Rationing scarce healthcare capacity: A study of the ventilator allocation guidelines during the COVID-19 pandemic

Abstract

In the United States, even though national guidelines for allocating scarce healthcare resources are lacking, 26 states have specific ventilator allocation guidelines to be invoked in case of a shortage. While several states developed their guidelines in response to the recent COVID-19 pandemic, New York State developed these guidelines in 2015 as "pandemic influenza is a foreseeable threat, one that we cannot ignore." The primary objective of this study is to assess the existing procedures and priority rules in place for allocating/rationing scarce ventilator capacity and propose alternative (and improved) priority schemes. We first build machine learning models using inpatient records of COVID-19 patients admitted to New York-Presbyterian/Columbia University Irving Medical Center and an affiliated community health center to predict survival probabilities as well as ventilator length-of-use. Then, we use the resulting point estimators and their uncertainties as inputs for a multiclass priority queueing model with abandonments to assess three priority schemes: (i) SOFA-P (Sequential Organ Failure Assessment based prioritization), which most closely mimics the existing practice by prioritizing patients with sufficiently low SOFA scores; (ii) ISP (incremental survival probability), which assigns priority based on patient-level survival predictions; and (iii) ISP-LU (incremental survival probability per length-of-use), which takes into account survival predictions and resource use duration. Our findings highlight that our proposed priority scheme, ISP-LU, achieves a demonstrable improvement over the other two alternatives. Specifically, the expected number of survivals increases and death risk while waiting for ventilator use decreases. We also show that ISP-LU is a robust priority scheme whose implementation yields a Pareto-improvement over both SOFA-P and ISP in terms of maximizing saved lives after mechanical ventilation while limiting racial disparity in access to the priority queue.

Keywords: COVID‐19; fairness; machine learning; multiclass queueing with abandonments; priority scheduling; resource allocation; scarce ventilator capacity.

FIGURE 1

Critical standards of care and ventilator allocation rules in (a) Idaho as of late 2020, (b) Minnesota as of August 2021, and (c) New York State as of 2015

FIGURE 2

ROC curves for the mortality model with ventilation using the available information versus for a model using only the SOFA score proxy

FIGURE 3

An example instance with implied utilization of 183.5% highlighting which patient classes are routed to the RED and YELLOW queues by (a) SOFA‐P, (b) ISP, and (c) ISP‐LU

FIGURE 4

An example instance with implied utilization of 183.5% highlighting (a) the optimal ${\alpha }_{\text{SOFA-P}}$, ${\alpha }_{\text{ISP}}$, and ${\alpha }_{\text{ISP-LU}}$ values, as well as the differences in (b) the probability of death while waiting, and (c) the expected number of surviving patients for SOFA‐P, ISP, and ISP‐LU

FIGURE 5

Key performance metrics: (a) expected number of surviving patients and (b) death probability while waiting as we vary implied utilization values from 131.1% to 229.3%

FIGURE 6

Group fairness metrics: (a) range: ${\varphi }_{\text{Range}}(\alpha )$ and (b) standard deviation: ${\varphi }_{S.Dev}(\alpha )$ for SOFA‐P, ISP, and ISP‐LU at 183.5% implied utilization

FIGURE 7

Absolute cost of fairness at 183.5% implied utilization when the racial dispersion metric is (a) ${\varphi }_{\text{Range}}(\alpha )$ and (b) ${\varphi }_{\text{S.Dev}}(\alpha )$

FIGURE 8

Relative cost of fairness at 183.5% implied utilization when the racial dispersion metric is (a) ${\varphi }_{\text{Range}}(\alpha )$ and (b) ${\varphi }_{\text{S.Dev}}(\alpha )$

FIGURE B1

ROC curves for different models

FIGURE C1

Expected number of survivals as a function of fraction α routed to the RED queue at each implied utilization level

FIGURE C2

Abandonment probability at each implied utilization level

FIGURE C3

Distribution of the expected number of surviving patients at each implied utilization level

FIGURE C4

Absolute cost of fairness using the standard deviation based dispersion metric at each implied utilization level

FIGURE C5

Absolute cost of fairness using range dispersion metric at each implied utilization level

FIGURE C6

Relative cost of fairness using the standard deviation dispersion metric relative to best priority scheme (ISP‐LU) at each implied utilization level

FIGURE C7

Relative cost of fairness using the range dispersion metric relative to best priority scheme (ISP‐LU) at each implied utilization level