Simulation of Medical DecisionsStephen D. RobertsEdward P. Fitts Department of Industrial and Systems EngineeringNorth Carolina State UniversityRaleigh, North Carolina

IERC, May 21, 2007

Outline for this talk Introduction to medical decision-making Case: Colorectal Cancer (CRC) Evaluating consequences of medical decisions Simulating the natural history of disease Adding intervention through screening Incorporating parameter uncertainty Concluding comments Topics for future study

Acknowledgements From Vanderbilt University

Medical Center: Dr. Robert Dittus, Dr. Reid Ness Health Services Research: Lijun Wang

From NC State University Graduate students: Cindy Leibsch, Dan Cubbage,

Ali Tafazzoli, Kiavash Kianfar From Industry

MDM, Inc.: Robert Klein

Healthcare in Transition Growth in national health expenditures

From 7.5 % in 1980 to 16.5% in 2010 (?) Complicating healthcare

From fringe benefit to entitlement Aging population requires more medical care New, expensive technology – overused? Growing malpractice claims on liability insurance Rising administrative costs Uninsured and limited access

Role of Medical Decisions Influence greater than 50% of the costs Changing practice of medical decision-making

From cottage industry to corporate practice From general practice to subspecialties From individual doctor to healthcare network

Medical decisions include Prevention (vaccination, screening) Diagnosis and Treatment Surveillance and monitoring

Case: Colorectal Cancer (CRC)

About 150,000 people diagnosed each yearSecond leading cause of cancer deathsAbout 90M people considered at riskMost prominent in western industrialized societies

Key Characteristics Cancer is a disease of the DNA Usually not symptomatic until late Deadly if not found early

Only 8.5% five-year survival if found late Over 90% five-year survival if found early

Risk factors include: Age, race, gender Personal or Family history Other related diseases Lifestyle (?) Diet (?)

Screening for CRC

Endoscopic tests Colonoscopy Sigmoidoscopy

Non-Endoscopic tests Fecal Occult Blood Test (FOBT) Double Contract Barium Enema (DCBE) Virtual Colonoscopy Fecal DNA

Treatment and Intervention Treatment

Surgery Resection: removal of “sections” of the colon Ostomy

Chemotherapy Radiation Combination therapy

Medical screening interventions Accepted practice

Taught in medical school (“experts”) Stated in recognized medical literature

Recommended guidelines American Cancer Society American Gastroenterological Society

An Example Clinical Guideline

Screening Decisions How “patient-centric”?

age, gender, race, family history, compliance? What screening method?

Endoscopic and non-endoscopic When to start screening? Protocol if screen is positive?

Verification and treatment Protocol if screen is negative?

Time to next screening When to stop screening

How to evaluate medical decisions? Health burden

Mortality – life years Morbidity – quality-adjusted life years (QALY)

Cost burden Cost of intervention Cost of maintenance and surveillance

Value for cost Cost-effectiveness (CE): cost per QALY Cost-benefit (CB): net cost

Comparing Alternatives Incremental CE comparing a Base with

Alternative policy:

In a stochastic environment:

A B

A B

C CICER

E E

A B

A B

C CICER

E E

Graphical Interpretation:Cost-Effectiveness Plane

ΔCost

ΔEffect(0,0)

Greater Cost, Greater Effect

Less Cost, Greater Effect

Greater Cost, Less Effect

Less Cost, Less Effect

Unacceptable

Cost Saving

CE > 0

Course of Disease (Natural History)

A1 – undetected first AdenomaA2 – undetected second Adenoma

C1 – invasive Cancer from A1C2 – invasive cancer from A2

CO – Colonoscopy/surgery to remove C1CD – Cancer DeathND – “Natural” Death

A10 A2 C1 CO CD ND C2

Medical TimelineBirth Death

Modeling Natural History Fundamentally stochastic Intermediate relevant events

Start of disease (adenoma) Pathway and Progression

“Natural death” without the disease Marginal life expectancies Modify actuarial data (eliminating CRC)

Complex Adenoma Pathways Non Visible

Adenoma Created

Adenoma Progresses Immediately to Cancer

Non - Progressing

Progressive Adenoma

Advanced Adenoma Non-Cancerous

Advanced Adenoma Cancerous

Follow Cancer Pathway

Local

Regional

Distant

SymptomaticCancer

Death

Why Simulation Non-Markovian

No geometric or exponential state occupancy State explosion to achieve memoryless property

