section of decision sciences and clinical systems modeling optimal organ allocation policies: an...

Section of Decision Sciences and Clinical Systems ModelingSECTION OFDECISION SCIENCESAND CLINICAL SYSTEMSMODELING

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Optimal Organ Allocation Policies:An application of discrete event simulation

Mark S. Roberts, MD, MPP

Associate Professor of Medicine, Health Policy and Management and Industrial Engineering

Chief, Section of Decision Sciences and Clinical Systems ModelingUniversity of Pittsburgh School of Medicine

University of Pittsburgh

SECTION OFDECISION SCIENCESAND CLINICAL SYSTEMSMODELING

SDSCSM


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2

The general problem of Organ Allocation

• Organs are a scare resource, and waiting lists are increasing

• The debate (in the US) surrounds– Who gets transplanted? (or retransplanted)

– What determines selection priority and site?• UNOS (Has changed allocation rules 3 times)

• HCFA (rules about success rates required for sites)

– What level of regional preference is appropriate?

– Organs to the sickest or to those who would benefit most?

• What are the appropriate methods to analyze this problem?

• As much a talk about the value of simulation as a talk about transplantation allocation


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3

What is the Clinical and Policy Problem?

• There are two very distinct questions that can be asked regarding transplantation:– CLINICAL Question: given a specific patient with a specific

disease and a set of clinical characteristics, what is the optimal timing in the declining course of disease to transplant that specific patient?

– POLICY Question: What set of selection, listing criteria and allocation rules maximize the utility of the limited supply of organs? (What is the optimal timing from the point of view of the society?)


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4

Allocation of organs to Patients

• In the US, organs are allocated (in theory) with a balance of efficiency and fairness

• The United Network for Organ Sharing (UNOS) is responsible for implementing and setting allocation policy

• Current rules are essentially a combination of two concepts:– PRIORITIZATION: where a patient falls in the waiting list

– ALLOCATION: how many lists there are in the country• For example, there are different lists for each region, and acute liver

disease is treated differently from chronic liver disease


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US Organ Procurement Organizations (OPOs)

OPOs are aggregated into 11 regions


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Prioritization

• As changed several times over the past decade:

• Prior to 2002– 4 “Status” groups

• 1 (acute, fulminate liver failure)

• 2a (chronic liver failure, need ICU care for survival)

• 2b (chronic liver failure, need hospitalization)

• 3 (chronic liver failure, not in hospital)

– Several other “status” levels for special circumstances• Status 7 (“too sick” at the moment)

– Order within status mainly determined by waiting time

– Allows for gaming the system


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Prioritization (MELD score since 2002)

• Prioritization was changed to rank people based on level of illness (transplant the sickest first)

• Model for End-stage Liver Disease (MELD score)– Predicts the probability of survival for the next three months

– Scaled to an integer between 6 (lowest probability of death) and 40 (highest probability of death)

• Status 1’s are the same (fulminate, with p(death in 7 days) > 50%)

• The remainder are grouped by MELD, rank within MELD is where wait time, blood type compatibility matter

MELD Score = 10*(0.957 x ln(creatinine) + 0. 378 x ln(bilirubin) + 1.120 x ln(INR) + 0.643)


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Allocation Hierarchy: OPO to Region to Nation

• Livers are divided into two major groups:– STATUS 1: patients with acute

liver failure with a LE of <7 days

– CHRONIC patients, allocated by MELD Score (a statistical score representing probability of dying in 3 months) that varies between 6 (healthiest) and 40 (sickest)

OPO

Region

Nation

Status 1

MELD Score

1

2

3

4

5

6


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Goal of overall modeling effort

• Goal is to build a model that represents the clinical natural history of ESLD and then superimpose selection, timing and allocation policies on top of that model

• Requires a clinically robust, detailed model of the progression and natural history of liver disease

Waiting list

Organ

Different rules will imply that different patients receive organs at different times in their disease: post transplant success is a function of clinical characteristics of the recipient and the donor


