Design of a National Paired Donation Clearinghouse

1. Design of a National Paired Donation Clearinghouse Alvin E. Roth, Harvard University M. Utku Ünver, University of Pittsburgh UNOS, Richmond VA, Feb 4 2008

2. Four related presentations • Economists • Multi-center clearinghouses need to be able to attract participation by dealing with the diversity of needs of different centers • Software exists to enable a flexible clearinghouse with a menu of choices: 2 and 3-way exchanges, NDD and List exchange chains of different lengths • NEPKE • Clinical and organizational experience with the 14 Region 1 transplant centers and those in the New Jersey Sharing Network (6 in Mid-Atlantic Paired Exchange Program) • APD • Clinical and organizational experience with 60 transplant centers…:…HLA data issues, organizational issues • Computer Scientists (Carnegie Mellon University) • Flexible software has been developed and tested in the field to efficiently accommodate varieties of exchange at national scale.

3. Outline • Why economists? (what is market design?) • How clearinghouses succeed and fail • How a national kidney paired donation clearinghouse will be different from • Managing deceased organ donors • Kidney exchange at a single dominant hospital • Getting transplant centers to participate • Flexible menu of possibilities, constraints • Optimization criteria • Our successes and failures and what we’ve learned from them • Software and implementation • Examples • Software choices both implement current policy, and has the potential to constrain future policy choices

4. What do market-design economists have to do with paired donation? • Market designers study what makes marketplaces work, or fail. • A clearinghouse is a kind of marketplace. • To work well clearinghouses need to • attract participation (by transplant centers) • deal with the resulting congestion (by being able to handle matches involving lots of pairs) • make it safe/attractive for transplant centers to participate • In the national exchange as opposed to in regional exchanges or going it alone • Full participation: making it safe to show all patient-donor pairs (and not withhold pairs that can be matched internally)

5. Participation is a big issue in multi-center exchange: Examples from other domains • Resident matching, NRMP: Different constituencies have different needs (Roth-Peranson algorithm since 1998) • Almost all PGY1 programs participate • Fellowship matching • Schools: NYC schools had a problem with full participation • Principals withheld capacity under the old system

6. Clearinghouse Rules encourage participation? Still in use (halted unraveling) • NRMP yes yes (many specialties) • Edinburgh ('69) yes yes • Cardiffyes yes • Birmingham no no • Edinburgh ('67) no no • Newcastleno no • Sheffield no no • Cambridge (1 hosp) no yes • London Hospital (1 hosp) no yes • U.S.Medical Fellowships yes yes (~30 markets, 2 failures) • Canadian Lawyers yes yes (Alberta, no BC, Ontario) • Dental Residencies yes yes (5 ) (no 2) • Osteopaths (< '94) no no • Osteopaths (> '94) yes yes • Pharmacists yes yes • Reform rabbis yes (first used in ‘97-98) yes • Clinical psych yes (first used in ‘99) yes • Lab experiments yes yes. (Kagel&Roth QJE 2000) no no Good participation incentives are an important criterion for a successful clearinghouse.

7. Current NRMP match (Roth/Peranson algorithm) Menu of options for applicants and programs: • Married couples (used to defect under old algorithm) • Can submit preferences over pairs of positions • Individual applicants can match to pairs of jobs, PGY1&2 • They can submit supplementary preference lists • Reversions of positions from one program to another

