME was the lowest (Table 3). Nevertheless, Kruskal–Wallis testing revealed no statistically significant differences in ME between the different IOL power calculation methods (*p* = 0.16).

**Table 3.** Formula performance in comparison.


D, diopters; PE, prediction error; SD, standard deviation.

**Figure 1.** Prediction errors of IOL power calculation formulae. Blue boxplots show formulae that incorporate clinical history data and green boxplots show formulae that do not use any prior keratorefractive surgery data. The red boxplots represent ray tracing. (**A**) IOL power calculation formulae ranked from left to right according to their arithmetic prediction errors. (**B**) IOL power calculation formulae ranked from left to right according to their MAE. Circles demonstrate the respective MAE of each formula. (**C**) IOL power calculation formulae ranked from left to right according to their MedAE. (D, diopter).

With respect to MAE and MedAE, ray tracing achieved the smallest MAE (0.40 D) and MedAE (0.36 D) of all examined methods. Of the various tested formulae from the ASCRS calculator, the Potvin–Hill formula yield the smallest MAE (0.66 D), closely followed by the Barrett True-K (0.80 D) and the Masket formula (0.81 D). The Potvin–Hill formula also yielded the smallest MedAE (0.52 D) of all conventional IOL formulae. Kruskal–Wallis testing, however, revealed no statistically significant differences in MAE (*p* = 0.085) and on MedAE (*p* = 0.095). Regarding the variance of ME, the ray-tracing method showed the

smallest variance (0.23 D2), followed by the Potvin–Hill (0.74 D2) and Modified Masket (0.83 D2) formulae. The Haigis-L formula showed the highest variance (1.63 D2).

With 82%, the ray-tracing method yielded the highest percentage of eyes within a refractive prediction error of ±0.50 D (Figure 2). The next best conventional formula was the Potvin–Hill formula with an ±0.50 D accuracy of 45%. The Haigis-L formula showed the lowest ±0.50 D accuracy of 9%. The Fisher's exact test indicated significant differences between proportions of eyes with PEs of ±0.50 D (*p* = 0.034). The Bonferroni correction was employed to investigate these differences in detail, showing statistically significant differences between the ray-tracing method and each of the conventional IOL power calculation formulae (all with *p* < 0.001). No statistically significant differences could be found in the proportions of eyes with PEs of ±1.00 D (*p* = 0.754). Nevertheless, the ray-tracing method achieved the highest ±1.00 D accuracy (91%), followed by the Potvin–Hill, Barrett True-K and Barrett True-K no history formulae (all 73%). The Shammas formula showed the lowest ±1.00 D accuracy of 55%.

**Figure 2.** Histogram analysis comparing the percentage of eyes within given prediction error ranges. The formulas were sorted by the proportion of eyes within ±0.50 D in descending order.
