Quantifying Uncertainty of the Estimated Visual Acuity Behavioral Function With Hierarchical Bayesian Modeling.

The goal of this study is to develop a hierarchical Bayesian model (HBM) to better quantify uncertainty in visual acuity (VA) tests by incorporating the relationship between VA threshold and range across multiple individuals and tests. The three-level HBM consisted of multiple two-dimensional Gaussian distributions of hyperparameters and parameters of the VA behavioral function (VABF) at the population, individual, and test levels. The model was applied to a dataset of quantitative VA (qVA) assessments of 14 eyes in 4 Bangerter foil conditions. We quantified uncertainties of the estimated VABF parameters (VA threshold and range) from the HBM and compared them with those from the qVA. The HBM recovered covariances between VABF parameters and provided better fits to the data than the qVA. It reduced the uncertainty of their estimates by 4.2% to 45.8%. The reduction of uncertainty, on average, resulted in 3 fewer rows needed to reach a 95% accuracy in detecting a 0.15 logMAR change of VA threshold or both parameters than the qVA. The HBM utilized knowledge across individuals and tests in a single model and provided better quantification of the uncertainty of the estimated VABF, especially when the number of tested rows was relatively small. The HBM can increase the accuracy in detecting VA changes. Further research is necessary to evaluate its potential in clinical populations.