LIVER TRANSPLANT WAITING LIST SIMULATION

An Agent based Model

Alexander Fl´avio de Oliveira

Instituto de Inform´atica, Pontif´ıcia Universidade Cat´olica de Minas Gerais, Belo Horizonte, Brazil

Ricardo Poley Martins Ferreira

Departamento de Engenharia Mecˆanica, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

Agnaldo Soares de Lima

Instituto Alfa de Gastroenterologia do Hospital das Cl´ınicas, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

Keywords:

Multi-agent systems, Agent based simulation, Simulation, Liver transplant waiting list, Queue discipline.

Abstract:

Generally, Prioritizing is not a simple task. Given a waiting list for organ transplantation with dozens of

patients, which patient must be prioritized at the time of an organ donation? Which patient has been waiting

for longer time or which patient has the worst health? What policy would be fairer and more efﬁcient? The

search for an answer to this question can become a complex decision-making problem. The process for testing

various policies and verifying whether each one of them can bring beneﬁts or not, can be slow and consume

valuable resources. Computer simulations can help by allowing, at a lower cost and with greater security and

ﬂexibility, reproduction and study of events whose real occurrence would not be desirable or even possible.

These efforts result in the creation of tools for modeling and simulation. In this work, a model based on multi-

agent systems was developed and implemented by using the Repast framework. The model was calibrated by

using information taken from a real situation. Experiments were carried out illustrating situations in which the

simulation model could be used. The results demonstrated the ability of the model to capture details of reality

and to simulate deﬁned situations.

1 INTRODUCTION

Waiting lists exist in many situations and their study

and analysis attract researchers from different areas

of knowledge. As a result of their research, models

are proposed to represent queues and their applica-

tions (Gross and Harris, 1998). However, although

useful, the mathematical models have difﬁculty to

capture details of the environment and to represent

qualitative aspects such as preferences and behaviors,

which are usually associated with individual charac-

teristics. Given these limits of classical queue math-

ematical models, there have been studies using ap-

proaches based on agents. Their main feature is the

fact that the focus is kept on individuals, being able to

capture details of reality (North and Macal, 2007).

Medical science has made organ transplants pos-

sible, and many lives have been saved. In Brazil,

there were more than 1,000 liver transplants in 2006,

and in 2007 more than 7,000 were waiting for a

liver transplant. Patients waiting for a donated or-

gan are organized in waiting lists. This measure,

however, raises some questions: What queue prior-

ity policy should be used? How should the waiting

list be organized? Which patients are to be priori-

tized? Who has been waiting for more time or who

has the worst clinical condition? Studies on priority

policies (Howard, 2001)(Thompson et al., 2004) seek

answers to these complex decision-making questions.

They seek to improve the system efﬁciency, respect-

ing medical ethics, human rights and distributive jus-

tice.

In 1997, the liver transplant waiting list was or-

ganized by order of patient registration. The objec-

tive was to inhibit frauds in an attempt to minimally

fair organize the access to the grafts (Freeman et al.,

2002). Although objective and transparent, this ﬁrst-

come ﬁrst-served service policy caused side effects.

462

Flávio de Oliveira A., Poley Martins Ferreira R. and Soares de Lima A..

LIVER TRANSPLANT WAITING LIST SIMULATION - An Agent based Model.

DOI: 10.5220/0003188904620468

In Proceedings of the 3rd International Conference on Agents and Artiﬁcial Intelligence (ICAART-2011), pages 462-468

ISBN: 978-989-8425-41-6

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

Knowing that in the future, their patients will need a

transplant, doctors began to enroll them early in the

waiting list, in order that, when they would need the

transplant, the patients would be in top positions of

the queue and thus they would have a greater chance

of receiving the transplant(Freeman et al., 2002). This

behavior caused a generalized queue swelling, harm-

ing those patients with urgent transplant needs who

arrived in the waiting list with lower priority than pa-

tients with better health who were already waiting.

