Bayes’ theorem applied to perimetric progression detection in glaucoma: from specificity to positive predictive value

Abstract

Purpose

To estimate the specificity of a clinical evaluation of a series of visual fields and to calculate the positive predictive value of progression.

Methods

The specificity of a clinical evaluation of a series of visual fields was estimated using nonparametric ranking and probability calculus. The positive predictive value of progression was calculated using Bayes’ theorem. The literature suggests a prior probability of progression of typically 0.10 in the case of one visual field per year. Three different prior probability values were used: 0.05, 0.10, and 0.20. Calculations were performed for a sensitivity of 0.50, 0.80, and 1.00.

Results

Specificity of a clinical evaluation of a series of visual fields was calculated as 0.83 for four fields (two baseline fields, one follow-up field with suspected progression, and one confirmation of the suspected progression), 0.90 for five fields, and 0.95 for six fields. Positive predictive values ranged from 0.14 to 0.83. Positive predictive value was approximately 0.5 for a prior probability of 0.10, a sensitivity of 0.80, and a specificity of 0.90.

Conclusions

Realistic series of visual fields that are apparently progressive have a positive predictive value of typically 0.5, i.e., half of them are stable. In the case of a high prior probability (uncontrolled glaucoma or long interval between successive fields), four fields may suffice to diagnose progression, whereas at least six fields are required if the prior probability is low.