Fifty-six eyes of fifty-six patients were included in the final analysis. A summary of the demographic data can be found in Table 1.
Table 1
Demographics of the study participants.
Variables | Mean Value ± SD (Range) |
Number of eyes | 56 eyes of 56 patients |
Right/Left | 32/24 |
Male/Female | 31/25 |
Age at time of surgery (years) | 59.2 ± 9.2 (39–77) |
Axial Length (mm) | 26.58 ± 1.39 (23.91–29.88) |
Keratometry (D) | 39.82 ± 2.39 (32.17–45.07) |
Total Keratometry (D) | 38.73 ± 2.58 (31.20–44.97) |
Anterior Chamber Depth (mm) | 3.27 ± 0.32 (2.62–4.02) |
Lens Thickness (mm) | 4.34 ± 0.42 (3.18–5.17) |
Central Corneal Thickness (µm) | 485 ± 45 (376–568) |
IOL Power Implanted (D) | 20.37 ± 2.33 (14.0–25.0) |
All biometric measurements obtained preoperatively using IOL Master700 (Carl Zeiss Meditec AG, Jena, Germany). D = Diopter; SD = Standard deviation.
Table 2 and Fig. 1 show the prediction errors for each formula. The Barrett True-K TK had the lowest mean and median predicted refractive error of all the formulas considered, while the EVO K had the largest median predicted error. The Haigis-L formula and the Pearl-DGS formula demonstrated a myopic average predicted error. The Haigis-L also had the largest range in predicted values of all the formulas considered.
Table 2
Prediction error of each formula.
Formulae | Mean (D) | SD (D) | Median(D) | Min(D) | Max (D) |
Barrett True K | 0.18 | 0.56 | 0.17 | -0.80 | 2.45 |
Barrett True-K TK | 0.02 | 0.58 | -0.01 | -0.97 | 1.94 |
Haigis-L | -0.18 | 0.81 | -0.16 | -3.55 | 1.27 |
Haigis TK | 0.12 | 0.53 | 0.11 | -0.77 | 1.67 |
EVO K | 0.37 | 0.60 | 0.28 | -0.67 | 2.15 |
EVO PK | 0.18 | 0.47 | 0.11 | -0.68 | 1.74 |
Pearl-DGS | -0.13 | 0.53 | -0.17 | -1.11 | 1.68 |
Hoffer QST | 0.40 | 0.66 | 0.24 | -0.74 | 2.16 |
Hoffer QST PK | 0.26 | 0.58 | 0.16 | -0.76 | 2.15 |
Prediction error calculated by subtracting the predicted value with the IOL implant from the postoperative subjective spherical equivalent.
D = Diopter; SD = Standard deviation; Min = Minimum; Max = Maximum.
The prediction error values of the Haigis-L were significantly myopic compared with other methods: the Barrett True-K (p < 0.001), Haigis TK (p < 0.01), Hoffer QST (p < 0.01), EVO K (p < 0.001), EVO TK (p < 0.001), and Hoffer QST PK (p < 0.01). The prediction error of the Barrett True-K TK was also statistically significantly smaller when compared to the Barrett True-K (p < 0.01), Hoffer QST (p < 0.001), and EVO K (p < 0.001). The prediction error of the Pearl-DGS was statistically more myopic compared to the Barrett True-K TK (p < 0.001). The prediction error of the Haigis TK was statistically smaller than those using the EVO K (p < 0.001), Hoffer QST (p < 0.001), and Pearl-DGS (p < 0.001). The prediction error of the EVO PK was statistically smaller than those using the EVO PK (p < 0.01). The prediction error of the Pearl-DGS was statistically more myopic than the Barrett True-K (p < 0.001), EVO K (p < 0.001), EVO TK (p < 0.001), Hoffer QST PK (p < 0.001), and Hoffer QST (p < 0.001). The Hoffer QST prediction error was significantly larger than that of the Hoffer QST PK (p < 0.01) and EVO TK (p < 0.001). The Hoffer QST PK prediction error was significantly lower than the EVO K (p < 0.05).
Table 3 and Fig. 2 display the absolute error associated with each formula. The EVO PK demonstrated the lowest median absolute error, while the Haigis-L had the largest median absolute error. For the absolute error values, the EVO TK was significantly lower than the EVO K (p < 0.05), Haigis-L (p < 0.01), and Hoffer QST (p < 0.001). There was a notable outlier for the Haigis-L predicted and absolute error calculations, but this calculation was confirmed to be correct and left in the analysis. The other formulas predicted much lower absolute errors for the same case.
Table 3
Absolute prediction error of each formula.
Formulae | Mean (D) | SD (D) | Median (D) | Min (D) | Max (D) |
Barrett True K | 0.39 | 0.44 | 0.26 | 0.01 | 2.45 |
Barrett True-K TK | 0.43 | 0.39 | 0.32 | 0.01 | 1.94 |
Haigis-L | 0.59 | 0.58 | 0.46 | 0.01 | 3.55 |
Haigis TK | 0.40 | 0.37 | 0.26 | 0.03 | 1.67 |
EVO K | 0.52 | 0.47 | 0.36 | 0.03 | 2.15 |
EVO PK | 0.34 | 0.37 | 0.20 | 0.01 | 1.74 |
Pearl-DGS | 0.41 | 0.36 | 0.28 | 0.00 | 1.68 |
Hoffer QST | 0.58 | 0.51 | 0.41 | 0.01 | 2.16 |
Hoffer QST PK | 0.44 | 0.46 | 0.28 | 0.03 | 2.15 |
Absolute error calculated as the absolute value of the prediction error.
