Forecasting mean deviation in glaucoma patients using an irregular autoregressive time series method

Accurate forecasting of disease progression is vital in glaucoma management. Ordinary least square regression (OLSR) analyses are not appropriate to perform trend analysis on longitudinally collected perimetry data. This study examines the applicability of an irregular autoregressive of order 1 (IAR (1)) method to model mean deviation (MD) series and investigates if IAR (1) improves validity of the model and results better forecasts then OLSR. Longitudinal data from eyes with progressive glaucoma were used. A total of 1200 MD data from forty-two eyes were included in this study. MD series from the eyes were fitted using both OLSR and an IAR (1) methods. A correlogram was used to determine if errors of the fitted OLSR and IAR (1) were correlated. Predictability of the IAR (1) method was then compared with OLSR using forecast Mean Square Error (MSE). Residuals from the OLSR were correlated and did not satisfy the assumption of normality. On the other hand, the IAR (1) model markedly improved the validity of the model as evidenced by insignificant autocorrelation functions (p-value > 0.05) and model's ability to fit heavy-tailed distribution. Compared to the OLSR fit, significantly higher percentages of eyes resulted smaller MSE (62% vs. 38%, P = 0.02) when fitted with IAR (1) method. The IAR (1) method adequately addresses the shortcomings of OLSR when fitting repeatedly collected perimetry data. The IAR (1) method appears to be statistically more valid method for fitting MD series and more accurately forecasts MD progression when compared with OLSR fit.