Looking for deterioration in any one of multiple clusters would be expected to increase sensitivity, but this would inevitably come at the cost of reduced specificity. To avoid this confound, we equalize specificity by using a permutation technique to determine whether an eye is “deteriorating,”
14 rather than using the same
P value cutoff for both overlapping and nonoverlapping cluster analyses.
8 The method for detecting deterioration was based on the published permutation analyses of pointwise linear regression approach
14 and implemented in R statistical programming language (version 3.5.0).
15 For a series of
V visual fields, where
V ≥ 5, the “observed” significance of the rate of change was defined as the
P value from an ordinary least squares regression over time. Next, a permutation distribution for this
P value was derived. The values of MD for visits 1-
V were reordered, and these reordered MD values were regressed against the original test dates. For
V = 5, this was done for all 120 possible reorderings of the five visits; for
V > 5, 475 randomly chosen reorderings were used to avoid excessive computation time.
Deterioration in MD was “detected” at the first visit
V for which the observed significance was below the fifth percentile of the permutation distribution. Therefore this criterion has a specificity of 95% and, based on a binomial distribution 475 reorderings, gives a confidence interval for this specificity of ±1%.
Note that this procedure gives very similar results to just “detecting” deterioration on the first visit at which the observed one-sided
P value for the rate of change is less than 5%. However, it makes fewer distributional assumptions, particularly concerning homoscedasticity. More importantly, it can more easily be extended to cluster analyses, as detailed in the next section, to ensure consistency between the analysis types.
14