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D. W. Richards, S. Roland; Combining Pointwise Regression and Spatial Averaging Produces a Low-Noise Global Measure of Visual-Field Change, via Transformation of Variables and Computation of Weighted Means. Invest. Ophthalmol. Vis. Sci. 2010;51(13):5497.
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We hypothesized that change-over-time of automated visual fields could be made more precise if spatial averages are computed in a weighted fashion, where weights are appropriately chosen to de-emphasize the impact of "noisy" data points.
92 Zeiss-Humphrey 24-2 Sita-Standard visual fields (VF’s) of 10 eyes of 10 glaucoma patients were retrospectively analyzed. There were 7 to11 serial VF’s per eye extending over 4 to 8 years. MD ranged from -19 to 0. Pointwise straight-line regression over time was calculated at each of the 520 loci (10 eyes x 52 per eye), using linearized TD values ( "x" ). The ratio, var(x)/mean(x), was determined to be nearly constant, indicating that x has an approximately Poisson distribution; therefore y = square root(x) is approximately Normal. We then used 1/var(y), as weights at the corresponding 52 loci for each eye, to compute chi-square Maximum-Likelihood weighted means of y for each VF for that eye, finally converting back to db to yield a weighted MD, "MDW", for each VF.
As a function of time, fitted by a straight line, variance of MDW was reduced compared to that of MD in all 10 cases. RMS residual decreased from an average of 1.06 db to 0.63 db ( p< 0.01, Mann-Whitney U Test). Slopes (db/y) decreased in 3 cases and increased in 7 cases; slope changed sign in one case.
Pointwise linear regression provides estimates of "noisiness" of individual loci in automated VF’s. In a chi-square Maximum-Likelihood model, "noisy" loci are weighted less heavily than "quiet" loci during spatial averaging, and this reduces "noise" of global progression analysis.
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