Multiple Non-Linear Additive Modelling Compared With Machine Learning For 3-Month Icl Vault Prediction
Published 2026 - 44th Congress of the ESCRS
Reference: POREF154 | Type: Free paper | DOI: 10.82333/b4q4-5g61
Authors: Prof. Dan Reinstein* 1 , Dr Timothy Archer 2 , Mr Joseph Potter 2 , Ms Ruchi Gupta 2
1London Vision Clinic,London,United Kingdom;Columbia University Medical Center,New York,United States;Sorbonne Université,Paris,France;Ulster University,Biomedical Science Research Institute,Coleraine,Ireland, 2London Vision Clinic,London,United Kingdom
Purpose
To compare a structured nonlinear generalised additive model (GAM) with machine learning algorithms (Random Forest and XGBoost) for prediction of 3-month postoperative ICL vault, and to determine whether vault behaviour demonstrates intrinsic nonlinear characteristics.
Setting
Private Practice Academic Unit Reinstein Vision, London Vision Clinic, EuroEyes Group, UK
Methods
Retrospective analysis of 407 eyes implanted with EVO/EVO+ ICL with complete preoperative biometric predictors (Artemis Insight 100 VHFDU; MS-39 AS-OCT) and 3-month vault. A structured GAM modelled smooth nonlinear effects with automatic penalisation to control overfitting, incorporating tensor interaction terms to represent anatomical dependencies. Machine learning comparators were Random Forest (1000 trees) and XGBoost (500 boosting rounds; eta 0.05; max_depth 4). All models were assessed using leave-one-out cross-validation with RMSE, MAE, IQR, mean prediction bias, and absolute error within ±50–500 µm.
Results
Several GAM smooth and tensor interaction terms demonstrated effective degrees of freedom >1, most notably s(LensSph)=3.89 and ti(STS,CBID)=3.21, confirming nonlinear and interaction effects across key predictors. In leave-one-out validation, the GAM achieved the lowest error across metrics: RMSE 172.6 µm versus 175.5 µm (RF) and 176.0 µm (XGB); MAE 126.6 µm versus 132.1 µm and 130.5 µm; and IQR 193.9 µm versus 196.3 µm and 197.0 µm. Mean prediction bias was minimal for all models (−0.8, −1.6, −3.9 µm). Absolute error was within ±50 µm in 29.5% (GAM), 26.8% (RF), and 24.6% (XGB), and within ±200 µm in 81.6%, 76.9%, and 79.4%, respectively.
Conclusions
In leave-one-out validation, a structured nonlinear GAM with anatomically motivated interaction terms achieved the most accurate vault predictions while retaining transparent, clinically interpretable predictor relationships. Higher-order smooths and tensor interactions confirm intrinsically nonlinear vault behaviour across key biometric predictors. In this dataset, more flexible “black box” machine-learning models did not improve performance, likely reflecting their greater data requirements. Structured additive modelling therefore provides superior predictive accuracy with clearer clinical insight for ICL vault prediction.