Prediction accuracy of a novel dynamic structure-function model for glaucoma progression

Abstract

Purpose: To assess the prediction accuracy of a novel dynamic structure-function (DSF) model to monitor glaucoma progression.

Methods: Longitudinal data of paired rim area (RA) and mean sensitivity (MS) from 220 eyes with ocular hypertension or primary open-angle glaucoma enrolled in the Diagnostic Innovations in Glaucoma Study or the African Descent and Glaucoma Evaluation Study were included. Rim area and MS were expressed as percent of mean normal based on an independent dataset of 91 healthy eyes. The DSF model uses centroids as estimates of the current state of the disease and velocity vectors as estimates of direction and rate of change over time. The first three visits were used to predict the fourth visit; the first four visits were used to predict the fifth visit, and so on up to the 11th visit. The prediction error (PE) was compared to that of ordinary least squares linear regression (OLSLR) using Wilcoxon signed-rank test.

Results: For predictions at visit 4 to visit 7, the average PE for the DSF model was significantly lower than OLSLR by 1.19% to 3.42% of mean normal. No significant difference was observed for the predictions at visit 8 to visit 11. The DSF model had lower PE than OLSLR for 70% of eyes in predicting visit 4 and approximately 60% in predicting visits 5, 6, and 7.

Conclusions: The two models had similar prediction capabilities, and the DSF model performed better in shorter time series. The DSF model could be clinically useful when only limited follow-ups are available. (ClinicalTrials.gov numbers, NCT00221923, NCT00221897.).

Keywords: computational modeling; glaucoma progression; structure–function.

Copyright 2014 The Association for Research in Vision and Ophthalmology, Inc.

Figures

Figure 1

An illustration of the dynamic structure–function (DSF) model is presented. Four longitudinal paired measurements of rim area and mean sensitivity for a subject (black solid circles, labeled from X1 to X4) are plotted in a two-dimensional space showing structural and functional values. Structural and functional measurements are expressed in percent of mean normal, which could be greater than 100% in an individual eye. In the DSF model, the centroid (empty circles, labeled from X̄1 to X̄4) is an estimate of the current stage of the disease. The velocity vector (arrow) describes the direction and rate at which structure and function are jointly changing over time. The velocity vector may point toward any of the four quadrants (labeled from Q1 to Q4 in counterclockwise order). Q1, observed improvement on both RA and MS; Q2, observed worsening of MS and improvement of RA; Q3, observed worsening in both RA and MS; Q4, observed worsening of RA and improvement of MS. Based on the last centroid X̄4 and an estimated velocity vector, the future state (gray solid circle labeled X̂5) can be predicted.

Figure 2

Comparisons of prediction errors in predicting RA and MS for visit 4 to visit 11. The empty and solid circles represent the median PE with the OLSLR and the DSF model, respectively. The horizontal bars show the 95% confidence intervals for the median PE. The asterisks denote the significant differences between the OLSLR and the DSF model based on Wilcoxon signed-rank test.

Figure 3

Limits of agreement between the OLSLR and the DSF model on the prediction errors for visit 4 to visit 11. The horizontal axis shows the mean PE of the OLSLR and DSF model for each eye. The vertical axis shows the PE difference calculated by the DSF model minus the OLSLR model. The solid lines and the dashed lines represent the mean difference and corresponding 95% limits of agreement. Six eyes (four eyes with an absolute difference in PE larger than 50% of mean normal and two eyes with a mean PE larger than 80% of mean normal) are not shown for clarity, but they were used in the calculation of the limits of agreement.

Figure 4

Patient examples with the OLSLR and the DSF models based on series of RA and MS measurements. In each part of the figure, paired RA and MS data are plotted as circles coded with the numbers that identify the chronological order of the visits. The black triangle represents the predicted RA and MS measurements with the OLSLR model. The gray circle represents the latest centroid, and the black circle represents the predicted RA and MS measurements with the DSF model, respectively. The arrow shows the vector of change connecting the latest centroid and the predicted measurements in the DSF model. The predictions of the OLSLR and DSF models are compared with the actual RA and MS measurements at that future visit (black square).

Figure 5

Comparisons of prediction errors for visit 4 to visit 11 in the subset of 94 eyes that are progressing significantly according to OLSLR. The empty and solid circles represent the median PE with the OLSLR and the DSF model, respectively. The horizontal bars show the 95% confidence intervals for the median PE. The asterisks denote the significant differences between the OLSLR and the DSF model based on Wilcoxon signed-rank test.

Figure 6

Analysis of the impact of the magnitude of changes observed over time on the differences in PE between the DSF model and OLSLR for 220 eyes. The absolute values of the slope of MS using OLSLR (in percent of mean normal per month) for the first seven visits are plotted on the x-axis, and the differences in PE between the DSF model and OLSLR at visit 7 are plotted on the y-axis. Each dot is shaded according to the magnitude of the absolute values of the slope of RA using OLSLR for the first seven visits: Light shades represent shallower slopes and dark shades represent steeper slopes.