A Comparison of the Prediction Error of Two Structure-Function Models of Glaucoma Progression in Patients with Ocular Hypertension

Abstract

Purpose: Combining structural and functional data may improve our ability to predict glaucoma progression. In this analysis performed on prospective data collected in an observational clinical study, we compared the prediction accuracy of two glaucoma progression models that use structural and functional data.

Methods: Longitudinal series of paired mean sensitivity (MS) and neuroretinal rim area (RA) from 464 eyes of 264 participants were included from the Confocal Scanning Laser Ophthalmoscopy Ancillary Study of the Ocular Hypertension Treatment Study. All patients had at least 7 pairs of data separated by a minimum of 3 months. The first 6 visits were used to predict the 7^th visit. We compared the prediction accuracy of a Bayesian Linear Regression (BLR) model (Russell et al, IOVS, 2012; 53:2760−69) to that of a dynamic structure-function (DSF) model (Hu et al, IOVS, 2014; In Press). For the BLR model, we used RA as a prior to predict MS (BLR-MS), as it was originally intended, and we also MS as a prior to predict RA (BLR-RA). For the DSF model, MS and RA were used jointly to predict the 7^th pair and the marginal predictions of MS (DSF-MS) and RA (DSF-RA) compared against those of BLR. The 95% confidence intervals of the root-median-square prediction error (RMSPE) of each model were derived using bootstrap.

Results: The RMSPE of the DSF-MS was 12.0% (10.8%−13.5%); significantly lower than that of the BLR-MS, with a RMSPE of 16.8% (14.6%−18.9%). The DSF model yielded lower prediction error in 62.3% of eyes than BLR. The median RMSPE of the DSF-RA was 2.1% (2.0%−2.4%); significantly lower than that of the BLR-RA, with a RMSPE of 2.5% (2.3%−2.9%). The DSF model yielded lower prediction error than BLR in 56.3% of eyes.

Conclusions: As shown in previous work, BLR and the DSF model have lower prediction error than simple linear regression for short test series (Russell et al; Hu et al). Here we have shown better performance for DSF than BLR in patients with ocular hypertension. Estimating prediction error is the first step in assessing these glaucoma progression models; the second step is the assessment of sensitivity and specificity, which requires the development of significance tests.