8. NRMP / SMS: Roth Peranson Algorithm Medical Residencies in the U.S. (NRMP) (1952) Abdominal Transplant Surgery (2005) Child & Adolescent Psychiatry (1995) Colon & Rectal Surgery (1984) Combined Musculoskeletal Matching Program (CMMP) Hand Surgery (1990) Medical Specialties Matching Program (MSMP) Cardiovascular Disease (1986) Gastroenterology (1986-1999; rejoined in 2006) Hematology (2006) Hematology/Oncology (2006) Infectious Disease (1986-1990; rejoined in 1994) Oncology (2006) Pulmonary and Critical Medicine (1986) Rheumatology (2005) Minimally Invasive and Gastrointestinal Surgery (2003) Obstetrics/Gynecology Reproductive Endocrinology (1991) Gynecologic Oncology (1993) Maternal-Fetal Medicine (1994) Female Pelvic Medicine & Reconstructive Surgery (2001) Ophthalmic Plastic & Reconstructive Surgery (1991) Pediatric Cardiology (1999) Pediatric Critical Care Medicine (2000) Pediatric Emergency Medicine (1994) Pediatric Hematology/Oncology (2001) Pediatric Rheumatology (2004) Pediatric Surgery (1992) Primary Care Sports Medicine (1994) Radiology Interventional Radiology (2002) Neuroradiology (2001) Pediatric Radiology (2003) Surgical Critical Care (2004) Thoracic Surgery (1988) Vascular Surgery (1988) Postdoctoral Dental Residencies in the United States Oral and Maxillofacial Surgery (1985) General Practice Residency (1986) Advanced Education in General Dentistry (1986) Pediatric Dentistry (1989) Orthodontics (1996) Psychology Internships in the U.S. and CA (1999) Neuropsychology Residencies in the U.S. & CA (2001) Osteopathic Internships in the U.S. (before 1995) Pharmacy Practice Residencies in the U.S. (1994) Articling Positions with Law Firms in Alberta, CA(1993) Medical Residencies in CA (CaRMS) (before 1970) ******************** British (medical) house officer positions Edinburgh (1969) Cardiff (197x) New York City High Schools (2003) Boston Public Schools (2006) Stable Centralized Clearinghouses

9. Full participation: the case of NYC high school matching Abdulkadiroğlu, Atila, Parag A. Pathak, and Alvin E. Roth, “The New York City High School Match,” American Economic Review, Papers and Proceedings, 95,2, May, 2005, 364-367. • Old NYC high school choice system • Decentralized application and admission • congested: left 30,000 kids each year to be administratively assigned (while about 17,000 got multiple offers) • Gaming by schools: Principals concealing capacities Deputy Chancellor (NYT 11/19/04): “Before you might have had a situation where a school was going to take 100 new children for 9th grade, they might have declared only 40 seats and then placed the other 60 children outside the process.” .

10. Our involvement in kidney exchange 2003: • Roth, Sonmez, and Unver, "Kidney Exchange," NBER, 2003. (QJE, 2004. ) [considered potentially large cycles and chains] • Began discussions w/ Frank Delmonico and Susan Saidman on implementation 2004: • Roth, Sonmez , and Unver, "Pairwise Kidney Exchange," NBER, 2004 (JET, 2005.) [considered only pairwise exchanges, Edmonds’ algorithm] • NEPKE approved by Renal Transplant Oversight Committee of New England (Delmonico, Saidman, Roth, Sonmez, Unver). 2005: • We (Utku) begin to run matches for Utku runs matches with Jon Kopke’s compatibility matrices as input for OSDTOC-LDKEP (Woodle-Rees) • Larger (3-way) matches and longer chains considered 2006: • APD formed, Utku starts running matches for APD 2007 • NEPKE incorporates Utku’s software into its internal system. • Abraham, Blum, and Sandholm (CMU) scale up software to 10,000 pairs • APD matches in 2007 run by Utku, CMU, Utku (presently)

11. NEPKE and APD experimented with expanded exchanges • Roth, Sonmez , Unver, "Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences,"  NBER 2005. (AER 2007.) [introduced flexible integer programming formulation] • Saidman, Susan L., Alvin E. Roth, Tayfun Sönmez, M. Utku Ünver, and Francis L. Delmonico, " Increasing the Opportunity of Live Kidney Donation By Matching for Two and Three Way Exchanges," Transplantation, 2006. • Roth, Alvin E., Tayfun Sönmez, M. Utku Ünver,  Francis L. Delmonico, and Susan L. Saidman, ''Utilizing List Exchange and Undirected Good Samaritan Donation through 'Chain' Paired Kidney Donations," American Journal of Transplantation 2006.

12. A Menu of options we’ve implemented • “Traditional” options • 2-way exchanges • List exchange (2-way) • Non-directed donors (to the list) • Newer developments—particularly in 2007 • Bigger exchanges and chains • 3-way list exchanges • Longer non-directed donor chains • Non-simultaneous altruistic donor chains • 3-way exchanges • Compatible pairs • All of these can easily be implemented as a menu of constraints

13. NEPKE: Integrating paired exchange and list exchange Deceased donor P1-D1 P3 P1-D1 P2-D2 Deceased donor P3

14. NEPKE: Non-directed donors ND-D P1 P2-D2 P1-D1 ND-D P3

15. APD: Non-simultaneous altruistic donor chains (reduced risk from a broken link) Since NEAD chains don’t need to be simultaneous, they can be long…if the ‘bridge donors’ are properly identified.

