Patient-level forecasting of geographic atrophy with a biologically grounded Gompertz model

We tested whether a Gompertz growth curve better describes and predicts geographic atrophy lesion enlargement than linear and effective-radius (square-root) models. We analyzed a retrospective, single-center cohort of 121 patients (181 eyes) with serial fundus autofluorescence imaging from October 2012 to April 2023, excluding eyes that had received prior geographic atrophy therapies or fewer than five gradable visits, creating a natural-history cohort. We fitted four candidate models (Gompertz, logistic, linear, and effective radius) within a hierarchical framework. We evaluated model accuracy using rolling out-of-sample forecasts, as assessed by continuous ranked probability scores. We assessed calibration by the prediction-interval width and coverage. The median follow-up was 5.8 years (IQR, 2.8 years), the mean age was 79.2 years (SD, 7.9 years), and 60% of the cohort were female. Gompertz achieved the lowest forecast error (0.45 mm²) versus logistic (0.48 mm²), linear (0.52 mm²), and effective radius (0.62 mm²), and received the highest pseudo-Bayesian model averaging weight (0.994). It yielded narrower 90% prediction intervals (2.41 mm² vs. 3.99 mm² for linear) and maintained these advantages at longer forecast horizons, where traditional models tended to overpredict. Differences were most pronounced during late (decelerating) growth. These findings demonstrate that Gompertz trajectories better capture lesion enlargement and modestly improve probabilistic forecasts compared with conventional approaches, supporting their use for patient counseling and for trial designs that account for natural growth deceleration.