External validation
APEX formula accuracy
in real clinical practice
The APEX formula was built on a sample drawn from a clinical base of 42,000 surgeries. On held-out eyes that were not used to develop the formula, APEX matches the Kane formula in accuracy and outperforms the classic formulas.
42 000
surgeries
in the APEX clinical base
in the APEX clinical base
78%
of eyes within ±0.5 D
for the table leader
for the table leader
№1
rank by the FPI index
among the compared formulas
among the compared formulas
Formula comparison
Accuracy of hitting the target refraction, measured on 837 held-out eyes that were not used to develop the formula. Each formula was computed with its own optimized constant under equal conditions. The EVO, PEARL-DGS and Kane formulas were included as external benchmarks — computed on the authors' own calculators. Results are sorted by mean absolute error.
Single-center retrospective data. The full methodology and statistical analysis will be published separately.
| Formula | MAE (D) | MedAE | ±0.5 D | FPI | vs APEX |
|---|---|---|---|---|---|
| 1APEX | 0.346 | 0.274 | 78% | 0.649 | leader |
| 2EVOexternal | 0.348 | 0.276 | 76% | 0.643 | comparable |
| 3Kaneexternal | 0.349 | 0.275 | 76% | 0.643 | comparable |
| 4PEARL-DGSexternal | 0.352 | 0.279 | 74% | 0.637 | comparable |
| 5Holladay 1 | 0.363 | 0.300 | 73% | 0.619 | lower |
| 6T2 | 0.367 | 0.290 | 73% | 0.617 | lower |
| 7SRK/T | 0.376 | 0.311 | 73% | 0.602 | lower |
| 8Haigis | 0.394 | 0.319 | 69% | 0.578 | lower |
| 9Hoffer Q | 0.417 | 0.331 | 67% | 0.553 | lower |
Optimization
The formula constants were estimated on a sample drawn from a clinical base of 42,000 surgeries.
Validation
837 held-out eyes not used to develop the formula. All formulas were computed on the same sample, each with its own optimized constant (Hoffer–Savini 2021 protocol).
FPI
A composite accuracy index for the formula. Higher values reflect better overall accuracy.
“Comparable”
The difference from APEX is not statistically significant.