Collective endpoint of visual acuity and contrast sensitivity function from hierarchical Bayesian joint modeling.

Clinical trials typically analyze multiple endpoints for signals of efficacy. To improve signal detection for treatment effects using the high-dimensional data collected in trials, we developed a hierarchical Bayesian joint model (HBJM) to compute a five-dimensional collective endpoint (CE5D) of contrast sensitivity function (CSF) and visual acuity (VA). The HBJM analyzes row-by-row CSF and VA data across multiple conditions, and describes visual functions across a hierarchy of population, individuals, and tests. It generates joint posterior distributions of CE5D that combines CSF (peak gain, peak frequency, and bandwidth) and VA (threshold and range) parameters. The HBJM was applied to an existing dataset of 14 eyes, each tested with the quantitative VA and quantitative CSF procedures in four Bangerter foil conditions. The HBJM recovered strong correlations among CE5D components at all levels. With 15 qVA and 25 qCSF rows, it reduced the variance of the estimated components by 72% on average. Combining signals from VA and CSF and reducing noises, CE5D exhibited significantly higher sensitivity and accuracy in discriminating performance differences between foil conditions at both the group and test levels than the original tests. The HBJM extracts valuable information about covariance of CSF and VA parameters, improves precision of the estimated parameters, and increases the statistical power in detecting vision changes. By combining signals and reducing noise from multiple tests for detecting vision changes, the HBJM framework exhibits potential to increase statistical power for combining multi-modality data in ophthalmic trials.