Abstract
Purpose :
For consideration as a safety and efficacy endpoint in clinical trials, contrast sensitivity (CS) must be measured at multiple spatial frequencies. We developed two non-parametric hierarchical Bayesian models (HBM) to enable advanced statistical inference on CS estimated with qCSF.
Methods :
The HBMc and HBMv computed the joint posterior CS distribution at six traditional spatial frequencies (1, 1.5, 3, 6, 12, and 18 cpd) across the population, individual and test levels. The HBMc incorporated covariance hyperparameters at the population and individual levels to capture the relationship between CSs across SFs; HBMv did not. In addition, we applied a Bayesian inference procedure (BIP) to estimate the posterior CS distribution from each qCSF test independently. The three procedures were applied to a dataset of 112 subjects tested with qCSF 50 trials in each of three (L, M, & H) luminance conditions (Hou et al., 2016).
Results :
The HBMc generated the most precise CS estimates (average 68.2% HWCI in log10 units= 0.06 for HBMc, 0.07 for HBMv, 0.16 for BIP). HBMc recovered correlations between CSs in pairs of SFs, with r=0.74 to 0.95 for population, 0.02 to 0.63 for individual, and -0.06 to 0.4 at test levels. CS difference distributions between luminance conditions were constructed from the HBMc joint posterior distribution. At the group level, luminance had highly significant effects on CS both across six SFs jointly and at each SF (all p< 0.0001). At the individual level, 100%, 93%, and 73% of the subjects exhibited significant luminance effects across six SFs jointly in L-H, L-M, and H-M comparisons, respectively (p< 0.05), and 99%, 48%, 9.8% of the subjects exhibited significant luminance effects in at least two SFs (p<0.05). With only 25 qCSF trials, the average 68.2% HWCI from HBMc was 0.07 log10 units, and the luminance effects on CS across six SFs jointly and at each SF remained significant (all p< 0.0025).
Conclusions :
The HBMc and HBMv generated precise CS estimates at individual SFs for each subject and therefore improved statistical power. The joint posterior distribution from non-parametric hierarchical Bayesian modeling enabled independent evaluation of statistically significant CS differences at multiple SFs.
This abstract was presented at the 2023 ARVO Annual Meeting, held in New Orleans, LA, April 23-27, 2023.