Patient Prioritization and Resource Allocation in Mass Casualty Incidents

134 Pages·2012·0.82 MB·English

Patient Prioritization and Resource Allocation
in Mass Casualty Incidents
Alex F. Mills
A dissertation submitted to the faculty of the University of North Carolina at Chapel
Hill in partial fulfillment of the requirements for the degree of Doctor of Philosophy
in the Department of Statistics and Operations Research.
Chapel Hill
2012
Approved by:
Nilay Tanık Argon
Wendell G. Gilland
Kristen Hassmiller Lich
Vidyadhar G. Kulkarni
Serhan Ziya
c 2012
(cid:13)
Alex F. Mills
ALL RIGHTS RESERVED
ii
Abstract
ALEX F. MILLS: Patient Prioritization and Resource Allocation
in Mass Casualty Incidents.
(Under the direction of Nilay Tanık Argon and Serhan Ziya.)
Mass-casualty incidents, such as multi-car traffic accidents, plane crashes, and terrorist
bombings, create a sudden spike in demand for emergency resources in an area. Providers
of emergency medical services must act quickly to make decisions that will affect the lives
of injured patients. Particularly important is triage, the process of classifying patients and
prioritizing them for transportation from the scene of the incident. The most widely used
standard for mass-casualty triage, START, prescribes a fixed priority ordering among the
different classes of patients, without explicitly accounting for resource limitations. We de-
veloppoliciestoimprovetheresourceallocation phaseofSTARTbyexplicitly incorporating
resource limitations. Next, we develop policies for assigning resources when two or more
incidents occur at the same time and demand the same set of resources. Currentstandards,
such as START, do not prescribe how to handle such situations—these decisions are most
often made in an ad hoc manner. Finally, we examine the problem of efficiently routing a
large number of patients affected by a major disaster, such as a biological, chemical, or nu-
clear incident, to facilities where they can be treated. We provide insight on how resources
can be used effectively to treat patients as quickly as possible. Throughout this work, we
focus on policies that are analytically justified, intuitive, broadly applicable, and easy to
implement. Using numerical results and simulation, we demonstrate that implementing
policies based on quantitative analysis can make a meaningful impact by increasing the
expected number of survivors in a mass-casualty incident.
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Acknowledgments
A doctoral dissertation is never the product of just one person, and this dissertation is no
exception. I am grateful to themany family members, friends,teachers, andcolleagues who
have influenced me, supported me, and encouraged me to excel.
Several individuals deserve special acknowledgement for specific help in the completion
of this dissertation. My advisers, Nilay Tanık Argon and Serhan Ziya, have always given
me excellent advice throughout the time that I have worked with them. I am extremely
grateful for their support and I am proud to have been their student. James E. Winslow
provided perspective from the medical point of view, which greatly improved this work.
Finally, I am grateful for the love and support of all of my family, especially my wife, Alicia
M. Frame, without whom I never would have made it through graduate school.
The National Science Foundation (grant number CMMI 0927607) provided financial
support for this project, for which I am grateful.
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Table of Contents
List of Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
List of Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Literature Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Emergency Medicine Literature . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Operations Research Literature . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Patient Prioritization with Resource-Based START (ReSTART) . . . . 14
3.1 Model Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 A Simple Condition for Fixed-Priority Ordering . . . . . . . . . . . . . . . . 18
3.3 Priority Decisions for Two Classes of Patients . . . . . . . . . . . . . . . . . 21
3.3.1 Characterization of the Optimal Policy . . . . . . . . . . . . . . . . . 22
3.3.2 Determining the Optimal Threshold . . . . . . . . . . . . . . . . . . 23
3.3.3 Sensitivity of the Optimal Policy to the Number of Patients . . . . . 25
3.4 A New Policy for Patient Triage: ReSTART . . . . . . . . . . . . . . . . . . 26
3.4.1 QuickDynamic-ReSTART (QD-ReSTART) . . . . . . . . . . . . . . 27
3.4.2 QuickStatic-ReSTART (QS-ReSTART) . . . . . . . . . . . . . . . . 30
3.5 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5.2 ComparisonofQD-ReSTARTandQS-ReSTARTwithSTART
and InvSTART . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5.3 Sensitivity Analysis on the Reward Functions . . . . . . . . . . . . . 40
v
3.6 Adapting ReSTART to Changing Conditions on the Field . . . . . . . . . . 43
3.6.1 Adaptive QD-ReSTART and QS-ReSTART . . . . . . . . . . . . . . 44
3.6.2 Performance of Adaptive ReSTART policies . . . . . . . . . . . . . . 45
3.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4 Resource Allocation in a Multiple Location Mass-Casualty Incident . . 49
4.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2 Analysis of Two-Incident Problem . . . . . . . . . . . . . . . . . . . . . . . 53
4.2.1 Upper and lower bounds for t∗ . . . . . . . . . . . . . . . . . . . . . 54
4.2.2 Upper and lower bounds for t∗∗ . . . . . . . . . . . . . . . . . . . . . 56
