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Zhong-Lin Lu, Yukai Zhao, Luis Andres Lesmes, Michael Dorr; Hierarchical Bayesian modeling of E-ETDRS and FrACT test data. Invest. Ophthalmol. Vis. Sci. 2021;62(8):2821.
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E-ETDRS and FrACT are the two most popular electronic visual acuity (VA) tests. To improve the precision of VA threshold estimates from the tests, we re-analyzed the E-ETDRS and FrACT data from 14 eyes in four Bangerter foil conditions in Zhao et al. (2021) with the qVA method and a hierarchical Bayesian model (HBM) based on the qVA method (Lesmes & Dorr, 2019).
The HBM consisted of hyperparameters and parameters at the population and individual test levels, each of which is a 2-dimensional Gaussian distribution of VA threshold and range. The covariances were set up to capture the cross- and within-test regularities. We compared the average half width of the 68.2% credible interval (HWCI) of the VA threshold and range estimates from the qVA and HBM analyses.
The HBM analysis recovered the correlations between VA threshold and range from the E-ETDRS (0.527 and 0.058) and FrACT (0.755 and 0.218) datasets at the population and individual test levels (Fig. 1). Table 1 shows the average HWCI of the VA threshold and range estimates. The average HWCI of the VA threshold estimates from the E-ETDRS dataset were 0.050 and 0.039 logMAR from the qVA and HBM analyses, respectively, with a 22% reduction by the HBM. The average HWCI of the VA threshold estimates from the FrACT dataset were 0.049 and 0.043 logMAR, with an 11% reduction by the HBM. Compared with the qVA analysis, the HBM also significantly reduced the average HWCI of the range estimates from the E-ETDRS (from 0.148 to 0.072 logMAR, a 51% reduction) and FrACT (from 0.214 to 0.96 logMAR, a 55% reduction) datasets. In comparison, HBM analysis of the qVA data from the same subjects in the same testing conditions resulted in average HWCIs of 0.019 and 0.048 logMAR for VA threshold and range (Table 1).
Incorporating both cross- and within-test regularities, the HBM analysis greatly improved the precision of VA threshold and range estimates in the E-ETDRS (30 optotypes) and FrACT (45 optotypes) datasets, although the combination of the HBM and qVA test is the best option.
This is a 2021 ARVO Annual Meeting abstract.
Fig 1. Two-dimensional VA threshold vs range distributions at the (a, c) population and (b, d) individual test levels for the E-ETDRS and FrACT datasets in the HBM.
Table 1. 68.2% HWCI of VA threshold and range estimates (logMAR).
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