Quantifying Uncertainty of the Estimated Visual Acuity Behavioral Function With Hierarchical Bayesian Modeling
Yukai Zhao, Luis Andres Lesmes, Michael Dörr, Zhong‐Lin Lu
Abstract
Purpose: 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. Methods: 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. Results: 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. Conclusions: 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. Translational Relevance: The HBM can increase the accuracy in detecting VA changes. Further research is necessary to evaluate its potential in clinical populations.