Concurrent multiple precursors to CRC Multivariate and time-dependent processes (depend

on person and adenoma state) Discrete-event System (variable time updating) Object-oriented

Implementing the Simulation Object-oriented framework in Visual Studio .NET 2003:

Scenario object Person objects Adenoma objects

Four-tier object hierarchy

OOS Platform: Random Number Generation, Random Variate Generation, Events, Event Calendars, Entities, Statistics, Simulation Execution

CRC Objects: CRC Event Processes, Person and Adenoma Objects, CRC Database, Screening

.NET Framework: Multiple OOP language support, Simplified Deployment, InterfaceDevelopment, Framework Classes, Integrated Development Environment, ADO.NET

User Interface

Overall Software Design Strategy

Simulation Engine

User Interface

AccessDatabase

Results inExcel

Data Objects

Scenarios

CRC Variables

Report Writer

MedicalProtocolDesign

CRCExpertise

Main Scenario Display

Scenario

CRCSimulations

ScreeningVariables

SimulationVariables

Parameters

Data Available Cancer

National Cancer Institute (SEER) National Data

Centers for Disease Control (CDC) National Center for Health Statistics (NCHS) US Census Bureau Population Estimates Berkeley Mortality Statistics

Vanderbilt CRC Literature Database

Input Modeling Time to event: Johnson SB

Bounded (biomedical character) Non-symmetric (biomedical character) Flexible (four parameters) May be approximated by minimum, maximum, and mode

(with standard deviation being one-sixth of the range) Event process: Non-Homogeneous Poisson Process

(NHPP) Adenoma Incidence Time-dependent piece-wise linearly Poisson rate function

Visual Interactive Modeler (VIM)

Plots

DistributionParameters

Statistics

Non-Homogenous Poisson Process

Using “Expertise” for Input Many key variables not observable (can’t

allow “natural course” of CRC) Use of “expert opinion”

Collaborators Expert Panel

The Expert Panel A modified “Delphi” method

Collect a group of 19 “experts” Repeatedly

Request opinion Feedback results summary results (distribution) Add additional information

Fifteen completed all three iterations Produce distribution estimate (Johnson SB)

Random Number/Variate Generation Combined multiple recursive generator

proposed by L’Ecuyer Very long period Well-spaced seeds Object-oriented simulation (C++)

Inverse transform variate generation Correlation induction variance reduction Use of NORTA for multivariate generation

About the Natural History A “Grand Hypothesis”

Explicit “assumptions” Example: Risk is a characteristic of individuals,

dependent on family history, race, and gender and influences both the rate of adenoma appearance and the progression of the adenoma to cancer.

Example: The time to cancer incidence is described by a Johnson SB distribution whose mean is 22 and mode is 20.

Fundamental assumptions

Simulation Model Based on CRC event processes Structured by Event Graph

New Person Creation

Non-visible Adenoma Incidence Event

Natural Death Event

Age Based Utility Event

Scheduled when progression type is progressive or non-progressive

Scheduled when progression type is progressive or immediate

Verification, Calibration Verification

Program execution “Trace” analysis

“Calibration” Matching Output Targets:

Measuring “Goodness-of-Fit” Average error Maximum error Visual “smoothness of fit”

% *100TargetValue ModelOutput

ErrorTargetValue

Fitting Procedure

Fit Cancer Incidence by adjusting Adenoma

progression variables

Repeat initial step if risk adjustment makes error for people with adenomas too high

Fit People with Adenomas by adjusting incidence function

Fit Adenoma Prevalence by adjusting Risk function

Fit Percent of advanced adenomas to all adenomas

Validation Overall characteristics

SEER Data, Life-Table, Prior Model Screening validation: Minnesota Colon Cancer

Control Study Use FOBT relative to no screening (from 1975 through

1977 and followed until 1991 Randomized trial of three groups: annual screening,

biennial screening, and no screening Simulated population fit to Minnesota trial population and

some parameters had to be modified to be consistent with the inputs reported

Numerical Comparisons

Strategy

Simulation Cancer DeathTrial

Cancer DeathMean

Standard Deviation

Lower Bound

Upper Bound

Control Group 125 13.63 121 130 121

Annual Group 89 9.37 86 92 82

Cancer Death (Annual Group)

