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Neil O'Leary, Balwantray C. Chauhan, Paul H. Artes; Visual Field Progression In Glaucoma: Estimating The Overall Significance Of Deterioration With Permutation Analyses Of Point-wise Linear Regression. Invest. Ophthalmol. Vis. Sci. 2012;53(14):2265.
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Point-wise linear regression (PLR) is a sensitive method to measure visual field change. We introduce Permutations of PLR (PoPLR), a method for estimating the overall statistical significance of the observed pattern of change, and compare its sensitivity and specificity to other PLR criteria for progression.
A statistic S was designed to summarise evidence for deterioration in series of visual fields, by combining the one-sided significance values from PLR of individual test locations, using Fisher’s method. To determine the overall statistical significance (ps) of the observed S, its null distribution in individual field series was derived from repeated random reordering (permutation) of the visual field sequence. PoPLR was evaluated in a large clinical dataset from patients with glaucoma (n=944, median mean deviation [MD] -3.0 dB, interquartile range [IQR]: -6.3, -1.2 dB) followed for > 4 years (median 10 examinations, IQR 9, 12). The hit-rate (proportion of eyes with ps < α, the nominal significance level) was estimated at α between 0.001 and 0.10. To confirm that the false positive rate of PoPLR was equivalent to the nominal significance level, the false-positive rate was estimated from the randomly reordered sequences of the same dataset. Hit-rate and specificity were estimated at the 5th, 8th and final examinations, at which corresponding median follow-up periods were 4.3, 6.4 and 8.0 years.
Evidence for deterioration at ps < 0.05 was observed in 15%, 37% and 49% of series, at the 5th, 8th and final available examinations respectively. Corresponding false-positive rates were 6%, 5% and 5%; not significantly different from α. When compared to other PLR criteria (e.g., 1 point deteriorating at -1.0 dB/year at p < 0.01), the hit-rate of PoPLR was higher at the 5th exam (p=0.002, McNemar’s test) and similar at the 8th and final exam (p=0.96, p=0.49), at similar specificity. In series with ps < 0.05 the median of MD change from baseline was -2.6, -3.3 and -3.9 dB at the 5th, 8th and final examinations.
PoPLR combines evidence across visual field locations, to derive a single, straightforward, and accurate estimate of statistical significance for visual field progression. Unlike other methods, this approach is individualised to each patient’s own data.
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