Visual Field Progression In Glaucoma: Estimating The Overall Significance Of Deterioration With Permutation Analyses Of Point-wise Linear Regression

Abstract

Purpose: : 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.

Methods: : 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 (p_s) 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 p_s < 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.

Results: : Evidence for deterioration at p_s < 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.

Conclusions: : 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.

Keywords: visual fields • clinical research methodology