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12 13

Years in study

Cu

mu

lati

ve

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ath

(P

er

10

00

)

Simulation Annual Group Trial Annual Group

Low er Bound Upper Bound

Cancer Death (Control Group)

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1 2 3 4 5 6 7 8 9 10 11 12 13Years in Study

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Simulation Control Group Trial Control GroupLow er Bound Upper Bound

Result: Health and Cost Burden of CRC

Gender Race Family historyLife Years

LostQALYs Lost Costs of CRC

Female BlackNo Family

history10.83 (0.08) 10.24 (0.07) $123,714 (3736)

Female Black Family history 11.23 (0.06) 10.62 (0.05) $114,381 (2408)

Female WhiteNo Family

history11.68 (0.07) 10.99 (0.06) $124,875 (3320)

Female White Family history 12.15 (0.05) 11.45 (0.05) $118,188 (2283)

Male BlackNo Family

history10.19 (0.07) 9.74 (0.07) $110,460 (3188)

Male Black Family history 10.62 (0.05) 10.18 (0.05) $113,317 (2326)

Male WhiteNo Family

history 9.90 (0.06) 9.52 (0.06) $126,345 (3290)

Male White Family history 10.29 (0.05) 9.91 (0.04) $123,590 (2283)

Result: Effect of Colonoscopy Screening

Δ Cost

Δ LifeYears(0,0)

$500

.100.040 .160

(F,B,N - $8,342)

(F,W,N - $4,008)(M,B,N - $7,329)

(M,W,N - $2,571)

Higher (Poorer) Cost-Effectiveness

(F,B,F – Cost-Saving)

(F,W,F – Cost-Saving)(M,B,F – Cost-Saving)

(M,W,F – Cost-Saving)

Tests can be wrong!

True Positive

False Positive

False Negative

True Negative

DiseasePresent

DiseaseAbsent

TestPositive

TestNegative

Test Sensitivity = (True Positive)/(True Positive + False Negative)Test Specificity = (True Negative)/(False Positive + True Negative)

Screening is Voluntary Compliance

For ages > 50, only 20.6% had an FOBT within a year and only 33.6% had a sigmoidoscopy or colonoscopy within five years

Based on studies, apparently Is independent of age, gender, race, and family history Almost 30% will never comply with any screening test Only about 70% will undergo any screening

Compliance is unique person-specific characteristic

Result: Perfect Compliance

ΔCost

Δ LifeYears(0,0)

$500

.100.040 .160

(F,B,N - $10,150)

(F,W,N - $4,182)

(M,B,N - $6,350)

(M,W,N -$2,946)

(Family History – Cost Saving)

Investigating Screening Alternatives Simulation modeling

Assumptions New screening event processes Screening variables added to database User interface for specifying screening options

and parameters Validate model against Minnesota trial of

FOBT

Cost-Effectiveness Analysis Costs and Effects

Screening, diagnosis, treatment, surveillance costs Adjust time in “health state” by multiplying by “quality”

of that state (utility between 0 and 1) Discount each to time of screening decision

Base case Low risk Demographically similar to US Screening started at 50, ended at 80, but continued

surveillance

CE Plane and Average ICE “Frontier”

$1,300

$1,500

$1,700

$1,900

$2,100

$2,300

$2,500

$2,700

15.14 15.15 15.16 15.17 15.18 15.19 15.20

3% Discounted QALY

3%

Dis

co

un

ted

Co

st

A: No Screening B: FOBT C: Sig D: Sig & FOBT

E: DCBE F: Colon 10 G: Cotton 10 H: Pickhardt 10

I: FDNA 5 J: Pickhardt 5 K: Cotton 5 L: FDNA 3

C

D

B

A

F

JKL

HG

I

E

$4,204/QALY

$27,000/QALY

$23,154/QALY

Dominated (Simple)

Dominated (Extended)

ICE Frontier

Parameter Uncertainty N-way sensitivity analysis

One-at-a-time analysis How to coordinate parameter changes

Probabilistic sensitivity analysis (PSA) Exclude “natural variability” parameters Joint distribution of model parameters

Parameters for PSA Cost Parameters

Multivariate Beta with 0.5 bivariate correlation Screening Characteristics Parameters

