The next key step in the simulation was to add measurement variability to these true underlying values. Using the distribution of standard deviations (SDs) of MD from glaucomatous patients in a large longitudinal study,
17 Chauhan et al. (2008) defined patients exhibiting “moderate” measurement variability to have SD of MD of 1 dB.
8 For simplicity, this level of variability (SD = 1 dB) was adopted throughout all the simulation experiments, with a modification for progressing eyes. Variability was added to the MD recorded at each follow-up visit as a single number randomly sampled from a Normal distribution with mean 0 dB and SD of
x dB. For stable eyes,
x was fixed at 1 dB; for progressing eyes,
x was modified to increase as MD worsens to mimic the real situation where VF measurement variability increases as the VF deteriorates.
18 There are few examples in the literature quantifying exactly how the SD of MD increases as the MD in an individual worsens. One study,
19 using frequency-of-seeing (FOS) data collected in patients, indicated that response variability, albeit at individual VF locations rather than MD, was reasonably well represented by the function, log
e (SD) = A × sensitivity(dB) + B, where the constants A and B are −0.081 and 3.27, respectively. So, since our simulation assumed that the initial VF has an MD of approximately −4 dB then the sensitivity values across the VF will be, on average, approximately 26 dB. A progression rate of 2 dB loss per year will give an MD of −8 dB after 2 years, meaning that the sensitivity values across the VF will be, on average in our example eye, approximately 22 dB. By substituting these two values (26 and 22 dB) into the equation, and then subtracting one result from the other, an estimate of the increase in SD of the sensitivity at a single deteriorating location is yielded (1.23 dB). The variability at a VF test location will naturally be higher than that in a summary measure such as MD So, following simple statistical sampling theory, this value of 1.23 dB was then divided by the square root of the number of locations in a typical VF (
n ≈ 50) to give an estimate of the expected increase in SD of the MD over the 2-year period at this approximate level of VF defect severity; this gave a value of 0.2 dB when rounded to one decimal place. Consequently, for the progressing eyes the model fixed the SD of MD at 0.9 dB at baseline and 1.1 dB at 2 years, with every 1 dB of loss in MD accompanied by a 0.05-dB addition to the SD of MD In this way the measurement variability in the simulation still assumes an average SD of MD of 1 dB, allowing useful comparison with the results from Chauhan et al. (2008),
8 but it also accommodates the characteristic of VF variability increasing over the follow-up period, as would be expected with real data from a progressing eye (
Fig. 1B).