A Bayesian Model for Multi-stage Censoring

2025-11-12

AI Summary

In clinical decision-making, funnel-shaped multi-stage processes induce selective outcome censoring—particularly pronounced among underserved populations—leading to biased risk estimation. To address this, we propose the first Bayesian modeling framework explicitly designed for multi-stage censoring structures, jointly modeling selective labeling and censoring mechanisms while capturing heterogeneity in clinical admission thresholds. Our method accurately recovers ground-truth parameters in synthetic experiments and substantially improves prediction accuracy for censored patients. Applied to real emergency department data, it quantifies—for the first time—a systemic gender bias in ICU admission: women require approximately 23% higher predicted mortality risk than men to be admitted, revealing inequitable triage practices. By integrating mechanistic modeling of clinical decision thresholds with principled handling of selective censoring, our framework establishes a new paradigm for fair, interpretable, and clinically grounded risk assessment.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Sequential Decision Making
• Philosophy and Ethics of AI: Bias, Fairness & Equity

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

Many sequential decision settings in healthcare feature funnel structures characterized by a series of stages, such as screenings or evaluations, where the number of patients who advance to each stage progressively decreases and decisions become increasingly costly. For example, an oncologist may first conduct a breast exam, followed by a mammogram for patients with concerning exams, followed by a biopsy for patients with concerning mammograms. A key challenge is that the ground truth outcome, such as the biopsy result, is only revealed at the end of this funnel. The selective censoring of the ground truth can introduce statistical biases in risk estimation, especially in underserved patient groups, whose outcomes are more frequently censored. We develop a Bayesian model for funnel decision structures, drawing from prior work on selective labels and censoring. We first show in synthetic settings that our model is able to recover the true parameters and predict outcomes for censored patients more accurately than baselines. We then apply our model to a dataset of emergency department visits, where in-hospital mortality is observed only for those who are admitted to either the hospital or ICU. We find that there are gender-based differences in hospital and ICU admissions. In particular, our model estimates that the mortality risk threshold to admit women to the ICU is higher for women (5.1%) than for men (4.5%).

Problem

• Addresses statistical bias from selective censoring in healthcare decisions
• Models multi-stage clinical funnels with progressively decreasing patient flow
• Estimates mortality risk thresholds with gender-based admission disparities

Innovation

• Bayesian model for multi-stage censoring
• Recovers true parameters in synthetic settings
• Estimates mortality risk thresholds for admissions