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Simulation of Medical Decisions

Simulation of Medical Decisions. Stephen D. Roberts Edward P. Fitts Department of Industrial and Systems Engineering North Carolina State University Raleigh, North Carolina IERC, May 21, 2007. Outline for this talk. Introduction to medical decision-making

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Simulation of Medical Decisions

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  1. Simulation of Medical Decisions Stephen D. Roberts Edward P. Fitts Department of Industrial and Systems Engineering North Carolina State University Raleigh, North Carolina IERC, May 21, 2007

  2. 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

  3. 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

  4. 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

  5. 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

  6. About 150,000 people diagnosed each year Second leading cause of cancer deaths About 90M people considered at risk Most prominent in western industrialized societies Case: Colorectal Cancer (CRC)

  7. 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 (?)

  8. Screening for CRC • Endoscopic tests • Colonoscopy • Sigmoidoscopy • Non-Endoscopic tests • Fecal Occult Blood Test (FOBT) • Double Contract Barium Enema (DCBE) • Virtual Colonoscopy • Fecal DNA

  9. 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

  10. An Example Clinical Guideline

  11. 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

  12. 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

  13. Comparing Alternatives • Incremental CE comparing a Base with Alternative policy: • In a stochastic environment:

  14. Graphical Interpretation:Cost-Effectiveness Plane ΔCost Greater Cost, Greater Effect Greater Cost, Less Effect Unacceptable CE > 0 (0,0) ΔEffect Less Cost, Less Effect Less Cost, Greater Effect Cost Saving

  15. Course of Disease (Natural History) Medical Timeline Birth Death ND A1 CD 0 A2 C1 CO C2 A1 – undetected first Adenoma A2 – undetected second Adenoma C1 – invasive Cancer from A1 C2 – invasive cancer from A2 CO – Colonoscopy/surgery to remove C1 CD – Cancer Death ND – “Natural” Death

  16. 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)

  17. Complex Adenoma Pathways Non Visible Adenoma Created Adenoma Progresses Immediately to Cancer Progressive Adenoma Non - Progressing Advanced Adenoma Non-Cancerous Advanced Adenoma Cancerous Local SymptomaticCancer Follow Cancer Pathway Regional Death Distant

  18. 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

  19. Implementing the Simulation • Object-oriented framework in Visual Studio .NET 2003: • Scenario object • Person objects • Adenoma objects • Four-tier object hierarchy User Interface CRC Objects: CRC Event Processes, Person and Adenoma Objects, CRC Database, Screening OOS Platform: Random Number Generation, Random Variate Generation, Events, Event Calendars, Entities, Statistics, Simulation Execution .NET Framework:Multiple OOP language support, Simplified Deployment, InterfaceDevelopment, Framework Classes, Integrated Development Environment, ADO.NET

  20. Overall Software Design Strategy MedicalProtocolDesign User Interface Simulation Engine Results inExcel Data Objects Scenarios CRCExpertise Report Writer CRC Variables AccessDatabase

  21. Main Scenario Display Scenario CRC Simulations Simulation Variables Screening Variables Parameters

  22. 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

  23. 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

  24. Visual Interactive Modeler (VIM) Plots Distribution Parameters Statistics

  25. Non-Homogenous Poisson Process

  26. Using “Expertise” for Input • Many key variables not observable (can’t allow “natural course” of CRC) • Use of “expert opinion” • Collaborators • Expert Panel

  27. 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)

  28. 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

  29. 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

  30. 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 Simulation Model • Based on CRC event processes • Structured by Event Graph

  31. Verification, Calibration • Verification • Program execution • “Trace” analysis • “Calibration” • Matching Output Targets: • Measuring “Goodness-of-Fit” • Average error • Maximum error • Visual “smoothness of fit”

  32. Fitting Procedure Fit People with Adenomas by adjusting incidence function Repeat initial step if risk adjustment makes error for people with adenomas too high Fit Adenoma Prevalence by adjusting Risk function Fit Cancer Incidence by adjusting Adenoma progression variables Fit Percent of advanced adenomas to all adenomas

  33. 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

  34. Numerical Comparisons

  35. Result: Health and Cost Burden of CRC

  36. Result: Effect of Colonoscopy Screening ΔCost (F,B,N - $8,342) $500 (M,B,N - $7,329) Higher (Poorer) Cost-Effectiveness (F,W,N - $4,008) (M,W,N - $2,571) ΔLifeYears (0,0) .100 .160 .040 (F,B,F – Cost-Saving) (M,B,F – Cost-Saving) (F,W,F – Cost-Saving) (M,W,F – Cost-Saving)

  37. Tests can be wrong! DiseaseAbsent DiseasePresent TestPositive TestNegative Test Sensitivity = (True Positive)/(True Positive + False Negative) Test Specificity = (True Negative)/(False Positive + True Negative)

  38. 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

  39. Result: Perfect Compliance ΔCost (F,B,N - $10,150) $500 (F,W,N - $4,182) (M,B,N - $6,350) (M,W,N -$2,946) ΔLifeYears (0,0) .100 .160 .040 (Family History – Cost Saving)

  40. 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

  41. 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

  42. CE Plane and Average ICE “Frontier” Dominated (Simple) $2,700 L K J $2,500 Dominated (Extended) I $2,300 H G 3% Discounted Cost $2,100 F E $1,900 D $27,000/QALY C ICE Frontier $1,700 $23,154/QALY B $4,204/QALY A $1,500 3% Discounted QALY $1,300 15.14 15.15 15.16 15.17 15.18 15.19 15.20 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

  43. 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

  44. 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

  45. Probabilistic Sensitivity Analysis Fix the screening policy For 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 replication Next Replication Parameter Distributions Natural Variability

  46. Cost-Effectiveness Plane

  47. Proportion of times on Efficient Frontier

  48. Net Health Benefits • Net Health Benefit (NHB) • Incremental NHB of A compared with B

  49. Computing NHB within Simulation For 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 alternative Next λ Plot highest NHB for each value of λ

  50. Acceptability Curves

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