To inhibit early enrollment, and especially to reduce

mortality on the waiting list (Oton-Nieto et al., 2005),

the ﬁrst policy was changed in July 2006 in Brazil

when a health based policy was adopted. The new

policy is based on an index of severity MELD(Model

of End-Stage Liver Disease) of the patient. The pa-

tient’s MELD is calculated using a formula that takes

into consideration results obtained from three blood

tests, which measure how effectively the liver pro-

duces bile; how effectively the liver produces blood

clotting agents, and how effectively the kidneys are

functioning. The MELD score is used to estimate the

patient chances of dying within the next three months.

We proposeand implementan agent based simula-

tion model for the liver transplant waiting list (Weiss,

2000) (Sandholm, 1999). The proposed model is used

to explore, empirically, different situations and to an-

swer ”what-if” questions. The objective is to develop

a model which can help medical decision makers to

understand and to answer questions like: given an or-

gan transplant list with dozens of patients enrolled,

how to prioritize who has been waiting for a longer

time or who has the worst clinical condition? What

policy would be more fair and efﬁcient? To choose a

priority policy is not a simple task and can become a

complex decision-making problem.

In literature simulation models to study liver

transplant waiting lists were developed (Howard,

2001)(Teng and Kong, 2008)(Thompsonet al., 2004).

Most of these models use discrete event simulation.

Teng and Kong (Teng and Kong, 2008) proposed

an agent based simulation, describing their ideas and

presenting some design decisions. Their article is

aimed to study the allocation policy of donated liv-

ers from a geographical distribution point of view tak-

ing into consideration aspects related to organ deliver

logistics and organ quality at the of transplant time.

However, the article does not presentresults and states

that the simulator had not yet been calibrated and val-

idated.

Shechter et al (Shechter et al., 2005) proposed a

biologically based discrete-event simulation that rep-

resents the biology of end-stage liver disease and

the health care organization of transplantation in the

United States. They studied changes in the allocation

policies.

Thompson et al (Thompson et al., 2004) pre-

sented a tool called LSAM (Liver Simulated Alloca-

tion Model capable of simulating different aspects of

a liver transplant waiting list as the allocation poli-

cies. They argue that the simulation-based analysis

can inform the policy process by predicting the likely

effects of alternative policies.

In (Howard, 2001), they study how the ratio be-

tween liver demand and supply affects the waiting

time. The main conclusion was that the rule of

”worst-ﬁrst” is fair, but its efﬁciency, measured by

the loss of patient’s health decreases as the ratio of

demand-supply increases.

The outline of this paper is as follows. We ﬁrst

present the liver transplant waiting list model. Then

follows a section that presents computational exper-

iments made to calibrate and test the simulator, and

to show how it can be used to deal with a transplant

waiting list. Concluding remarks appear in section 4.

2 LIVER TRANSPLANT

WAITING LIST SIMULATION

MODEL

The proposed agent-based simulation model repre-

sents each recipient patient and his or her liver dis-

ease, the donated liver and its characteristics, the

waiting list, and the interactions among them. Each

agent interacts with other agents and entities accord-

ing to speciﬁc needs and objectives (North and Macal,

2007).

To overview the model some considerations are

presented: The model reproduces the liver transplan-

tation process from the moment an organ is available

until the end of post-transplant care which can last

up to one year; The model considers as available re-

sources: medical staff, material, equipment and op-

erating room necessary for the transplant; The model

considers that a donated liver can be used for only one

patient and it considers only adult patients.

The modeled process begins when a patient is

placed on the waiting list following the MELD based

assortment policy. While the patients wait for a com-

patible liver donation, their health changes because

of their diseases. During the waiting time, a patient

can die, but still has chance of recovering his or her

liver function, showingan improvementand no longer

needing a transplant. Waiting in the transplant list,

the patient might prefer to be transferred to another

waiting list, to give up the transplant, or simply loose

LIVER TRANSPLANT WAITING LIST SIMULATION - An Agent based Model

463

contact with the transplant control center for whatever

reason. These events deﬁne the abandon list.

