PURPOSE: To improve the accuracy of intraocular lens (IOL) power calculation formulas by modifying the effective lens position (ELP) equations for patients with Marfan syndrome (MFS) and ectopia lentis (EL) undergoing in-the-bag IOL implantation. SETTING: Eye and ENT Hospital of Fudan University, Shanghai, China. DESIGN: Retrospective cohort study. METHODS: The formula-specific ELP was obtained from the SRK/T, T2, Holladay 1, and HofferQ formulas. The back-calculated ELP was obtained based on the vergence formula using preoperative biometry, postoperative refraction, and IOL power. The generalized linear models (GLMs) or gradient boosting machines were used to predict ELP or ELP error. RESULTS: 255 patients (255 eyes) were assigned randomly into a training set and a validation set (7:3 ratio). Linear correlation identified axial length (AL), corneal height, and white-to-white distance as predictors of ELP and ELP error for patients with shorter AL (AL ≤24 mm). For those with longer AL (AL >
24 mm), AL and the central corneal radius were identified as the primary predictors. Incorporating these predictors into the modified ELP formula significantly improved the accuracy in the validation set, including SRK/T, T2, Haigis, Holladay 1, and HofferQ formulas. The improvement was more pronounced in patients with shorter AL. In addition, the GLM-modified formulas outperformed both the Barrett Universal II and Kane formulas. The accuracy across different ocular dimensions was comparable among the modified formulas, based on which an online calculator was developed. CONCLUSIONS: Using the more accurately predicted ELP can significantly improve the accuracy of existing formulas in patients with MFS.