A Bayesian Model for Multi-stage Censoring

TL;DR

This paper introduces a Bayesian model for multi-stage funnel decision processes in healthcare, addressing biases from censored ground truth data and improving outcome predictions, with applications to emergency department mortality risk assessment.

Contribution

The paper presents a novel Bayesian approach for modeling multi-stage censored data in healthcare, enabling more accurate risk estimation and bias correction in funnel decision structures.

Findings

The model accurately recovers true parameters in synthetic data.

It predicts outcomes for censored patients more effectively than baselines.

Identifies gender-based differences in ICU admission thresholds.

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%).