D = Diopter; SD = Standard deviation; Min = Minimum; Max = Maximum.
Table 4 and Figure 3 shows the percentage of eyes within ± 0.25 D, ± 0.50 D, and ± 1.00 D for each formula. The EVO PK resulted in the largest percentage of eyes within ±0.25 D of the predicted value, with 33 of the 56 eyes falling within ±0.25 D of the initially predicted value (59%). The percentage for EVO PK was significantly greater when compared to the percentage of eyes within ±0.25 D predicted by the Haigis-L (p=0.047).
Table 4
Prediction accuracy within +/- 0.25 D, +/- 0.50 D, and +/- 1.00 D for each formula (n = 56)
Formulae | Within +/-0.25 D | Within +/-0.50 D | Within +/-1.00 D |
Barrett True K | 48.2 | 82.1 | 92.9 |
Barrett True-K TK | 33.9 | 71.4 | 92.9 |
EVO K | 32.1 | 66.1 | 87.5 |
EVO PK | 58.9* | 80.4 | 94.6 |
Haigis-L | 26.8* | 57.1 | 85.7 |
Haigis TK | 48.2 | 73.2 | 92.9 |
Pearl-DGS | 39.3 | 66.1 | 91.1 |
Hoffer QST | 35.7 | 57.1 | 78.6 |
Hoffer QST PK | 46.4 | 66.1 | 89.3 |
p-value1 | < 0.0001 | < 0.0001 | < 0.0001 |
D = Diopter |
1 Significant difference among formulas calculated using Cochran’s Q test for the percentage; p < 0.05.
*Significant difference in EVO TK and Haigis-L at 0.25D limit in post-hoc analysis calculated using the McNemar test with Holm adjustment.
There was no statistically significant finding when comparing between the formulas with post hoc analysis for the percentage of eyes within ± 0.50 D and ± 1.00 D.
Table 5 shows the calculated RMSE of each formula. When considering the overall RMSE analysis, the EVO PK had the lowest mean RMSE value of all the formulas (0.499), while the Haigis-L had the largest mean RMSE value (0.825).
Table 5
RMSE of prediction error for each formula.
Formulae | Mean (D) | SD (D) | Median (D) | Min(D) | Max(D) |
Barrett True K | 0.571 | 0.103 | 0.574 | 0.323 | 0.800 |
Barrett True-K TK | 0.574 | 0.083 | 0.572 | 0.354 | 0.819 |
Haigis-L | 0.825 | 0.01 | 0.807 | 0.508 | 1.25 |
Haigis TK | 0.530 | 0.072 | 0.524 | 0.355 | 0.714 |
EVO K | 0.700 | 0.082 | 0.705 | 0.422 | 0.902 |
EVO PK | 0.499 | 0.079 | 0.499 | 0.294 | 0.696 |
Pearl-DGS | 0.541 | 0.065 | 0.541 | 0.384 | 0.740 |
Hoffer QST K | 0.777 | 0.078 | 0.780 | 0.561 | 0.955 |
Hoffer QST PK | 0.627 | 0.084 | 0.626 | 0.369 | 0.820 |
Calculated Root-Mean-Square Error (RMSE) of each formula.
D = Diopter.
When considering mean RMSE of predicted error via Welch’s test and pairwise t-test post-hoc testing with Hochberg adjustment, there were many statistically significant differences between the formulas. The Barrett True K was statistically significantly lower than the EVO K (p < 0.01), Haigis-L (p < 0.01), Hoffer QST (p < 0.01), and Hoffer QST PK (p < 0.01). The Barrett True K was statistically significantly larger than the EVO PK (p < 0.01), Haigis TK (p < 0.01), and the Pearl DGS (p = 0.002). The Barrett True-K TK was statistically significantly lower than the EVO K (p < 0.01), Haigis-L (p < 0.01), Hoffer QST (p < 0.01), and Hoffer QST PK (p < 0.01). The Barrett True-K TK was statistically significantly larger than the EVO PK (p < 0.01), Haigis TK (p < 0.01), and Pearl-DGS (p < 0.01). The EVO K was statistically significantly lower than the Haigis-L (p < 0.01), and Hoffer QST (p < 0.01). The EVO K was statistically significantly larger than the Barrett True K (p < 0.01), Barrett True-K TK (p < 0.01), EVO PK (p < 0.01), Hoffer QST PK (p < 0.01), Haigis TK (p < 0.01), and Pearl DGS (p < 0.01). The EVO PK was statistically significantly lower than the Barrett True K (p < 0.01), Barrett True-K TK (p < 0.01), Haigis-L (p < 0.01), Hoffer QST (p < 0.01), Hoffer QST PK (p < 0.01), Haigis TK (p < 0.01), and Pearl-DGS (p < 0.01). The Haigis-L was statistically significantly larger than the Hoffer QST (p < 0.01), Hoffer QST PK (p < 0.01), Haigis TK (p < 0.01), and Pearl-DGS (p < 0.01), EVO K (p < 0.01), EVO PK (p < 0.01), and Barrett True K (p < 0.01). The Hoffer QST was statistically significantly larger than the Hoffer QST PK (p < 0.01), Haigis TK (p < 0.01), and Pearl-DGS (p < 0.01). The Hoffer QST PK was statistically significantly larger than the EVO PK (p < 0.01), Barrett True K (p < 0.01), Barrett True-K TK (p < 0.01), Haigis TK (p < 0.01) and the Pearl-DGS (p < 0.01).
There was no statistically significant difference between the RMSE of the Haigis TK and Pearl-DGS or between the Barrett True K and Barrett True-K TK.