1. Section of Decision Sciences and Clinical Systems Modeling 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 Modeling University of Pittsburgh School of Medicine University of Pittsburgh

2. Section of Decision Sciences and Clinical Systems Modeling 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

3. Section of Decision Sciences and Clinical Systems Modeling 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?)

4. Section of Decision Sciences and Clinical Systems Modeling 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

5. Section of Decision Sciences and Clinical Systems Modeling 5 US Organ Procurement Organizations (OPOs) OPOs are aggregated into 11 regions

6. Section of Decision Sciences and Clinical Systems Modeling 6 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

7. Section of Decision Sciences and Clinical Systems Modeling 7 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)

8. Section of Decision Sciences and Clinical Systems Modeling 8 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

9. Section of Decision Sciences and Clinical Systems Modeling 9 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

10. Section of Decision Sciences and Clinical Systems Modeling 10 ESLD Clinical Model: Chronic Disease "LIVER FUNCTION" TIME THERAPY REQUIRED DEATH CHRONIC DISEASE SYMPTOM DEVELOPMENT “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

11. Section of Decision Sciences and Clinical Systems Modeling 11 Average Natural History: LIVER FUNCTION TIME Therapy required Death symptom development “Natural History”

12. Section of Decision Sciences and Clinical Systems Modeling 12 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% OPERATIVE MORTALITY POST TRANSPLANT SURVIVAL DECLINING LIVER FUNCTION (PROGRESSION OF DISEASE) POST-TRANSPLANT SURVIVAL (YRS)

13. Section of Decision Sciences and Clinical Systems Modeling 13 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 SURVIVAL Transplantation Survival by stage of disease

14. Section of Decision Sciences and Clinical Systems Modeling 14 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 transplant Intermediate Transplant Late Transplant SURVIVAL TIME Transplantation Survival vs. Natural History

15. Section of Decision Sciences and Clinical Systems Modeling 15 Markov Model: Initial attempts to model How do we do this part?

16. Section of Decision Sciences and Clinical Systems Modeling 16 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

17. Section of Decision Sciences and Clinical Systems Modeling 17 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

18. Section of Decision Sciences and Clinical Systems Modeling 18 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

19. Section of Decision Sciences and Clinical Systems Modeling 19 Basic Model Structure Discrete Event Simulation Model Patient Generator Organ Generator Survival Module Disease Progression Module Resource Use Module Quality of Life Module Selection and Allocation Rules Model Outputs User-defined Inputs Survival Quality-Adjusted Survival Costs spent on ESLD Number of deaths waiting Average waiting time Number of wasted organs

20. Section of Decision Sciences and Clinical Systems Modeling 20 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

21. Section of Decision Sciences and Clinical Systems Modeling 21 Organ Generator Organ Procurement Organizations (OPOs) OPO1 Gender Age Race Blood Type

22. Section of Decision Sciences and Clinical Systems Modeling 22 Data Dependencies

23. Section of Decision Sciences and Clinical Systems Modeling 23 Regional/Geographic Overlay Transplant Center Region 2 Region 1 DONOR POOL National Waiting List Center Waiting List Allocation Algorithm DONOR Region 1 Waiting List Region 2 Waiting List

24. Section of Decision Sciences and Clinical Systems Modeling 24 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

25. Section of Decision Sciences and Clinical Systems Modeling 25 Allocation Mechanism: Generic structure 1 2 3 4 Arbitrary number of PRIORITY LEVELS Arbitrary Number of LISTS (Regional/OPO, National) Criteria for Membership in LEVEL RANKING WITHIN PRIORITY LEVEL N PRIORITY LEVEL ORDER OF SEARH

26. Section of Decision Sciences and Clinical Systems Modeling 26 UNOS Algorithm (1999-2002) Priority 1 2 3 4 NOT USED 1 2a 2b 3 Regions:10 OPOs Status Levels:4 Ranked by points (ABO; relative time on list) In ICU LE < 7 days ….

27. Section of Decision Sciences and Clinical Systems Modeling 27 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 ICU LE < 7 days …. MELD 6

28. Section of Decision Sciences and Clinical Systems Modeling 28 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 X (t+1) = f (X (t) ) or X (t+  t) = f (X (t),  t) X = (x 1 x 2,x 3, x n ) Clinical covariates of interest

29. Section of Decision Sciences and Clinical Systems Modeling 29 Natural History Estimating Problem Time Bilirubin Observed values of variable “Average Natural History” Evaluation Transplant Natural history according to NIDDK Patients are “over-sampled” when they are sick, under sampled when they are healthy

30. Section of Decision Sciences and Clinical Systems Modeling 30 Natural History: Prior Simulation Efforts Status 1 Status 2a Status 2b Status 3 1 2a 2b 3 1 2a 2b 3 Time 2 Time 1 In earlier simulation (ULAM), by Pritzker and UNOS, the natural history model is directly tied to the allocation/selection model p 11 p 12a p 12b p 13 p 2a1 p 2a2a p 2b2b p 2a3 p 2b1 p 2b2a p 2b2b p 2b3 p 31 p 32a p 32b p 33 Cannot modify this to assess the effect of the change to the MELD score, for example

31. Section of Decision Sciences and Clinical Systems Modeling 31 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 bilirubin Estimated cubic spline Time t1t1 t2t2 t3t3 t4t4 t5t5 t6t6 t7t7 t8t8 t9t9 t 10 t 11 t 12 t 13 t 14 t 15 Bilirubin

32. Section of Decision Sciences and Clinical Systems Modeling 32 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

33. Section of Decision Sciences and Clinical Systems Modeling 33 Natural History: Stratification 1) Create splines 2) Cut into sequential triplets Patients with Primary Biliary Cirrhosis 3) Shuffle PBC 1) Create spline 2) Cut into sequential triplets 3) Shuffle Patients with Hepatitis B Hep B

