Using Bayesian Sequential Logistic Regression to Model the Organ Selection Process

Abstract

Organ transplantation evaluation is a multi-phase process characterized by sequential dependency and structural patient attrition. Conventional models that estimate stage-specific transitions independently often suffer from estimation uncertainty driven by late-stage data sparsity. To address these limitations, we propose a Bayesian sequential logistic regression framework. By formulating the multi-stage progression as a series of conditional Bernoulli distributions within a joint likelihood, the model formally accommodates chronological dependencies. Furthermore, the framework utilizes a hierarchical prior structure that decomposes covariate effects into an overall effect and deviation. This partial pooling mechanism shares information across the continuum. We applied this framework to evaluate factors associated with patient attrition in the kidney and liver transplantation cohorts from the CHART dataset. The posterior estimates reveal that the impact of clinical indicators and social determinants of health is not constant across the evaluation stages. While early administrative phases exhibit uniform progression, late-stage transitions are significantly influenced by physiological markers, such as the MELD score, and systemic non-clinical barriers. Compared to independent logistic regression, this model produced narrower credible intervals under structural sparsity, successfully isolating true stage-specific covariate variations from noise. Ultimately, this methodology provides a reliable approach for evaluating sequential medical pathways.