Comparison of regression models for serial visual field analysis.

Abstract

Our aim was to compare fit and predictive performance effectiveness of four pointwise regression models in measuring the visual field (VF) decay rate of progression in patients with open-angle glaucoma. We selected Humphrey VF data of patients with open-angle glaucoma with a minimum follow-up time of 6 years. For each eye (n = 798 from 588 patients), we regressed threshold sensitivity (y) at each VF test location for the entire VF series against follow-up time (x), with four candidate first-order regression models: (1) ordinary least-squares linear regression model (y = β 0 + β 1 x); (2) nondecay exponential regression model (y = β 0 + β 1e (x) ); (3) decay exponential regression model ([Formula: see text]); (4) Tobit-censored, maximum-likelihood linear regression model (y* = [Formula: see text], ε ~ N(0, σ(2))), where x is follow-up time and y is threshold sensitivity. The average [± standard deviation (SD)] baseline VF mean deviation (MD) was -8.2 (±5.5) dB, the mean follow-up was 8.7 (±1.9) years, and the number of follow-up VFs was 14.7 (±4.4). The decay exponential model was the best-fitting (42.7 % of locations) and best-forecasting (65.5 % of locations) model. The decay exponential model was the best prediction model in all categories of severity. It is not clear that the ordinary least-squares linear regression model is always the favored model for fitting and forecasting VF data in patients with glaucoma. The pointwise decay exponential regression (PER) model was the best-fitting and best-predicting model across a wide range of glaucoma severity and can be readily understood by clinicians.