34. Section of Decision Sciences and Clinical Systems Modeling 34 Natural History, Stratification DZ 1DZ 2DZ 3DZ 4DZ 5 DZ 1DZ 2DZ 3DZ 4DZ 5 DZ 1DZ 2DZ 3DZ 4DZ 5 Five Disease Groups Out of Hospital In Hospital In Intensive Care

35. Section of Decision Sciences and Clinical Systems Modeling 35 Disease Progression Mechanism t-1 0.9 3.9 1.2 17 28 t 1.0 3.9 1.3 18 29 t+1 1.2 3.6 1.8 21 35 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 timet+1values become the current patient’stime t+1 values. Creat ALB tBILI PT ALT t+1 ? ? ? ? ? t-1 1.2 4.2 1.0 15 30 t 1.3 4.0 1.8 18 45 1 2 3 Creat ALB tBILI PT ALT Creat ALB tBILI PT ALT t-1 1.2 4.2 1.0 15 30 t 1.3 4.0 1.8 18 45 t+1 1.2 3.6 1.8 21 35

36. Section of Decision Sciences and Clinical Systems Modeling 36 Determining “similarity” Assessed TX surgeons, gastroenterologists Determined how different each lab had to be to be “clinically important”

37. Section of Decision Sciences and Clinical Systems Modeling 37 Modeling Natural History 50 year old Hispanic female with Alcoholic Liver disease

38. Section of Decision Sciences and Clinical Systems Modeling 38 Modeling Natural History 50 year old Hispanic female with Alcoholic Liver disease

39. Section of Decision Sciences and Clinical Systems Modeling 39 Modeling Natural History

40. Section of Decision Sciences and Clinical Systems Modeling 40 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.

41. Section of Decision Sciences and Clinical Systems Modeling 41 Modeling Natural History Results: Correlations between Clinical Covariates

42. Section of Decision Sciences and Clinical Systems Modeling 42 Pre-transplant survival Proportion Surviving 0100200300400 Days 1.0 0.9 0.8 0.7 0.6 0.5 Actual Modelp=0.26

43. Section of Decision Sciences and Clinical Systems Modeling 43 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

44. Section of Decision Sciences and Clinical Systems Modeling 44 Post Transplant Survival

45. Section of Decision Sciences and Clinical Systems Modeling 45 Post Transplant Survival 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

46. Section of Decision Sciences and Clinical Systems Modeling 46 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

47. Section of Decision Sciences and Clinical Systems Modeling 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 Hospital In Hospital In ICU Post Transplant TTO.74.54.40.84 SG.67.41.40.64 From literature

48. Section of Decision Sciences and Clinical Systems Modeling 48 Patient Generator Alive on Waiting List Improved “Too sick” Refused Transplant Alive Post Transplant Dead Organ Match Organ Generator Unused Die Post Transplant Organ Failure Die While Waiting Post Transplant Survival 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 prior to transplant # removed from list Bilirubin Albumin Creatinine INR Arbitrary priority scheme Arbitrary allocation rules

49. Section of Decision Sciences and Clinical Systems Modeling 49 Calibration and Validation Variable # of Transplants # Waiting Deaths while waiting Waiting Time (median) 1992 2614 2599 1903 1880 516 473 124 142 1993 2947 2946 2809 2548 567 514 175 193 1994 3129 3124 3838 3544 671 589 242 217 1995 3470 3460 5365 5072 835 754 345 316 1996 3567 3583 7203 6795 1000 919 n/a Model UNOS Model UNOS Model UNOS Model UNOS

50. Section of Decision Sciences and Clinical Systems Modeling 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

51. Section of Decision Sciences and Clinical Systems Modeling 51 Results: Outcome measure Patients relisted Deaths while waiting 1 year patient survival 1 year graft survival median wait time (days) mean survival (years) Mean survival (QALYS) UNOS Regional 1622 3589 0.84 0.78 252 9.51 6.65 UNOS National 1947 3169 0.82 0.75 346 9.63 6.56 MELD Regional 1670 3612 0.84 0.78 181 9.32 6.67 MELD National 1985 3149 0.82 0.75 284 9.46 6.65

52. Section of Decision Sciences and Clinical Systems Modeling 52 Geographic Variability Model captures the remarkable geographic variability in waiting times, which is eliminated with move to national list

53. Section of Decision Sciences and Clinical Systems Modeling 53 SRTR efforts: Simulation Allocation Models (SAMs) Simulation Allocation Model (SAM) Donor Organs Transplant Candidates Outcomes Under Policy A Outcomes Under Policy B Disease Progression Waiting List Unused Organs Compare Policies Post Transplant Events

54. Section of Decision Sciences and Clinical Systems Modeling 54 SRTR Natural History Model time Bilirubin Albumin Prothrombin time Pick one individual, use that person’s actual history What do you do when model  actual history? How to interpolate?

55. Section of Decision Sciences and Clinical Systems Modeling 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

56. Section of Decision Sciences and Clinical Systems Modeling 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.

57. Section of Decision Sciences and Clinical Systems Modeling 57 Current allocation question 141517192124252628313436 141517192124252628313436 Sickest first Largest Net Benefit First 14 Survival with THIS organ (S tx ) Survival with NO organ (S no-tx ) NET Benefit = S tx – S no-tx 6.97.26.76.37.27.67.38.18.27.47.87.5NB: Patients ranked by MELD score (probability of death in 3 months)

58. Section of Decision Sciences and Clinical Systems Modeling 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?

59. Section of Decision Sciences and Clinical Systems Modeling 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

60. Section of Decision Sciences and Clinical Systems Modeling 60