Robust and censored modeling and prediction of progression in glaucomatous visual fields

Classic regression is based on certain assumptions that conflict with visual field (VF) data. We investigate and evaluate different regression models and their assumptions in order to determine point-wise VF progression in glaucoma and to better predict future field loss for personalised clinical glaucoma management.

Standard automated visual fields of 130 patients with primary glaucoma with a minimum of 6 years of follow-up were included. Sensitivity estimates at each VF location were regressed on time with classical linear and exponential regression models, as well as different variants of these models that take into account censoring and allow for robust fits. These models were compared for the best fit and for their predictive ability. The prediction was evaluated at six measurements (approximately 3 years) ahead using varying numbers of measurements.

For fitting the data, the classical uncensored linear regression model had the lowest root mean square error and 95th percentile of the absolute errors. These errors were reduced in all models when increasing the number of measurements used for the prediction of future measurements, with the classical uncensored linear regression model having the lowest values for these errors irrespective of how many measurements were included.

All models performed similarly. Despite violation of its assumptions, the classical uncensored linear regression model appeared to provide the best fit for our data. In addition, this model appeared to perform the best when predicting future VFs. However, more advanced regression models exploring any temporal-spatial relationships of glaucomatous progression are needed to reduce prediction errors to clinically meaningful levels.