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ESLD Clinical Model: Chronic Disease"L

IVE

R F

UN

CT

ION

"

TIME

THERAPY REQUIRED

DEATH

CHRONIC DISEASE

SYMPTOMDEVELOPMENT “Natural History”

COMPLICATIONS

Imagine there was a single marker of “liver function” that could be tracked over time. As liver function declines, various clinical events begin to occur


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Average Natural History:LI

VE

R F

UN

CT

ION

TIME

Therapyrequired

Death

symptomdevelopment

“Natural History”


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Effect of Natural HX on Transplant Success

• As liver disease progresses,the success of transplantation changes:– Increase operative death

– Decreased post-op survival

100%

80%

60%

40%

20%

0%

OP

ER

AT

IVE

MO

RT

AL

ITY

OPERATIVE MORTALITY

POST TRANSPLANT SURVIVAL

DECLINING LIVER FUNCTION(PROGRESSION OF DISEASE)

PO

ST

-TR

AN

SP

LA

NT

SU

RV

IVA

L (

YR

S)


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Post Transplant Survival by Severity of Disease

• If transplanted early, there is little operative death

• As disease progresses, operation carries higher mortality risk, and post TX survival declines

• Eventually patients become extremely high risk

Early (Asymptomatic)

Intermediate(sick)

Late (very sick)

TIME

SU

RV

IVA

L

Transplantation Survival by stage of disease


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Natural History and Post TX Survival

• Transplantation early may provide less post-tx survival than Nat Hx

• Transplanting too late may provide post tx survival that is to short

Natural History(no transplant)

Early transplantIntermediateTransplant

Late Transplant

SU

RV

IVA

L

TIME

Transplantation Survival vs. Natural History


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Markov Model: Initial attempts to modelSTABLEWITHESLD

AWAITTRANSPLANT

RECEIVEGRAFT

STABLEAFTER

TRANSPLANT

GRAFTFAILURE

DEATH

TRANSPLANTSELECTION

TRANSPLANT

(2) ELECTIVELY (1) EMERGENTLY(3) WAIT

NO

YES

YES

NO

NO

YES

YES

NO

NO YES

DIE 1st 24 HOURS

p(die)=Logit(Age, bilirubin, creatinine ..., etc ...)

p=BOOLEAN(EMERGENT TX CRITERIA)

p=BOOLEAN(ELECTIVE TX CRITERIA)

COMPLICATION

p(die)=f(covariate vector)

NO YES

REPLICA OFSUBTREE # 1

COMPLICATION(Subtree #1)

FATALNOYES

YES

YES

NO

NO

YES

NO

COMA

SEPSIS

COMA

MEDICAL

THERAPY

SUCCEEDSFAILS

RENALFAILURE

p=f(COMPLICATIONS, SEVERITY, TIME IN QUE)

UPDATE TIME-DEPENDENT PORTIONSOF COVARIATE VECTOR

EMERGENT DUMMY SET = TO 1

COMPLICATION

YES

NO

TO STABLE

WITH ESLD

SEPSIS

SEPSIS

SEPSIS

(using various non-parametric and semi-parametric models of survivalanalysis that allow for time-varying covariate effects)

How do we do this part?


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Optimal Timing: asking the wrong question

• We (society) doesn’t chose a “time”, we choose a strategy

• When different people are transplanted is a function of the system

• This question is much more relevant in living donor transplants

• You have seen the work by Oguzhan Alagoz, PhD (a former student) on optimizing this problem

• So, we wanted to look at the societal question: what are the consequences of various allocation rules


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Discrete Event Simulation

• Methodology directly applicable to the problem

• Can model the queues formed, and the other characteristics of the natural history, survival, etc.

