Future visual field prediction in glaucoma: an application of first-order autoregressive approach

To compare first-order autoregressive (AR(1)), ordinary linear regression (OLR), exponential, and polynomial regression models in predicting pointwise visual field (VF) and Humphrey Field Analyzer (HFA) global indices in glaucoma across disease severity levels.

Data from a cohort at the Rotterdam Eye Hospital were investigated, including 277 eyes from 139 subjects. Eyes were classified as having mild, moderate, or advanced glaucoma. Threshold sensitivity and Humphrey Field Analyzer Mean Deviation (HFA-MD) were predicted at the sixth visit using the first five VF examinations. OLR, AR(1), exponential, and polynomial regression models were fitted separately for each eye and VF location. Prediction accuracy was assessed using root mean squared error (RMSE) and pointwise mean absolute error (PMAE) and compared among the models by the mixed-effects model.

A total of 261 eyes from 131 subjects were analyzed. AR(1) demonstrated the lowest pointwise prediction errors in most severity groups. Compared with OLR, AR(1) showed lower PMAE in mild (2.57 vs. 2.75 dB, p = 0.015) and moderate glaucoma (3.24 vs. 3.59 dB, p < 0.001). In advanced glaucoma, AR(1) achieved significantly lower RMSE and PMAE than OLR, exponential, and polynomial models (all p < 0.001). For HFA-MD prediction, no significant differences were observed among AR(1), OLR, and exponential models, whereas polynomial regression consistently showed higher errors.

AR(1) provides superior pointwise prediction accuracy, particularly in advanced glaucoma, while HFA-MD predictions are generally comparable among AR(1), OLR, and exponential approaches. These findings support AR(1) as an effective tool in predicting future VF for glaucoma subjects.