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Manoj Pathak, Stuart Keith Gardiner, Shaban Demirel; Forecasting Retinal Nerve Fiber Layer Thinning and Visual Field Decay in Glaucoma. Invest. Ophthalmol. Vis. Sci. 2014;55(13):989.
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© ARVO (1962-2015); The Authors (2016-present)
This study investigates whether glaucomatous change is better described by a linear or nonlinear model, when assessing function (perimetric Mean Deviation [MD]) or structure (OCT retinal nerve fiber layer thickness [RNFLT]). Models are compared both in terms of their fit to the data, and their ability to predict the next measurement in the series.
Longitudinal sequences of average RNFLT (Spectralis RNFLT Ave) and MD (Humphrey SITA Std, 24-2) measurements (either 5 or 8 observations per eye) from 188 eyes of 94 participants were used. Two-level mixed effects models were constructed to examine whether RNFL thinning and MD decay over time were linear (blue line in schematic figure) or exponential with with yt=λ-eκt (red line) and their fits to the data were compared using ANOVA. To assess predictive ability, RNFLT and MD measured on the last test date were forecast using a model fit from the earlier test dates in the sequence. The means of the prediction errors were compared using a Wilcoxon test to assess accuracy, and the root means square (RMS) of the prediction errors were compared to assess precision.
Using the entire sequences, the linear model provided a better fit to RNFLT data than the exponential model for both sequence lengths (p<0.0001). For MD, the exponential model outperformed the linear model for longer sequences (p<0.0001), but no difference was found for shorter sequences (p=0.70). As seen in the table, when predicting the last test in the sequences, the linear model produced more accurate and precise RNFLT estimates for shorter sequences (p<0.0001). The same pattern was observed for longer sequences but did not reach significance. For MD, the exponential model predicted the next observation slightly better (p=0.04) than the linear model for sequence of length 8, but the linear model was adequate for shorter sequences.
OCT-derived measures of RNFLT appear to change linearly over time in this cohort. For SAP MD, an exponential model provides a better fit to the data and slightly better predictive ability for longer sequences, supporting the reported exponential relation between sensitivities and RNFLT. However when sequences are shorter, a linear model for MD is adequate.
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