Models of glaucomatous visual field loss

Abstract

Purpose: To evaluate and compare the ability of pointwise linear, exponential, and logistic functions, and combinations of functions, to model the longitudinal behavior of visual field (VF) series and predict future VF loss in patients with glaucoma.

Methods: Visual field series from 782 eyes (572 patients) with open-angle glaucoma had greater than 6 years of follow-up and 12 VFs performed. Threshold sensitivities from the first 5 years at each location were regressed with linear, exponential, and logistic functions to estimate model parameters. A multiple-model approach applied the model with the lowest root mean square error (RMSE) at each location as the preferred model for future predictions. Predictions for each model were compared at 1, 2, 3, and 5 years after the last VF used to determine model parameters.

Results: There were no clinically important differences between any of the models tested for fit; however, the logistic function had the lowest average RMSE (P < 0.001). For predictions, the exponential model consistently had the lowest average prediction RMSE for all time intervals (P < 0.001); the multiple-model approach did not perform better than the exponential model (P < 0.001).

Conclusions: While the logistic model best fit glaucomatous VF behavior over a long time period, the exponential model provided the best average predictions. A multiple-model approach for VF predictions was associated with a greater prediction error than with the best-performing single-model approach. A model's goodness of fit is not indicative of its predictive ability for measurements of glaucomatous VFs.

Keywords: pointwise exponential regression; regression modeling; standard automated perimetry; visual field prediction.