Model Development

This prognosis-predicting model was developed to predict changes in the MD value over the lifetime of individual patients using our formula for estimating the MD slope of POAG patients. The details of formula development were previously reported,12 and can be summarized in the outline as follows. This formula was obtained using a multiple regression analysis with data on 20 clinical parameters, belonging to six categories, from the above patient population (191 eyes of 191 patients). The severity of glaucomatous structural abnormalities (baseline RNFLD angle and baseline vertical C/D), presence or absence of DH, and mean percent change in IOP were selected as predictive parameters by stepwise regression and the population of 133 eyes of 133 patients that included all four predictive parameters. The RNFLD angle was defined by constructing a 3.4 mm circle centered on the disc center, and finding the angle subtended at the center by the arc that covered the entire RNFLD (Figure 1).

Definition of RNFLD Angle. Draw a circle with a diameter of 3.4 mm centered on the disc center. Determine the points where the circle intersects the RNFLD. Draw a line between each point of intersection and the disc center. The RNFLD angle is defined as the angle between the two resulting lines.

Abbreviation: RNFLD, retinal nerve fiber layer defect.

Formula for predicting the MD slope (dB/year)

MD slope = 0.581 + [(Baseline RNFLD angle) × −0.002] + [(Baseline vertical C/D) × −1.079] + [(Presence of DH) × −0.184] + [(Mean IOP change (%)) × −0.006]

The coefficient of determination for this formula was 0.195. Its internal validity was confirmed using a random sampling method (bootstrap method). Furthermore, the discriminative ability was confirmed to have moderate performance by calculating the area under the curve (AUC) of the receiver-operating characteristic (ROC) curves for detecting an MD slope between −0.1 and −0.5 (dB/year), resulting in a calculated AUC that ranged from 0.736 to 0.772.

Lifetime changes in the MD value in individual patients are predicted based on the MD slope estimated using the above formula, taking into account the patient’s age and MD value. This model was developed using Microsoft Excel, and predicts changes in the MD value over the patient’s lifetime until the average Japanese life expectancy, 84 years,13 is reached. The MD slope was recalculated using the RNFLD angle and vertical C/D every 6 years using the rates of change in the two parameters obtained in a previous study (RNFLD angle: +9.3 degrees/6 years, vertical C/D: +0.0096/6 years).

In this model, lifetime changes in the MD value in 10,000 virtual patients were estimated using Monte Carlo simulation of the MD slope in these patients. Monte Carlo simulation is a method used to estimate an output distribution by setting up probability distributions for each input variable in the model. This technique was also used by Anderson et al to estimate the distribution of the rate of visual field progression in a population consisting of glaucoma patients.14 Various range- or incidence-designated simulation conditions can be readily prepared through random sampling from the distribution of each variable.

To predict the MD slope, the baseline RNFLD angle and baseline vertical C/D were set based on normal distributions calculated from the mean and standard deviation (SD) (baseline RNFLD angle: 46.5 ± 25.8, baseline vertical C/D: 0.79 ± 0.1) in the development sample. Based on this distribution, 10,000 combinations of the baseline RNFLD angle and baseline vertical C/D were prepared through random sampling.