GLOBAL VISIT EFFECTS IN POINTWISE LONGITUDINAL MODELING OF GLAUCOMATOUS VISUAL FIELDS

Abstract

 

Purpose

 

Evaluation of a longitudinal series of visual fields (VF) provides a method to detect glaucoma and to determine functional deterioration. One of the difficulties in modeling VF data is the amount and type of measurement error or variability in the sensitivity estimates. This may be due to factors that are not measured, such as fatigue, inexperience of the operator, and delayed reaction time. Although the magnitude may vary, these factors affect all locations belonging to the same VF. We propose to model them as overall visit effects. The evaluation is done by determining the contribution these effects have on the model fit.

 

Methods

 

VFs (24-2 Full Threshold) of 50 patients from The Rotterdam Eye Hospital with primary glaucoma were included in the analysis (data available at http://orgids.com). Sensitivity estimates in 52 locations in both eyes were included as the response in a hierarchical Bayesian mixed effects model for each individual with 3 levels: eye, hemisphere and location. Censoring was taken into account at 0 dB. In addition, an overall visit effect was included which takes into account the common, visit-dependent sensitivity change at all locations. The contribution of this effect was evaluated by comparing the differences between the posterior predicted values and the observed data for the models with and without this effect. An example of the model fits can be seen in Figure 1.

 

Results

 

The pointwise absolute errors were significantly reduced by including the overall visit effect (p < 0.001). The mean absolute error (MAE) was reduced from 2.3 dB to 2.1 dB while the 95th percentile of the absolute error was reduced from 7.8 dB to 7.0 dB. The distributions of the errors are shown in Figure 2.

 

Conclusions

 

Including an overall visit effect showed a highly significant improvement in the model fit. This effect accounts for factors not included in the model but that affect all measurements belonging to the same eye at each visit. By lowering the residual error, better estimates of the real evolution of the sensitivity over time may be obtained.

 

 

Figure 1: The scatter plot represents the retinal sensitivity estimates over time for each location of the VF in an example (right) eye. The lines represent the model fits with (blue) and without (red) the visit effect.

 

 

Figure 2: Distribution of errors including the 2.5 and 97.5 percentiles for the model fits with (blue) and without (red) the visit effect.

 

Keywords: 758 visual fields • 473 computational modeling • 642 perimetry