Using Hierarchical Bayesian Modeling to Enhance Statistical Inference on Contrast Sensitivity

Abstract

Purpose: The purpose of this study is to introduce a nonparametric hierarchical Bayesian model (HBM) that enables advanced statistical inference on contrast sensitivity (CS) both at individual spatial frequencies (SFs) and across multiple SFs in clinical trials, where CS measurements are crucial for assessing safety and efficacy. Methods: The HBM computes the joint posterior distribution of CS at six Food and Drug Administration–designated SFs across the population, individual, and test levels. It incorporates covariances at both population and individual levels to capture the relationship between CSs across SFs. A Bayesian inference procedure (BIP) is also used to estimate the posterior distribution of CS at each SF independently. Both methods are applied to a quantitative CSF (qCSF) dataset of 112 subjects and compared in terms of precision, test-retest reliability of CS estimates, sensitivity, accuracy, and statistical power in detecting CS changes. Results: The HBM reveals correlations between CSs in pairs of SFs and provides significantly more precise estimates and higher test-retest reliability compared to the BIP. Additionally, it improves the average sensitivity and accuracy in detecting CS changes for individual subjects, as well as statistical power for detecting group-level CS changes at individual and combinations of multiple SFs between luminance conditions. Conclusions: The HBM establishes a comprehensive framework to enhance sensitivity, accuracy, and statistical power for detecting CS changes in hierarchical experimental designs. Translational Relevance: The HBM presents a valuable tool for advancing CS assessments in the clinic and clinical trials, potentially improving the evaluation of treatment efficacy and patient outcomes.