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Manoj Pathak, Shaban Demirel, Stuart Gardiner; Autoregressive Mixed Effects Approach for Modeling Longitudinal Standard Automated Perimetry Data in Glaucoma. Invest. Ophthalmol. Vis. Sci. 2013;54(15):1884.
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Trend analyses are increasingly being performed on perimetry data from patients with glaucoma, for example, trend analyses of the Visual Field Index or pointwise linear regression. However, ordinary least squares (OLS) regression analyses are inappropriate for modeling longitudinal data, and may underestimate true p-values. Models that account for group effects and within-group correlation structure are more suited to longitudinal data. This study examines these methods to model longitudinally collected perimetry data, and determines whether it provides significant improvements over OLS.
This study used longitudinal data from 168 eyes of 84 subjects with early or suspected glaucoma in the ongoing Portland Progression Project. Data from 1344 visual fields (eight visits per subject) were used. Models were formed to predict Mean Deviation (MD) from age and rim area (from confocal scanning laser ophthalmoscopy). Linear mixed effects models with one level of nesting (subject) or two levels (subject, eye within subject) were examined. An exponential temporal correlation structure with nugget effect was applied to account for same day test-retest variability. Sensitivity at each of the 52 non-blindspot locations (HFA 24-2) was also modeled to determine the performance of the model with pointwise data. Mixed effects models were compared using ANOVA. AICs were also compared against OLS.
For MD, the two level mixed effect model accounting for temporal autocorrelation was significantly better than the two level model not accounting for temporal autocorrelation (p<0.0001). The correlation between residuals on the same day was 0.7, decreasing to 0.61 (95% CI [0.47, 0.72]), when one year apart. Two level models significantly improved the model fit compared to one level models (p<0.0001). For the pointwise data, two level models were significantly better than single level models (p<0.0001) at all visual field locations. For both MD and point wise data, mixed effect models had smaller (better) AICs than OLS regression.
Errors from linear fits of longitudinal data are temporally correlated and OLS regression will underestimate true p-values and overstate the significance of trends. Autoregressive mixed effects models provide a better fit to the test data by accounting for group effects and within-group correlation.
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