4.2.3 Application of Lower and Upper Bounds . . . . . . . . . . . . . . . . 58
4.2.4 Decentralized Resource Allocation . . . . . . . . . . . . . . . . . . . 59
4.3 Analysis for More than Two Incidents . . . . . . . . . . . . . . . . . . . . . 61
4.4 Heuristic Policies and Simulation Study . . . . . . . . . . . . . . . . . . . . 63
4.4.1 Policy Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.4.2 Simulation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5 Dynamic Routing of Casualties in a Mass-Casualty Incident . . . . . . . 70
5.1 Dynamic programming formulation . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 Analytical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.3 Heuristic Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.3.1 Marginal value approximation . . . . . . . . . . . . . . . . . . . . . . 81
5.3.2 Policy improvement heuristics . . . . . . . . . . . . . . . . . . . . . . 82
5.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.5 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
vi
Appendix Proofs of Analytical Results. . . . . . . . . . . . . . . . . . . . 95
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
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List of Tables
3.1 Fitted parameters for the five survival scenarios. . . . . . . . . . . . . . . . 34
3.2 Mean values of φ over 500 instances for the five survival scenarios,
excluding instances for which t∗ = 0. All 95% half-widths are less
than 0.01. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Mean reduction in the critical mortality rate obtained using QD-
ReSTART instead of START. . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4 Mean reduction in the critical mortality rate obtained using QD-
ReSTART instead of InvSTART. . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5 Mean reduction in the critical mortality rate obtained using QS-
ReSTART as opposed to START, InvSTART, or QD-ReSTART
(negative numbers indicate an increase in critical mortality). . . . . . . . . 41
3.6 Mean reduction in the critical mortality rate obtained using QD-
ReSTART(0.5) and QS-ReSTART(0.5) instead of START on in-
stances with perturbed reward function parameters. . . . . . . . . . . . . . 42
3.7 Meanand95%half-widthforreductioninthecriticalmortality rate
obtained using adaptive ReSTART policies instead of START for
different simulated scenarios. . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.1 Summary of heuristic policies for two-location and multi-location
MCI response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2 Mean decrease in critical mortality over 200 instances compared to
Decentralized-Simul-S with fluid optimal resource allocation. . . . . . . . . 68
5.1 Heuristic results as a percentage of optimal value. Minimum, quar-
tiles, maximum, and mean are calculated across 10,000 randomly
generated instances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.2 Simulation results for m = 3,n = 3,4,5 ,p = 50. (*) indicates
{ }
significance at the 0.05 level. . . . . . . . . . . . . . . . . . . . . . . . . . . 90
viii
List of Figures
3.1 Example of reward functions satisfying Assumption 3.1. . . . . . . . . . . . 22
3.2 Visualizations of QD-ReSTART(0.5) and QS-ReSTART(0.5). . . . . . . . . 30
3.3 Survival probability (reward) functions, g(t), and START class dis-
tributions for the five scenarios. . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1 Histograms for ψ∗ (left) and ψ∗∗ (right) from the numerical experiment. . . 64
5.1 Evacuation and decontamination of casualties in the aftermath of a
mass-casualty event involving the release of a hazardous substance. . . . . . 73
5.2 Example problem instance with = 1,2 and = A,B ; num-
R { } S { }
bers on arcs indicate mean travel times 1/τ for i ,j . . . . . . . . 78
ij
∈ R ∈ S
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Chapter 1
Introduction
In a mass-casualty incident (MCI), the number of patients is large enough to overwhelm
the emergency responseresources in an area, so even critically injuredpatients may have to
wait to be transported to a hospital. Managing the emergency response in an MCI requires
making many decisions. Depending on the scale of the incident and the severity of the
patients’ injuries, these decisions may include how many resources are needed to respond
to the incident or incidents, how to classify patients, which patients should get priority for
transportation to a hospital, and to which facility each patient should be sent. Because of
thetime-sensitive natureof emergency medicine andthechaotic environmentpresentat the
scene of an MCI, these decisions must be made quickly, and often with limited information.
Thisdissertation analyzes someof theimportantprioritization andresourceallocation deci-
sions thatmustbemadewhenrespondingtoan MCI.We examineseveral of these decisions
with the goals of developing policies that are practical and effective, and providing insights
that can guide decision makers in an emergency. We consider improvements to patient pri-
oritization that can bemade within the framework of existing triage standards, we examine
how to allocate resources in scenarios not considered by current protocols, and we attempt
to quantify some of the observations that have been made by experts in the medical field.
Oneofthemostimportantconcepts involved intheresponsetoamass-casualty incident
is triage. Triage is the process of classifying patients according to their medical conditions
and injury characteristics and then determining the order in which they will be treated.
According to the current practice, priority assignments in an MCI are made in a very