• DES simulation allows for competition between resources

• DES models the specifics of the situation – Actual number of people on the list

– Number of transplants

– Number on waiting list

• These are questions that CANNOT be addressed by RCTs or standard statistical methods


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Discrete Event Simulation: The Liver Transplant Model

• Model individual patients presenting with liver disease

• Model individual organs generated by donors

• Model individual transplant centers

• Model pre and post-transplant survival

• Model natural history


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Basic Model Structure

Discrete EventSimulation Model

Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module

Selection and Allocation

Rules

Model OutputsUser-defined

Inputs SurvivalQuality-Adjusted Survival Costs spent on ESLDNumber of deaths waitingAverage waiting timeNumber of wasted organs


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Patient Generator

• Disease (10 Groups)

• Gender

• Age

• Race

• Blood Type

• Laboratory values– Bilirubin– Creatinine– PT– Albumin

Organ Procurement Organizations (OPOs)(which are clustered into

Regions)

OPO1


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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Organ Generator

Organ Procurement Organizations (OPOs)

OPO1

• Gender• Age• Race• Blood Type


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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Data Dependencies

PBC

Female

Home

AlbuminBilirubin

CreatinineProthrombin timeEncephalopathy

PSC Hepatitis Other

Male

Hospital ICU

Age (category)

Caucasian

Arrival rate

Year 1990 1991 1992 1993 1996

Hepatitis

Disease (10 groups)

Age

Location

AA Hispanic

Race

Gender

LaboratoryValues

Other

Type A

Caucasian

Type O

Blood Type


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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Regional/Geographic Overlay

Transplant Center

Transplant Center

Transplant CenterRegion 2

Region 1

DONOR

DONORPOOL

National Waiting List

Center Waiting List

Center Waiting List

Center Waiting List

AllocationAlgorithm

DONOR

Region 1 Waiting List

Region 2 Waiting List


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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Model incorporates current regional preference

• Model could arbitrarily change to any level of regional prioritization or not

OPO

Region

Nation

Status 1

MELD Score

1

2

3

4

5

6


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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Allocation Mechanism: Generic structure

1

2

3

4

Arbitrary number ofPRIORITY LEVELS

Arbitrary Number of LISTS (Regional/OPO, National)

Criteria for Membership in LEVEL

RANKING WITHIN PRIORITY LEVEL

N

PRIORITY LEVEL

•••

OR

DE

R O

F S

EA

RH


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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UNOS Algorithm (1999-2002)

Priority

1

2

3

4

NOT USED

NOT USED

1

2a

2b

3

Regions: 10 OPOsStatus Levels: 4

Ranked by points (ABO; relative time on list)

In ICULE < 7 days….


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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MELD Algorithm (post 2002)

Priority

1

MELD 40

MELD 39

MELD 38

Ranked by points (relative time on list at that score or worse)

In ICULE < 7 days….


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules



•••

MELD 6


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Disease Progression Module

• Modeling natural history– Discrete event simulation requires the ability to predict

(quantitatively) the changes in clinical parameters over time

• Traditional statistical methods are not suited to do this concurrently

where

• Data available is likely biased


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules



X(t+1) = f(X(t))or

X(t+t) = f(X(t),t)

X = (x1x2,x3, ••• xn)

Clinical covariates of interest


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Natural History Estimating Problem

Time

Bili

rub

in

Observed values of variable

“Average Natural History”

Evaluation

Transplant

Natural history according to NIDDK


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules



Patients are “over-sampled” when they are sick, under sampled when they are healthy


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Natural History: Prior Simulation Efforts

Status 1

Status 2a

Status 2b

Status 3

12a2b3

1 2a 2b 3

Time 2

Tim

e 1

In earlier simulation (ULAM), by Pritzker and UNOS, the natural history model is directly tied to the allocation/selection model

p11 p12a p12b p13

p2a1 p2a2a p2b2b p2a3

p2b1 p2b2a p2b2b p2b3

p31 p32a p32b p33

Cannot modify this to assess the effect of the change to the MELD score, for example


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Natural History Modeling

• Laboratory data does not come at regular intervals:– More dense when patient is sick (over-sampled)

