Bayesian Semi-Supervised Learning with Prior-Informed Regression: Predicting Psychosocial Distress in Glaucoma Patients

Music City Center 

Glaucoma is a chronic condition that can cause significant psychosocial distress, yet screening for distress remains rare due to the high cost of collecting gold-standard labels. To address this challenge, we develop a novel semi-supervised learning approach that leverages a large historical dataset containing proxy indicators of distress to inform prediction in a smaller, prospectively collected cohort with gold-standard outcomes. Rather than treating the historical data as directly labeled, we use it to construct informative priors on model parameters in a Bayesian regression framework, while explicitly accounting for discrepancies between proxy and true outcomes. This prior-informed strategy enables us to borrow strength from the large but imperfect dataset without assuming outcome equivalence, a common limitation in traditional semi-supervised methods. We demonstrate our approach through simulation studies and real-world data from glaucoma patients at the Duke Eye Center, showing improved prediction accuracy and robust uncertainty quantification in low-label clinical settings.