Reference-based sensitivity analysis for bounded longitudinal outcomes

Abstract

Reference-based sensitivity analysis is widely used to assess departures from the assumption that data are missing at random in longitudinal randomized trials, but existing methods are typically formulated for approximately Gaussian continuous outcomes and do not directly accommodate bounded outcomes, particularly when exact lower or upper bounds may occur with appreciable probability. We propose a Bayesian reference-based sensitivity analysis framework for bounded longitudinal outcomes, based on a thresholded latent Gaussian working model. Interior observations are mapped one-to-one to the latent scale, whereas boundary observations correspond to latent values below or above prespecified thresholds, yielding a distribution on the observed scale with a continuous interior density and positive mass at the bounds. Reference-based rules are imposed on the latent scale, and posterior predictive imputation proceeds on that scale before mapping back to the original outcome scale. Simulations assessed model calibration, recovery of complete data contrasts, and population treatment effect inference after imputation. For the proposed model, population treatment effect inference showed small bias when the analysis rule matched the truth rule after the trigger, but conservative Rubin intervals, particularly under jump to reference. The method is illustrated using the BtheB study, a longitudinal trial with a bounded depression outcome and incomplete follow-up.