Bayesian Benefit-Risk Assessment with Dependent Outcomes via Latent Factor Models

Abstract

Approving and assessing new drugs is complex because multiple criteria must be considered simultaneously. A common approach is benefit-risk analysis, often conducted within a Bayesian framework to account for uncertainty and combine data with expert judgement, typically through multi-criteria decision analysis (MCDA) scores. This requires models that accommodate mixed and potentially correlated outcomes; latent factor models provide a natural framework. We develop a coherent Bayesian framework for benefit-risk analysis that addresses these challenges and supports sequential decision-making. We extend structured factor models to mixed outcomes and introduce a principled approach for selecting among competing specifications that combines model fit with out-of-sample predictive performance. We then develop a sequential estimation framework that updates MCDA scores as new data become available, allowing treatment comparisons to evolve over time. This supports early stopping when conclusions are clear and permits dynamic treatment allocation aligned with study objectives. To make this feasible, we develop tailored sequential Monte Carlo methods adapted to the model structure. The methodology is illustrated using data on patients with type II diabetes treated with Metformin, Rosiglitazone, and their combination.