– Less dense when patient is healthy (under-sampled)

• Actual laboratory data is interpolated using cubic splines

Observed bilirubin

Cubic spline estimated bilirubinEstimated cubic spline

Time

t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15

Bil

iru

bin


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules



Time 1 Time 2 Time 3 t1 t2 t3 t2 t3 t4 t3 t4 t5

t13 t14 t15


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Maintaining correlations in the data

• All of the laboratories are sampled at the same time, keeping relationships between laboratories

• Each persons laboratory history is decomposed into a series of overlapping triplets– Each triplet characterizes

a short time interval for that patient: labs yesterday, today, and tomorrow

Time


Bili

rub

in L

ev

el (

mg

/dL

)

Bilirubin Albumin

t 1 t 2 t 3 t 1 t 2 t 3

t 2 t 3 t 4 t 2 t 3 t 4

t 3 t 4 t 5 t 3 t 4 t 5. . . . . .. . . . . .. . . . . .t n-2 t n-1 t n t n-2 t n-1 t n

Time


Alb

um

in L

ev

el (

mg

/dL

)


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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Natural History: Stratification


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules



1) Create splines


t13 t14 t15


t13 t14 t15


t13 t14 t15

2) Cut into sequential triplets

Patients with Primary Biliary Cirrhosis

3) Shuffle

PBC

1) Create spline


t13 t14 t15


t13 t14 t15


t13 t14 t15

2) Cut into sequential triplets

3) Shuffle

Patients with Hepatitis B

Hep B


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34

Natural History, Stratification

DZ 1 DZ 2 DZ 3 DZ 4 DZ 5



Five Disease Groups

Out of Hospital

In Hospital

In Intensive Care


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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Disease Progression Mechanism

t-10.93.91.21728

t1.03.91.31829

t+11.23.61.82135

A 42 year old male with hepatitis C

Among all 40-50 old male patients with hepatitis C, find one with “similar” laboratory profile

The “similar” patient’s time t+1 values become the current patient’s time t+1

values.

CreatALBtBILIPTALT

t+1?????

t-11.24.21.01530

t1.34.01.81845

1

2

3

CreatALBtBILIPTALT

CreatALBtBILIPTALT

t-11.24.21.01530

t1.34.01.81845

t+11.23.61.82135


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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36

Determining “similarity”

• Assessed TX surgeons, gastroenterologists

• Determined how different each lab had to be to be “clinically important”


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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37

Modeling Natural History

50 year old Hispanic female with Alcoholic Liver disease

Patient #1

0

5

10

15

20

25

Days

La

bo

rato

ry v

alu

es

0 200 400 600 800

Prothrombin time (sec)Bilirubin (mg/dL)Albumin (g/dL)Creatinine (mg/dL)

1000 1200


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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Modeling Natural HistoryPatient #2

0

5

10

15

20

25

0 200 400 600 800 1000 1200Days

Lab

ora

tory

val

ues

50 year old Hispanic female with Alcoholic Liver disease


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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Modeling Natural History

0

5

10

15

20

25

0 2 4 6 8 10 12 14 16 18Days

La

bo

rato

ry v

alu

es

ICU Hospital ICU

Death


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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Modeling Natural History Results:

* Shown only for one group of ESLD diagnoses (primary biliary cirrhosis, primary sclerosing cholangitis, alcoholic liver disease, and autoimmune disorders). Differences between actual and simulated change are within levels considered “clinically insignificant” by clinical advisory group.


