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

Carlyn Childress1, Stuart K Gardiner2, Manoj Pathak3

  • 1Murray State University, Murray, KY, 42071, USA.

Scientific Reports
|December 19, 2025
PubMed
Summary
This summary is machine-generated.

Forecasting glaucoma progression using irregular autoregressive of order 1 (IAR (1)) is more accurate than ordinary least square regression (OLSR). The IAR (1) method provides a statistically valid approach for analyzing perimetry data and predicting disease progression.

Keywords:
Irregular autoregressiveMean deviationOrdinary least square regressionVisual field

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Area of Science:

  • Ophthalmology
  • Biostatistics
  • Medical Data Analysis

Background:

  • Accurate forecasting of glaucoma progression is crucial for effective patient management.
  • Ordinary least square regression (OLSR) is often inappropriate for analyzing longitudinal perimetry data due to violated assumptions.
  • Mean deviation (MD) series from perimetry are key indicators of glaucoma progression.

Purpose of the Study:

  • To examine the applicability of the irregular autoregressive of order 1 (IAR (1)) method for modeling glaucoma mean deviation (MD) series.
  • To compare the validity and forecasting accuracy of IAR (1) against OLSR for longitudinal perimetry data.
  • To determine if IAR (1) offers a statistically superior method for glaucoma progression analysis.

Main Methods:

  • Longitudinal perimetry data from 42 eyes with progressive glaucoma were analyzed.
  • Mean deviation (MD) series were fitted using both Ordinary Least Square Regression (OLSR) and Irregular Autoregressive of order 1 (IAR (1)) methods.
  • Model validity was assessed using correlograms to check for correlated errors and normality assumptions. Forecast accuracy was compared using Mean Square Error (MSE).

Main Results:

  • Residuals from OLSR were correlated and did not meet normality assumptions, indicating model inadequacy.
  • The IAR (1) model demonstrated improved validity with insignificant autocorrelation (p > 0.05) and better fit for heavy-tailed distributions.
  • Significantly more eyes fitted with IAR (1) showed smaller forecast Mean Square Error (MSE) compared to OLSR (62% vs. 38%, P = 0.02).

Conclusions:

  • The IAR (1) method effectively addresses the limitations of OLSR when analyzing repeated perimetry measurements in glaucoma.
  • IAR (1) provides a statistically more valid approach for fitting MD series in glaucoma.
  • The IAR (1) method offers more accurate forecasting of glaucoma mean deviation progression compared to OLSR.