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Interpretable Machine Learning for Resource Allocation with Application to Ventilator Triage

Julien Grand-Clément, You Hui Goh, Carri Chan, Vineet Goyal, Elizabeth Chuang

TL;DR

This work proposes a novel data-driven model to compute interpretable triage guidelines based on policies for Markov Decision Process that can be represented as simple sequences of decision trees ("tree policies").

Abstract

Rationing of healthcare resources is a challenging decision that policy makers and providers may be forced to make during a pandemic, natural disaster, or mass casualty event. Well-defined guidelines to triage scarce life-saving resources must be designed to promote transparency, trust, and consistency. To facilitate buy-in and use during high-stress situations, these guidelines need to be interpretable and operational. We propose a novel data-driven model to compute interpretable triage guidelines based on policies for Markov Decision Process that can be represented as simple sequences of decision trees ("tree policies"). In particular, we characterize the properties of optimal tree policies and present an algorithm based on dynamic programming recursions to compute good tree policies. We utilize this methodology to obtain simple, novel triage guidelines for ventilator allocations for COVID-19 patients, based on real patient data from Montefiore hospitals. We also compare the performance of our guidelines to the official New York State guidelines that were developed in 2015 (well before the COVID-19 pandemic). Our empirical study shows that the number of excess deaths associated with ventilator shortages could be reduced significantly using our policy. Our work highlights the limitations of the existing official triage guidelines, which need to be adapted specifically to COVID-19 before being successfully deployed.

Interpretable Machine Learning for Resource Allocation with Application to Ventilator Triage

TL;DR

This work proposes a novel data-driven model to compute interpretable triage guidelines based on policies for Markov Decision Process that can be represented as simple sequences of decision trees ("tree policies").

Abstract

Rationing of healthcare resources is a challenging decision that policy makers and providers may be forced to make during a pandemic, natural disaster, or mass casualty event. Well-defined guidelines to triage scarce life-saving resources must be designed to promote transparency, trust, and consistency. To facilitate buy-in and use during high-stress situations, these guidelines need to be interpretable and operational. We propose a novel data-driven model to compute interpretable triage guidelines based on policies for Markov Decision Process that can be represented as simple sequences of decision trees ("tree policies"). In particular, we characterize the properties of optimal tree policies and present an algorithm based on dynamic programming recursions to compute good tree policies. We utilize this methodology to obtain simple, novel triage guidelines for ventilator allocations for COVID-19 patients, based on real patient data from Montefiore hospitals. We also compare the performance of our guidelines to the official New York State guidelines that were developed in 2015 (well before the COVID-19 pandemic). Our empirical study shows that the number of excess deaths associated with ventilator shortages could be reduced significantly using our policy. Our work highlights the limitations of the existing official triage guidelines, which need to be adapted specifically to COVID-19 before being successfully deployed.

Paper Structure

This paper contains 59 sections, 6 theorems, 12 equations, 25 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Outline.
  3. Related literature
  4. Triage guidelines in the Operations Management literature.
  5. Decision trees and MDPs in healthcare.
  6. Interpretable sequential decision-making.
  7. Model of sequential decisions
  8. Evolution of Patient Health and Action Space
  9. Capacity Constraint
  10. Objective function and decision rule
  11. Interpretable Policies
  12. Classification trees
  13. Tree policies for Markov Decision Processes
  14. Structural Properties of optimal tree policies
  15. The case of Markovian tree policies
  16. ...and 44 more sections

Key Result

Proposition 1

Consider an MDP instance $\mathcal{M}$, a set of sequence of trees $\mathbb{T}$ admissible for $\mathcal{M}$ and an admissible sequence of trees $T \in \mathbb{T}$.

Figures (25)

  • Figure 1: Example of two decision trees with three branching nodes, four classes (indicated by the four colors at the leaves), and two labels $y_{1}, y_{2}$. The labeling rules are different in Figure \ref{['fig:tree-label-1']} and in Figure \ref{['fig:tree-label-2']}.
  • Figure 2: Example of a decision tree $T$ with four classes (Figure \ref{['fig:tree-zero']}), a deterministic tree policy in $\Pi_{T}$ (Figure \ref{['fig:tree-policy-deterministic']}) and a randomized tree policy in $\Pi_{T}$ (Figure \ref{['fig:tree-policy-randomized']}).
  • Figure 3: States and transitions in our MDP model with actions 'maintain' and 'exclude'.
  • Figure 4: The experiments pipeline for our numerical results.
  • Figure 5: Number of deaths for various triage guidelines at hypothetical levels of ventilator capacities, for $p=0.99$.
  • ...and 20 more figures

Theorems & Definitions (15)

  • Definition 1: Decision tree and labeling rule
  • Remark 1
  • Definition 2
  • Proposition 1
  • Definition 3: Markovian tree policies
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • Remark 2
  • Remark 3: The case of stationary policies.
  • ...and 5 more