Purchase this article with an account.
Zhong-Lin Lu, Yukai Zhao, Luis A Lesmes, Michael Dorr; Predicting contrast sensitivity functions with digital twins generated by Hierarchical Bayesian modelling. Invest. Ophthalmol. Vis. Sci. 2022;63(7):2328.
Download citation file:
© ARVO (1962-2015); The Authors (2016-present)
We developed a hierarchical Bayesian model (HBM) based on repeated measures of contrast sensitivity functions (CSF) obtained across three luminance conditions (Zhao et al., 2021). Here we use the HBM, which extracts covariant features within and between individuals and luminances, to generate digital twins for contrast sensitivity (CS) and predict yet-observed results.
The HBM describes CS across a hierarchy of population, individual, and luminance, with hyperparameters at population/individual levels that quantify the covariant relationship between CS parameters (peak gain, peak spatial frequency, and bandwidth) across individuals and luminances. We evenly split 112 subjects in Hou et al. (2016) into Group I (N=56), in which CSF data included three luminances, and Group II (N=56), in which partial data from 0, 1, or 2 luminances were used to train and predict data observed in non-included conditions. Parameter uncertainty was quantified by half-width confidence intervals (HWCI), with smaller HWCI indicating higher model precision.
Group I data exhibited an average HWCI of 0.061 log10, which was expected to be lower than Group II, for which HWCIs decreased (from 0.101 to 0.089 and 0.084) as the number of training conditions increased (from 0 to 1 and 2). The mean absolute error of Group II predictions likewise decreased from 0.048 to 0.036 and 0.034. HBM predictions accounted for 77% and 83% of the variance of observed AULCSF values, using 1 or 2 luminances. Fig. 1 presents the example of one subject, with observed estimates for peak gain and peak frequency (left; top row), and CSF with confidence intervals (right, top row), in addition to digital twin predications for different training conditions (2nd-4th row). When predictions were used to seed analysis of the observed data, only 30-60% of the data collection was needed to reach the accuracy and precision of original analyses.
The HBM for contrast sensitivity extracted valuable information about covariant features within and between individuals and luminances. The HBM enabled the generation of digital twins for CS that predict yet-observed data, significantly reduces testing burden, and exhibits potential for improving real-world testing of functional vision.
This abstract was presented at the 2022 ARVO Annual Meeting, held in Denver, CO, May 1-4, 2022, and virtually.
Observed and predicted CSF parameter and CSF distributions. ‘o’ and ‘x’ represent correct and incorrect trials.
This PDF is available to Subscribers Only