An Agent-based Simulation Model to Analyze the US Liver Allocation Policy Yu Teng, Nan Kong Weldon School of Biomedical Engineering Purdue University West.

An Agent-based Simulation Model to Analyze the US Liver Allocation Policy

Yu Teng, Nan KongWeldon School of Biomedical Engineering

Purdue UniversityWest Lafayette, IN

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Background • Organ transplantation and allocation has been a

contentious issue in the U.S. for decades.• End-stage liver disease (ESLD) is the 12th leading cause

of death in the U.S..• Liver transplantation is the only viable therapy at

present.• Limitations of liver transplantation

– Cost: $500,000– Scarcity (in 2008): 17,000 patients in waiting list 11,000 new patients 7,000 donors– Perishable: cold ischemic time (CIT) 12-18 hours

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Organ Transplantation

• Living donor vs. Deceased donor

ESLD Patient

Transplant Waiting List

Living Donor

Deceased Donor

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Construction of an Organ Allocation Policy

• Medical urgency– Before 2002: status 1, 2A, 2B and 3 – After 2002: status 1, MELD 6-40

Model for End-Stage Liver Disease (MELD)

• Geographic proximity – Transplant center, organ procurement organization

(OPO),region, nation • Waiting time

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Objectives of an Organ Allocation Policy

Efficiency:• Pre-transplant: death in waiting list• Transplant: average CIT, average organ travel

distance• Post-transplant: average patient survival,

average graft survival• Death/Tx RatioEquity:

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Development of Organ Allocation Policy

• “Local preference” policy– Reflect the efficiency consideration– Patients with greatest medical need within the

ischemic restraints may not get a donor organ

• “National sharing” policy– A notion of equity– Organ viability of livers cannot be ensured after

long travels

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Current Organ Transplantation and Allocation Policy

• Geographic proximity– Local

• 58 OPOs (50 recipient OPOs)

– Regional• 11 regions

– National

• Medical urgency– Status 1– MELD 6-40 (healthy-sick)

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Current Allocation PolicyVery sick

Healthy

High

LowLocal (OPO)

Regional

National

Status 1

MELD 6-14

2

1

3

5

4 6 HealthLevel

MELD

MELD 15-40Local

Regional

National

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8

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Algorithm for Status 1 Patients Algorithm for MELD Patients

Priority: 1st: MELD 2nd: Blood Compatibility 3rd: Waiting time

Priority is a function of blood compatibility and waiting time.

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Introduction to ABMS• Agent-based modeling and simulation (ABMS) models a system as a collection of autonomous decision-making entities called agents. • Based on a set of rules, each agent individually assesses its situation, makes decisions and executes various

behaviors.• Applications– Epidemiology– Marketing– Emergency response– Organizational decision making

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Why Choose ABMS

In our system, both patients and OPOs in the system can be naturally modeled as agents: •Decision for OPO – What is the optimal prioritization rule– Which region to join •Decision for patients– Where to register– Whether to accept an organ offer– Multiple Listing

• ~ 3.3% patients choose Multiple-listing• Multi-listing patients gain significantly higher transplantation rates

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Conceptual Model

Patient Generator

Pre-transplant Medical History

Organ Generator

Matching Algorithm

Post-transplant Medical History

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Simulation Modeling• 58 OPO network• Initial patient waitlist

– Uncorrelated: blood type, OPO, MELD– Correlated: waiting time, MELD

• Organ arrival• Patient arrival• Patient disease progression

– Time-independent state transition model• Patient removal

– Removal rate dependent upon blood type, OPO and MELD.• CIT based on distance• Patient transplantation outcome:

– function of CIT; – from the literature

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Model Implementation

Repast Symphony 1.1 –Developed in Argonne National Laboratory, Decision and Information Science Division. –Includes advanced point-and-click features for agent behavioral specification and dynamic model self-assembly.–The model components can be developed using any mixture of Java, Groovy and flowcharts.