Multivariate Beta with high positive correlation for sensitivity and high negative for specificity

Utility Parameters Beta skewed toward maximum value

Compliance Parameters Dirichlet yielding compliance states

Fix the screening policyFor 1 to Replications Establish costs, screening, utilities, and compliance by a sampling

from {η} For 1 to Patients

Simulate life-time of patient, sampling from {ξ}Save discounted total costs and discounted QALY

Next Patient Compute average discounted total costs and QALY for the replication Save average costs, QALY, and cost-effectiveness ratio for replicationNext Replication

Probabilistic Sensitivity AnalysisParameter

Distributions

Natural Variability

Cost-Effectiveness Plane

$1,300

$1,500

$1,700

$1,900

$2,100

$2,300

$2,500

15.13 15.14 15.15 15.16 15.17 15.18 15.19 15.203% Discounted QALY

3% D

isco

un

ted

Co

st

A: No Screening B: FOBT C:Sig D: Sig & FOBT E: Colon 10

C

E

D

B

A

Proportion of times on Efficient Frontier

Strategy% Formed Part of Frontier

Line

No Screening 100%

FOBT 100%

Sig 46%

Sig & FOBT 46%

Colon 10 99%

Net Health Benefits Net Health Benefit (NHB)

Incremental NHB of A compared with B

/ ,A ANHB E C / ,A ANHB E C

/ ,

where is willingness to payA ANHB E C

( / ) ( / ) ( ) ( ) / ,A A B B A B A BE C E C E E C C

Computing NHB within SimulationFor every value of λ

For each replication Compute the NHB for every screening alternative

Choose that screening alternative with the highest NHB Next replication For each screening alternative

Compute proportion of replications in which this was highest

Next alternativeNext λPlot highest NHB for each value of λ

Acceptability Curves

0

0.1

0.2

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0.4

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0.7

0.8

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0 10 20 30 40 50 60 70 80

ThousandsCeiling Ratio

Pro

ba

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A: No Screening B: FOBT C: Sig D: Sig & FOBT E: Colon 10

A

E

DC

B

No Screening FOBT Colon 10

4.1 25.3

Results

Willingness to Pay (λ) Screening Method

λ ≤ $4,100/QALY No Screening

$4,100/QALY < λ

λ ≤ $25,300/QALYFOBT

λ > $25,300/QALY Colon 10

Stochastic Dominance*

0.0

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Net Health Benefit

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B: FOBT C: Sig D: Sig & FOBT E: Colon 10

*Ceiling ratio = $25,000/QALY

Different Rule: More expensive must be significantly more cost-effective

0

0.1

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Pro

ba

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A: No Screening B: FOBTC: Sig D: Sig & FOBTE: Colon 10 F: Sig + Sig & FOBT + Colon 10

No Screening FOBT Sig +Sig & FOBT + Colon 10

AF

E

D

C

B

7 35.1

What seemed to work Benefits of a second generation simulation model

Object-oriented, extensible simulation platform for greater model fidelity

Data base separated from simulation accommodated re-modeling Collection of actual data and clinical judgment Available quality adjustment to life year

Using a patient/person simulation approach Each person is an independent replication Competition for time creates discrete events (event graph)

Having a “grand hypothesis” Explicit consistent and defensible assumptions Standard for transparent modeling and documentation

What seemed to work (contd) Careful attention to randomness

Use of high quality random number generator with well-spaced seeds Use of inverse-transform random variate generators facilitated use of

correlation induction variance reduction Johnson SB and NHPP were flexible representations

Use of Microsoft products was helpful in multi-investigator environment

Employed Cost-Effectiveness Acceptability Curves (CEAC) Separate “natural variability” and “parameter uncertainty” Use of marginals with bivariate correlation was satisfactory Provided “policy oriented” recommendations

Further Research Obtaining and characterizing “expert opinion” Better way to estimate “natural life” Determine adequacy of NHPP Generalizing the simulation modeling approach Cost-effectiveness is limited

Ratio eliminates magnitude Variability is problematic

Not clear how to extend simulation to competition for resources and resource implications

Net Health Benefit and CEAC are not fully accepted Continued “value for cost” analysis

Further Research (contd) For CRC

When to start and stop screening Single versus “mixed” screening strategy

Screening methods “risk” (age, gender, race, family history)

Resource implications People Facilities Location