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules



Laboratory ValueActual

ChangeModel

ChangeBilirubin -2.638 -2.515Creatinine -0.197 -0.528Albumin 0.334 0.221PT -0.838 -0.796


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Modeling Natural History Results:


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules



Correlations between Clinical Covariates

Bilirubin Creatinine Albumin PT

Bilirubin 1

Creatinine 0.329 1

Albumin -0.100 -0.006 1

PT 0.389 0.119 -0.273 1


Bilirubin 1

Creatinine 0.329 1

Albumin -0.100 -0.006 1

PT 0.389 0.119 -0.273 1

BilirubinBilirubin CreatinineCreatinine AlbuminAlbumin PTPT

BilirubinBilirubin 11

CreatinineCreatinine 0.3290.329 11

AlbuminAlbumin -0.100-0.100 -0.006-0.006 11

PTPT 0.3890.389 0.1190.119 -0.273-0.273 11

Actual Data


Bilirubin 1

Creatinine 0.332 1

Albumin -0.231 -0.024 1

PT 0.494 0.139 -0.431 1


Bilirubin 1

Creatinine 0.332 1

Albumin -0.231 -0.024 1

PT 0.494 0.139 -0.431 1

BilirubinBilirubin CreatinineCreatinine AlbuminAlbumin PTPT

BilirubinBilirubin 11

CreatinineCreatinine 0.3320.332 11

AlbuminAlbumin -0.231-0.231 -0.024-0.024 11

PTPT 0.4940.494 0.1390.139 -0.431-0.431 11

Simulated Data


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42

Pre-transplant survival


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules



Pro

po

rtio

n S

urv

ivin

g

0 100 200 300 400

Days

1.0

0.9

0.8

0.7

0.6

0.5

ActualModel p=0.26


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Post Transplant Survival

• Estimated disease-specific post transplant survival curves from sample of ~17,000 transplants from UNOS 1991-1996 w/ follow-up to 1999

• Cox proportional Hazards models• Model transplants the patient at a given time, and “knows”

the clinical covariate vector at that time– age, gender, bilirubin, creatinine, PT, albumin, encephalopathy

• Model generates a covariate-adjusted cumulative hazard• Hazard function is randomly samples to arrive at a specific

survival time• Re-estimated for Cox model predicting graft survival


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules



0.9

0.7

0.5

0.3

0.1

1.0

0.8

0.6

0.4

0.2

1 2 3 4 5 6 7 8 9

Years

Po

rtio

n s

urv

ivin

g

0

(1596)

(1487)

(4460)

(3150)

(784)

PBC

PSC

HEP C

ALD

HEP B

Autoimmune

Cancers

Metabolic

Fulminant

Other

(2839)

(538)

(583)

(954)

(653)


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45


• Cox proportional Hazard models by disease

Patient Survival

Graft Survival

If Patient Survival > Graft Survival, patient is RELISTED at time of graft failure

If Patient Survival < Graft Survival, patient dies at survival time

Organ characteristics

Patient characteristics


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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Cost Module

• Not yet implemented

• Extract of ~2000 patients from UNOS matched to CMS claims

• Costs of care– Pre-transplant/transplant/post-transplant

• Disease-specific, location (in hospital out of hospital) specific


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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47

Quality of Life module

• Prospective evaluation of patients awaiting transplant

• Formal Utility Assessments– Standard Gamble

– Time Trade off

– Visual Analog Scale

– NIDDK Quality of Life Questionnaire

• Hoped to predict utility from QOL question responses

• Entered ~ 130 patients

Out of HospitalIn HospitalIn ICUPost Transplant

TTO.74.54.40.84

SG.67.41.40.64

From literature


Patient Generator

Organ Generator

Survival Module

Disease Progression

Module

Resource Use

Module

Quality of Life

Module


Rules




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PatientGenerator

Alive on Waiting List

Improved

“Too sick”

RefusedTransplant

Alive Post Transplant

Dead

Organ MatchOrgan

Generator

Unused

Die Post Transplant

OrganFailure

Die WhileWaiting

Post TransplantSurvival

Quantitative Natural History

Waiting List

Removals

Distribution by:• Region/OPO• Disease• Age• Gender• Race• ABO

•Location• CMV• Prior TX• Clinical Hx• laboratories

Distribution by:• Region/OPO • Age• Race• Gender• CMV • ABO

Post Transplant Patient Survival

Post Transplant Graft Survival

# of organs wasted

# of organs transplanted

# died priorto transplant

# removed from list

• Bilirubin• Albumin

• Creatinine• INR

Arbitrary priority scheme

Arbitrary allocation

rules


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49

Calibration and Validation

Variable# of Transplants

# Waiting

Deaths while waiting

Waiting Time (median)