When a liver becomes available, there is an effort

to allocate it to a patient who meets compatibility cri-

teria, respecting his/her position in the waiting list.

Compatibility criteria consider ABO blood type, body

size of the donor and recipient, degree of medical ur-

gency and MELD score (Model for End-Stage Liver

Disease). The patient’s position in the waiting list, in

turn, will depend on the assortment discipline, which

may be ﬁrst-in ﬁrst-served, a random order, the worst-

ﬁrst or the best-ﬁrst. When a compatible patient is

found, the service is started, and the donated liver is

transplanted. After a liver transplant, the patient en-

ters post-transplant care where he or she can stay for

up to one year. During the post-transplant care, the

patient can die or a graft rejection may occur and the

patient must return to the transplant waiting list. The

model dynamic can be seen in the Figure 1.

Figure 1: Simulation model dinamics.

The model entities involved in the simulation:

• Patient: an agent that represents the recipient pa-

tient;

• Liver: an agent that represents the donated organ;

• Assortment discipline: entity that deﬁnes the

waiting list assortment policy;

• Source: an agent responsible for generate patients

and donated livers. We deﬁned two sources types:

patient source and liver source;

• Service: an agent that represents the transplant

surgery, where the donated liver is transplanted

into the recipient patient;

• System Waiting List: an agent responsible for

controlling the entry and the exit in the waiting

list by applying an assortment discipline, and to

verify the compatibility criteria, in order to allo-

cate the donated liver to the chosen patient and to

create services;

• Transplant Follow-up: an agent responsible for

maintaining in the simulation transplanted pa-

tients and to accompany them during a period

of one year. It is also responsible for removing

from the simulation those patients who died post-

transplant and to re-apply on the waiting list those

who have problems with the graft;

• Disease: entity responsible for changes in the pa-

tient’s MELD;

• Report: entity responsible for accounting and

recording on ﬁle the simulation results and indi-

cators.

The patient agent can assume different states:

”sick”, ”sick again”, ”transplanted”,”retransplanted”,

”cured” and ”deceased”. The state in which the pa-

tient lies deﬁnes its behavior. Figure 2 shows the pa-

tient agent states and the events that trigger the tran-

sition between these states.

Figure 2: Patient’s state diagram.

As the patient agent, the liver agent can assume

different states: ”useful”, ”useless” and ”used”. Its

state deﬁnes its behavior.

The patient and the donated liver arrivals are con-

trolled by the sources already deﬁned. When the sim-

ulation begins, the patient source populates the wait-

ing list with an initial number of patients reported by

the user. This step aims to leave the waiting list with

an initial size, deﬁned by the situation being simu-

lated. The source creates agents according to a Pois-

son distribution, assuming a central value entered by

the user. For each created agent, the source provides,

probabilistically, valuesfor someof its attributes. Fig-

ure 3 presents the simulator class model.

Considering the basic elements that describe the

waiting list system (Gross and Harris, 1998), some

model details are given below:

• Patient arrival pattern in the waiting list is repre-

sented by a Poisson distribution;

• The server pattern: each service attends a patient,

and the service time is predetermined and equal

ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence

464

Figure 3: Simulator class diagram.

for all services;

• Discipline: discipline implemented were: worst-

ﬁrst MELD based, Fist-In First-Served;

• System capacity: there is no restriction on the size

of the waiting list which is capable of receiving a

not-bounded number of patients;

• number of service channels: there is no restriction

on the amount of simultaneous services;

• Number of service stages: service (transplant) is

performed in one stage.

In this model, agents use probabilities as a basis

for controlling their behavior. The probability values

used were taken from historical database analysis and

deﬁned by expert ad hoc decision.

