Abstract
Purpose :
To quantify the classification performance of visual function testing, we introduce a metric from information theory, information gain (IG; or “mutual information”), defined as the difference between the total entropy of all possible outcomes and the average residual entropy of individual measurement (Fig. 1). In this study, we apply IG to evaluate the patient classification provided by Snellen, ETDRS and quantitative VA (qVA) tests.
Methods :
We performed Snellen, ETDRS, and qVA tests on 1000 simulated observers, randomly sampled from the population distribution of VA and VA range (Fig. 2B) derived from a dataset of 14 eyes tested with Bangerter foils that induced a wide range of VA (Zhao, et al., 2021). The VA behavioral psychometric function parametrized with VA and VA range determined the trial-by-trial response in each test. The “at least 50%” rule was used in the Snellen test; and the 3, 4, 5 mistakes, and whole chart rules were used in the ETDRS test. Both tests were repeated 10,000x to generate VA distributions for each observer (Figs. 2bd). For qVA, test lengths were 15, 30, or 45 rows of optotypes. Posterior distributions of VA only and of both VA and VA range were computed (Figs. 2fh). The distribution of all possible outcomes for each test was constructed by aggregating the outcome distributions from all the observers (Figs. 2cegi).
Results :
For Snellen, IG=1.51 bits (2.84 classes). For ETDRS, IG=2.09, 2.04, 1.94, and 1.97 bits for the four different stopping rules, corresponding to about 4 categories. For qVA scored with VA only, IG=2.67, 3.25, and 3.56 bits with 15, 30, and 45 rows, respectively, corresponding to 6.35, 9.53, and 11.79 classes. For qVA scored with both VA and VA range, IG=3.33, 4.04, and 4.43 bits with 15, 30, and 45 rows, respectively, corresponding to 10.0, 16.5, and 21.62 classes. The simulation results on qVA were consistent with those observed in the experiment (Zhao, et al., 2021).
Conclusions :
For classification of visual function, performance is limited by the number of distinct classes possible for an ophthalmic assessment. Even when equating for the number of optotypes tested, 15 qVA rows generated more information gain and more distinct observer categories than ETDRS and Snellen. Information gain can be used to evaluate any ophthalmic instrument, whether designed for assessment of visual function or anatomical structures.
This abstract was presented at the 2023 ARVO Annual Meeting, held in New Orleans, LA, April 23-27, 2023.