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Model Components• Agents:– Model Initializer– Organ-patient Generator– Organ

key property: ABO (blood type), location and cold ischemia time– Patient

key property: ABO, location, MELD and waiting time.– OPO

• 2D continuous space• Networks:– Region Network– Transplant Network

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Agent Behavior in Model Initialization

• Model Initializer– generates 58 OPOs

• OPO– generates the

Region Network• Organ-patient

Generator – generates patient

waitlist on Jan. 1st, 2004.

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Agent Behavior in an “Assignment Cycle”

Tick 1• Organ-patient Generator generates organs and patients Tick 2 to Tick 9• OPO agents carry the core matching algorithm.

– 8 behaviors to get different patient lists – 2 behaviors to select a patient on the list to offer the organ

Tick 10• Organ agents remove assigned organs in this cycle, and

record cold ischemia time• Patient agents remove assigned agents, remove dead

patients, change MELD and make records• OPO agents generate outputs

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Agent Behavior in an “Assignment Cycle”

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Experimental Design• 2 extreme cases: “local preference” and “national sharing”• 3 alternative region configurations:

• An alternative medical urgency classification:– S1+MELD 35-40, MELD 15-34, MELD 6-14

Current

Division Combination

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System Outcome Performances

Division Current CombinationLocal

National National S1 Extension

Death Number 972.2 979 1016.7 1010.2 1723.8 1092

Ave CIT (hr) 10.04 10.07 10.16 10.44 13.13 10.12Ave Patient Survival (%) 87.27 87.22 87.12 86.32 81.37 87.20Ave Graft

Survival (%) 80.85 80.75 80.55 79.32 70.74 80.67

Death/Tx Ratio 0.144 0.146 0.151 0.151 0.258 0.162

Ave Distance 47.53 59.48 87.41 182.96 1077.5 75.31

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Strategy Comparison: Paired-t Tests

P valueDivision vs.

CurrentCurrent vs.

CombinationCombination vs. Local National

Local National vs. National

Current vs. S1 Extension

Death Number 0.349 0.026 0.345 0.000 0.000

Ave CIT 0.000 0.000 0.000 0.000 0.000Ave Patient

Survival 0.000 0.000 0.000 0.000 0.000

Ave Graft Survival 0.000 0.000 0.000 0.000 0.000

Death/Tx Ratio 0.249 0.028 0.467 0.000 0.000

Ave Distance 0.000 0.000 0.000 0.000 0.000

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Death vs. Tx Ratio

Current

Division Combination

[0,0.1) [.11,.12) [.12,.13) [.13,.14) [.14,.15) [.15,.16) [.16,.17) [.17,.18) [.18,.19) >=.19

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Organ Transport Distance

Current

Division Combination

[0,10) [10,20) [20,30) [30,40) [40,50) [50,60) [60,70) [70,80) [80,90) >=90 miles

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Urgency Group Reclassification(Death vs. Tx Ratio)

Current

[0,0.1) [.11,.12) [.12,.13) [.13,.14) [.14,.15) [.15,.16) [.16,.17) [.17,.18) [.18,.19) >=.19

S1 Extension

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OPO Level (Death vs. Tx Ratio)

[0,0.1) [.11,.12) [.12,.13) [.13,.14) [.14,.15) [.15,.16) [.16,.17) [.17,.18) [.18,.19) >=.19

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Equity – Death/Tx Ratio• Regional level

• OPO level

Division Current Combination S1 Extension

Maximum 0.208 0.159 0.206 0.223

Minimum 0.107 0.140 0.105 0.111

Difference 0.101 0.019 0.101 0.112

Division Current Combination S1 Extension

Maximum 0.220 0.217 0.233 0.256

Minimum 0.065 0.081 0.074 0.065

Difference 0.155 0.137 0.159 0.191

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Equity – Ave Transport Distance• Regional level

• OPO level

Division Current Combination

Maximum 182.4 156.7 173.2

Minimum 1.593 47.96 1.978

Difference 180.8 108.8 171.2

Division Current Combination

Maximum 280.0 378.9 267.2

Minimum 0.649 14.78 1.559

Difference 279.3 364.1 265.6

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Future Research• Pre-transplant patient natural history• Post-transplant survival prediction

• A decentralized system: organ allocator’s autonomy

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Questions?

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