The abstract class Disease represents the common

behavior of all diseases that can affect the patient. A

disease has an attribute bonus which contains a value

passed as a parameter by the user. The bonus is a

correction value that is added to the patient MELD

according to their disease, since some disease types,

such as carcinomas, compromise the patient’s health

rapidly requiring urgent transplant.

The disease types implemented by the model are:

ethanolic cirrhosis, post-viral B and C cirrhosis, cryp-

togenic cirrhosis, Hepatocellular Carcinoma and oth-

ers. These types make up represents diseases that can

lead a patient to the transplant waiting list. Generic

graft rejection is implemented as a disease which

affects transplant patients who have problems after

surgery and require a new transplant.

Each disease type is a concrete implementation of

Disease. Thus, the method getHealthTransition (), re-

sponsible for deﬁning the evolution of the patient’s

MELD is deﬁned in Disease, but behaves as the im-

plementation of each patient disease (polymorphism).

This design allows each disease to cause a distinct im-

pact on the patient’s MELD evolution and allows a

greater model detail.

The possibility to register as the patient’s health

changes over time, according to (Howard, 2001), is

important to better capture the dynamic nature of the

problem. However, due to the lack of information, all

the diseases modeled used the same evolution of the

MELD. During this work, no information was found

on the impact of each disease type on MELD value.

So, all diseases evolve in the same way and the value

of the patient’s MELD is increased by a random num-

ber between 0 and 1 in each time interval, each day.

System Waiting List is the agent responsible for

controling and organizing the list agents (patients and

livers), to ﬁnd patients compatible with the available

organs respecting the deﬁned discipline, and to create

the service care . The class that represents this agent

is QueueSystem.

3 COMPUTATIONAL

EXPERIMENTS

Computational experiments were made in order to

calibrate and to test the simulator, as well as to il-

lustrate how it can be used to deal with real situations

and to study the transplant waiting list. The experi-

ments described in this section were performed with

a notebook with a AMD Athlon 64 X2 QL-64 pro-

cessor and 4 GB of RAM memory. Running Win-

dows Vista H.E. 64 bits and the Java version used

was 1.6.0 17. The model was implemented using the

Repast http://repast.sourceforge.net/).

3.1 Model Calibration

The chosen calibration situation was the liver trans-

plantation waiting list of the state of S˜ao Paulo,

Brazil. The obtained data was from the 2008 cen-

sus produced by the State Health Department (Censo

2007 and 2008). This information is presented in Ta-

ble 3. The comparison among the simulation results

output data and the real situation reference data was

made.

The model agents use information and probabili-

ties to control their behavior. These parameters were

obtained from data and were calibrated:

• Probability of health improve: in this context, the

improvement consists in the liver function recov-

ery: 1,15%;

• Probability of death after transplant: 31,78%;

• Probability of re-transplant: 10%.;

• Probability of death in a three months waiting pe-

riod: depending on the patient’s MELD;

• Probability of abandon the list: 23,03%;

• Patient gender probability: 65,7% to be male;

• Patient and liver donor blood types probabilities -

Table 1;

LIVER TRANSPLANT WAITING LIST SIMULATION - An Agent based Model

465

• Patient and liver donor body sizes probabilities:

Small 30%, Medium 40%, Large 30%;

• Initial MELD index probability - Table 2;

• Patient disease type probability: Ethanolic cir-

rhosis 25,71% , Post-viral B and C cirrhosis

28,57%, Cryptogenic cirrhosis 14,29%,Hepato-

cellular Carcinoma 1,43%, Others 30%.

Table 1: Patient and liver donor Brazil blood types proba-

bilities.

