Modeling of atrophy size trajectories: variable transformation, prediction and age-of-onset estimation

Abstract

Abstract Background To model the progression of geographic atrophy (GA) in patients with age-related macular degeneration (AMD) by building a suitable statistical regression model for GA size measurements obtained from fundus autofluorescence imaging. Methods Based on theoretical considerations, we develop a linear mixed-effects model for GA size progression that incorporates covariable-dependent enlargement rates as well as correlations between longitudinally collected GA size measurements. To capture nonlinear progression in a flexible way, we systematically assess Box-Cox transformations with different transformation parameters λ. Model evaluation is performed on data collected for two longitudinal, prospective multi-center cohort studies on GA size progression. Results A transformation parameter of λ=0.45 yielded the best model fit regarding the Akaike information criterion (AIC). When hypertension and hypercholesterolemia were included as risk factors in the model, they showed an association with progression of GA size. The mean estimated age-of-onset in this model was 67.21±6.49 years. Conclusions We provide a comprehensive framework for modeling the course of uni- or bilateral GA size progression in longitudinal observational studies. Specifically, the model allows for age-of-onset estimation, identification of risk factors and prediction of future GA size. A square-root transformation of atrophy size is recommended before model fitting.

Keywords

• Geographic atrophy
• Age-related macular degeneration
• Box-Cox transformation
• Mixed-effects models
• Prediction
• Age-of-onset estimation