Accuracy Of The Moussa Formula, A Novel Intraocular Lens Power Calculation Formula: A Multicentre Heteroscedastic Analysis

To evaluate the refractive predictive accuracy of the novel Moussa intraocular lens (IOL) power calculation formula and compare its performance against six established formulas (Kane, EVO, PEARL-DGS, K6, Hoffer QST, Barrett Universal II [BUII]) available on the ESCRS IOL Calculator.

Multicentre, retrospective, consecutive case series across three United Kingdom surgical centres: Birmingham Midland Eye Centre, Manchester Royal Eye Hospital, and Newmedica Manchester. This approach incorporates tertiary teaching hospitals and independent sector centres. Three distinct biometry devices (IOLMaster 700, Lenstar LS900, Pentacam AXL Wave) were utilised across the sites, ensuring a representative evaluation of real-world performance.

An initial dataset of 3,405 consecutive eyes was refined to 2,550 independent eyes following strict exclusion criteria, including sequential second eye removal to prevent statistical dependence. Lens constants were optimised to zero mean prediction error for each device and IOL combination via the freely available Moussa Research Suite, via the API for the K6 formula and PEARL-DGS formula, the online lens constant optimiser for Hoffer QST and through manual data entry for the BUII, Kane, Evo. Accuracy was rigorously evaluated using the Wilcox-Holladay-Wang-Koch heteroscedastic framework. The primary endpoint was Mean Absolute Error (MAE), evaluated via studentised bootstrap analysis (2,000 replicates) employing Holm-adjusted p-values.

In the overall cohort (N=2550), Moussa produced the lowest MAE (0.348 D), significantly outperforming Kane, EVO, PEARL-DGS, K6, Hoffer QST, and Barrett (all Holm p<0.001). In short eyes (N=193, <22.0 mm), Moussa achieved the lowest MAE (0.408 D), performing significantly better than Kane (p=0.046), EVO (p=0.015), PEARL-DGS (p=0.021), K6, Hoffer QST, and Barrett (all p<0.001). In long eyes (N=143, ≥26.0 mm), Moussa demonstrated the lowest MAE (0.343 D), showing significant superiority over Kane (p=0.010), Barrett (p=0.019), and Hoffer QST (p<0.001). 

Overall, Moussa achieved the highest proportion of eyes within ±0.50 D (75.98%), then Kane (75.12%), EVO (74.84%), PEARL-DGS (73.63%), K6 (73.39%), Barrett (73.04%), and Hoffer QST (72.88%).

The Moussa formula demonstrates predictive accuracy equalling or exceeding current gold-standard benchmarks like Kane and EVO across the axial length spectrum. By utilising symbolic regression, it functions as an interpretable geometric optics operator, overcoming the opacities of traditional black-box artificial intelligence. Robust studentised bootstrap analysis confirms its statistical stability, generalisability, and resistance to overfitting across varied biometry devices and IOL platforms. As an interpretable and accessible tool, it provides surgeons with a highly reliable method for optimising postoperative refractive outcomes.