Type - +

O 5,3% 42%

A 4,1% 32,2%

B 1,4% 11,1%

AB 0,4% 3,5%

The probability of death in the waiting list is not

a predeﬁned parameter, because the death is related

to the patients MELD. To initialize the simulation the

simulated situation must be deﬁned. The situation is

set up from input data. The data are shown in Table

3. Table 6 shows the obtained results. The ”initial

available livers” and ”special situation bonuses” re-

ceived the value 0, because these informations were

not available. Calculation methods for obtaining the

values of reference data are presented in Table 4 and

applying the formulas Reference and Input data were

obtained. Once deﬁned the situation, the values of

the input data, the comparison indicators and the ref-

erence data, ﬁve simulations were performed and the

average of the results were compared with the refer-

ence data. To compare the results of simulation with

real data we used the deﬁned error in the calibration

process. The error represents the relative difference

between output and the reference data. Table 6 shows

the obtained results. The error represents the relative

difference between the output data and the reference

data, and is deﬁned by the following formula:

erro

= (

OutputData

Ref erenceData

− 1) × 100 (1)

Table 2: Initial MELD index probability.

MELD Probability

6 - 10 43,22%

11 - 14 32,63%

15 - 20 19,92%

21 - 30 3,81%

30 0,42%

3.2 Testing the Simulation Model

A second test was made to observe the behavior of the

simulation model using another situation. The cho-

Table 3: 2007 and 2008 waiting list census of the state of

S˜ao Paulo, Brazil.

(P)Time 01/01/2007 01/01/2008

31/12/2007 31/12/2008

(Ci) Initial size of the

waiting list 3.904 3.493

(E)Arrival patients 1.021 1.212

(I)Inscriptions 1.021 1.212

(S) Patients who left 1.439 2.132

(Tdv)Living donor transplants 95 79

(Tfe)Transp. outside the State 5 8

(Tps)Transp. inside the State 331 455

(Tsc)Transp. without

conﬁrmation 5 3

(A)Abandon 5 10

(FHr)Liver function recovered 45 54

(NQT)Patient do not want be

transplanted 14 15

(Rid)Rem. (duplicate ) 5 2

(Rmv)Rem. MELD/PELD

( overdue 365 days) not informed 835

(Rs)Rem.(suspended 365days) 119 113

(Rpe)Rem. by the medical 44 32

(Rsc)Rem. without clinical

conditions 50 50

(Toe)Moved to another state 15 17

(O)Pre-transplant death 706 459

(Cf)FINAL RECORD 3.486 2.573

Removed(Rem.), Transplanted(Transp.).

Based on: (Censo 2007 and 2008).

sen situation was the 2007 S˜ao Paulo liver transplant

waiting list. Table 3 does not contain any informa-

tion about removedpatients from the list because their

MELD three blood tests were not made in the last 365

days. In the 2008 census, 835 patients were in this sit-

uation. This represents 17.75% of the total number of

patients. Therefore, the abandon probability used in

the validation process had to be adjusted. The input

values to the model were obtained using Table 4 for-

mula.

The data presented in Table 3 refers to an assorted

waiting list using the MELD index. Applying the

formulas presented in Table 4, we obtain the values

shown in the Table 5.

Once deﬁned the case to be studied, the input data

values, the comparison indicators and the reference

data, ﬁve simulations were performed and the aver-

age results were compared with the real data. Re-

sults presented in the Table 6 indicates the difference

between the real situation and the simulation results.

The health improvement rate increased by 31,59% in

relation to the real situation The pre-transplant death

and the abandon rates are larger than the real rates.

But the number of patients who died in the waiting

list and the number of patients who abandoned the list

were smaller than pre-transplant deaths increase.

ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence

466

Table 6: Calibration results Simulation results versus Reference data 2008 census and Validation results Simulation results

versus Reference data 2007 census.

Result Indicator Reference Simulation error

Year Data Result

Waiting list size 4.703 4.722 0,41%

Calibration Patients per day arrival rate 3,32 3,37 1,50%

Donated livers per day arrival rate 1,46 1,46 -0,23%

∗

2008 Health improvement rate 1,15% 1,10% -4,20%

Pre-transplant death rate 9,76% 9,64% -1,27%

Abandon rate 23,03% 23,46% 1,88%

Waiting list size 4.920 4.928 0,15%

Validation Patients per day arrival rate 2,78 2,80 0,71%

Average livers arrival rate per day 1,17 1,20 2,77%

2007 Health improvement rate 0,91% 1,20% 31,59%

Pre-transplant death rate 14,35% 11,22% -21,78%

Abandon rate 5,22% 6,39% 22,42%

Table 7: Comparing WF-Meld based versus First-in First-Served disciplines.