199226142599

19031880

516473

124142

199329472946

28092548

567514

175193

199431293124

38383544

671589

242217

199534703460

53655072

835754

345316

199635673583

72036795

1000919

n/an/a

ModelUNOS

ModelUNOS

ModelUNOS

ModelUNOS


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50

Allocation Rule Predictions

• We have examined 4 alternative strategies– Original UNOS ranking, local preference

– Original UNOS ranking, national List

– Current MELD ranking, local preference

– Current MELD ranking, national List

• Compare several outcome between multiple scenario runs under each set of conditions

• Use the model to develop (calculate) EMERGENT PROPERTIES – these are properties that are measurable in real world but are

calculated by the model, not used as inputs


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51

Results:

Outcome measure

Patients relistedDeaths while waiting1 year patient survival1 year graft survivalmedian wait time (days)mean survival (years)Mean survival (QALYS)

UNOS Regional

162235890.840.782529.516.65

UNOS National

194731690.820.753469.636.56

MELD Regional

167036120.840.781819.326.67

MELDNational

198531490.820.752849.466.65


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52

Geographic Variability

• Model captures the remarkable geographic variability in waiting times, which is eliminated with move to national list

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

900.00

1 2 3 4 5 6 7 8 9 10 11

Region

Med

ian

Wai

tin

g t

ime

Regional National


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53

SRTR efforts: Simulation Allocation Models (SAMs)

Simulation Allocation Model (SAM)

Donor Organs

Transplant Candidates

Outcomes Under Policy A

Outcomes Under Policy B

DiseaseProgression

Waiting List

Unused Organs

ComparePolicies

Post Transplant Events


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54

SRTR Natural History Model

time

time

time

Bili

rub

inA

lbu

min

Pro

thro

mb

in t

ime

Pick one individual, use that person’s actual history

•What do you do when model actual history?•How to interpolate?


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55

SRTR evaluation of transplant policy: Lung

• Lung transplant rules used waiting time as major prioritization

• Recently (2005) changed from longest wait first to sickest first

• Results have dramatically changed the survival in chronic progressive lung disease


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56

SRTR evaluation of transplant policy: Lung

September 24, 2006

Lung Patients See a New Era of Transplants

By Denise Grady

A quiet revolution in the world of lung transplants is saving the lives of people who, just two years ago, would have died on the waiting list.


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57

Current allocation question

14 15 17 19 21 24 25 26 28 31 34 36

14 15 17 19 21 24 25 26 28 31 34 36

Sickest first

Largest Net Benefit First

14

Survival with THIS organ (Stx)

Survival with NO organ (Sno-tx)

NET Benefit = Stx – Sno-tx

6.9 7.2 6.7 6.3 7.2 7.6 7.3 8.1 8.2 7.4 7.8 7.5NB:

Patients ranked by MELD score (probability of death in 3 months)


SDSCSM

58

Summary:

• Simulation methods match the problem in this context

• DES allows for queues, waiting times, etc to be emergent properties of the model

• Example of biological modeling with a policy overlay

• So, why is it so accepted?


SDSCSM

59

Simulation model acceptance by Transplant community

• Clear standard research methods won’t work– Impractical (and likely illegal) to randomize

• Model was built with clinical oversight and assistance

• Model demonstrates “predictive validity”– Model predicts the effects of rules change

– Rules are changed

– Observe the actual results


SDSCSM

60

section of decision sciences and clinical systems modeling optimal organ allocation policies: an...

Documents

section of decision

clinical question

allocation of organs

allocation rules

chronic liver disease

acute liver disease

b chronic liver failure

fulminate liver failure