Using Bayesian Sequential Logistic Regression to Model the Organ Transplant Selection Process

Abstract

Organ transplantation evaluation is a multi-stage process in which only patients who complete one stage remain eligible for the next, leading to patient attrition and reducing later-stage sample sizes. Covariate associations may differ across decision points, and identifying these stage-specific effects is necessary to target interventions and understand disparities. Conventional approaches that model each transition independently fail to distinguish stage-specific from shared associations and tend to produce imprecise estimates at later stages. We propose a Bayesian sequential logistic regression (BSLR) framework that represents progression as conditional Bernoulli distributions within a joint likelihood that preserves chronological ordering; we further show its equivalence to an adjusted continuation-ratio model. A hierarchical prior decomposes each covariate effect into an overall effect and a transition-specific deviation. This partial-pooling structure shares information across stages and stabilizes estimation where data are sparse, while a masking mechanism accommodates covariates structurally unavailable at particular stages without discarding records or imputing values. In simulations, BSLR achieved lower bias, posterior variance, and mean squared error than independent logistic regression. We demonstrated the utility of our model using a cohort of patients referred for kidney or liver transplant. Posterior estimates indicated that the associations of clinical indicators and social determinants of health with progression differed across care continuum phases. BSLR identified stage-specific heterogeneity in covariate associations, revealing factors whose effects reversed direction across evaluation stages and detecting associations at late-stage transitions that independent models failed to resolve due to insufficient precision.