Comparison indicator 2008 Values Simulation results

List size 4.703 4717

Number of patients with health improved 54 58

Pre-transplant number of deaths 459 428

Number of patient’s abandon 1083 1067

Discipline WF-MELD Based FIFS

Table 4: Input data equations and Reference data formulas.

Input data Formula

Number of simulated days (P)

Initial number of patients

in the waiting list (Ci)

Initial number of disponible livers -

Average patient arrival rate per day

(I)−(Rid)

(P)

Average liver arrival rate per day

(Tdv)+(T ps)

(P)

Spacial situation bonus -

Discipline Worst-First

Reference data Indicators Formula

List size (I) − (Rid) + (E)

Average patient arrival rate per day

(I)−(Rid)

(P)

Average liver arrival rate per day

(Tdv)+(T ps)

(P)

Health improvement rate

(FHr)

(Ci)+(E)

× 100

Pre-transplant death rate

(O)

(Ci)+(E)

× 100

The simulator allows the inclusion of other details.

As long as more information is available about a sit-

uation, you can represent them in the model. This

versatility allows the model gradually becomes more

complete and capable of reproducing complex situa-

tions.

With the objective of verifying what could be the

results if other waiting list assortment discipline was

used, a simulation was performed taking the 2008

scenario and changing the discipline from worst-ﬁrst

MELD based to the First-In First-Served discipline

which was adopted before 2006. The simulation re-

sults presented in Table 7 suggests that the old policy

Table 5: Input data extracted from the 2007 Census and

from the 2008 Census.

Input data 2007 2008

Number of simulated days 365 365

Initial number of patients

in the waiting list 3.904 3.493

Initial number of

disponible livers 0 0

Average patient arrival

rate per day 2,78 3,32

Average liver arrival

rate per day 1,17 1,46

Spacial situation bonus 0 0

Discipline WF-MELD WF-MELD

Based Based

FIFS (First-In First-Served) was more efﬁcient than

the new MELD based policy. According to the re-

sults, the FIFS policy provides a greater number of

patients with the improved health, a reduction in the

pre-transplant number of deaths, and in the number of

patients who abandon the list.

4 CONCLUDING REMARKS

This research is interested in the liver transplant pa-

tient waiting list organization,and considers problems

that arise from the decision-making process to deﬁne

what assortment policies to adopt.

LIVER TRANSPLANT WAITING LIST SIMULATION - An Agent based Model

467

Seeking to contribute to the study of this prob-

lem, this work developed an agent based simulation

model. The free open source framework Repast was

used. Each component of the process - the patient,

the liver, the waiting list, the transplantation, and the

sources of livers and patients were modeled as agents.

This approachallowed the characterization of the pro-

cess in detail and with a ﬁner granularity.

The simulator was calibrated and some ex-

ploratory experiments were performed. The per-

formed experiments in this study have a demonstra-

tive nature, i.e. they were performed in order to il-

lustrate situations where the simulation model could

be used. For these experiments, comparison indica-

tors were deﬁned and measured to compare the per-

formance of the waiting using a different waiting list

assortment discipline.

The obtained results show the expected behavior.

A more detailed interpretation of the results requires

further study. This effort, while important, goes be-

yond the scope of this paper. Theexperiments demon-

strated the ability of the model to capture details of re-

ality and to reproduce real situations. The model can

be extended, as needed, to represent more complex

situations.

ACKNOWLEDGEMENTS

This work has been supported by FAPEMIG (PPM-

00399-09), CNPQ (371756/2008-1).

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