Individualized prediction intervals for IOL power calculation: variance propagation, Monte Carlo verification, and clinical validation

Current intraocular lens (IOL) power calculation delivers a point prediction of the postoperative refraction without quantifying how uncertain that prediction is for the individual eye. Building on the closed-form sensitivity calculus established in a companion paper [J. Opt. Soc. Am. A43, 777 (2026)], we develop a formula-agnostic framework that converts the analytical partial derivatives of the spectacle-plane spherical equivalent (SE) with respect to effective lens position (ELP), axial length, corneal power, and IOL power into individualized prediction intervals. The shape of the ELP-error distribution was characterized from ELP-equivalent residuals obtained by back-calculation, whereas the variance assigned to the latent ELP error was corrected by subtracting the expected contributions of axial length, corneal power, and IOL manufacturing tolerance. Each eye receives its own variance from its measured biometry, and a single Student-calibrated distribution of standardized training residuals supplies the quantile multiplier. On a primary FineVision cohort (1197 test eyes; five formulas: Gatinel, Haigis, SRK/T, Hoffer Q, and Holladay 1), the calibrated 95% interval reached an empirical coverage of 95.46% with a mean half-width of 0.845 D. Within the held-out FineVision test set, which contained no eye used to develop the Gatinel ELP predictor, the Gatinel formula gave the lowest point error and the narrowest intervals; this remains a same-platform evaluation because the predictor had been developed on a historical dataset that included other FineVision eyes. Exact nonlinear Monte Carlo propagation of the four error sources reproduced these intervals closely (95.02% coverage, mean half-width 0.813 D), confirming the variance decomposition while remaining slightly narrower than the clinically calibrated analytical interval, whose heavier tails it does not fully reproduce. The same architecture was applied to a secondary non-toric PanOptix cohort (596 test eyes, 94.70% coverage) after implant-specific training. The deterministic equations and coefficients of the Gatinel formula are disclosed in Appendix B. The method converts a point prediction into an eye-specific prediction interval that a surgeon can use when selecting an implant.