16. First NEAD chains: Rees et al. 2007 • In July 2007, the Alliance for Paired Donation started the first of these chains when an altruistic donor in Michigan donated his kidney to a woman in Phoenix, Arizona. • As of the end of September this first NEAD chain was at 4 transplants (M. in MI gave to B. in AZ whose husband R. gave to An. in Toledo, whose mom La. gave to Ce. in Columbus whose daughter Li. gave to G. in Columbus simultaneously with Ce.'s transplant, and now G's sister Av. is the next bridge donor) …(3 bridge donors donated so far…) • The APD started a second NEAD chain on Dec 7, 2007 with a NDD T who gave to D in Columbus whose daughter M gave to S in Orlando, whose daughter E flew to Toledo to give to R from Tennessee which didn’t work, but she bridged instead to MT in Toledo, whose daughter A will be the next bridge donor (3 transplants so far, 1 from a bridge donor)

17. Why 3-way exchanges can add a lot Maximal (2-and) 3-way exchange:6 transplants 3-ways help make best use of O donors, and help highly sensitized patients Patient ABO Donor ABO A B O A B O O B Patient ABO Donor ABO A A A B B A x Maximal 2-way exchange: 2 transplants (positive xm between A donor and A recipient)

18. Include compatible pairs? • Make kidney exchange available not just to incompatible patient-donor pairs, but also to those who are compatible but might nevertheless benefit from exchange • E.g. a compatible middle aged patient-donor pair, and an incompatible patient-donor pair with a 25 year old donor could both benefit from exchange. • This would also relieve the present shortage of donors with blood type O in the kidney exchange pool, caused by the fact that O donors are only rarely incompatible with their intended recipient. • Adding compatible patient-donor pairs to the exchange pool has a big effect: Roth, Sönmez and Ünver (2004a and 2005b) • APD has included some compatible pairs in match runs

19. Weights • NEPKE weights nodes, i.e. priorities on patients • APD also weights edges, i.e. priorities on transplants • (These aren’t deeply different, node weighting is a simpler, more specialized formulation, internally to the software everything in either form can be done with edge weights) • Unlike options which can be flexibly implemented via constraints, choosing appropriate optimization criteria will involve wide consultation, consensus, and continued (post-implementation) study.

20. Incentives for Transplant Centers to fully participateThe exchange A1-A2 results in two transplantations, but the exchanges A1-B and A2-C results in four.(And you can see why, if Pairs A1 and A2 are at the same transplant center, it might be good for them to nevertheless be submitted to a regional match…)

21. Our success and failures (and what we’ve learned from them) • Successes • Helped NEPKE and APD design working, multi-center clearinghouses • Failures (or ‘not yet successes’:) • Failed to help NEPKE and Hopkins to join forces (after 2004 conference call) • The issue at the time was different rules about B-cell crossmatching tests for patients undergoing first transplants. • Haven’t yet gotten APD and NEPKE to closely cooperate because of different variety of practices • Haven’t yet gotten all centers in APD and NEPKE to contribute pairs that can be internally matched. • What we’ve learned • A menu of options is needed

22. Need for “evolvable systems” (and software) • Adopting software that is both flexible and “evolvable” will be particularly important. • Aside from adopting appropriately flexible software and procedures, UNOS should plan on an ongoing, comprehensive evaluative study including both participating and non-participating centers. • I’ve received permission to organize a Harvard Kidney Paired Donation Project to help support such an effort, if that would be welcome. • This project would be able to draw on resources across the schools of Medicine, Public Health, FAS, and HBS to help coordinate and possibly staff and fund some of the data analysis, in cooperation with everyone else who wants to participate.

23. Details of Our Optimization Engines Developed for the NEPKE and the APD 23

24. Optimization Engine Optimization engine uses CPLEX (by ILOG) commercial grade mixed integer programming software, whose license should be bought. We also have experimental versions that use public-domain optimization routines (LPK integer-programming software, Edmonds’ algorithm module etc) Our approaches helped conducting 19 transplants through the NEPKE and 11 transplants through the APD. • Input format: • Comma separated text files that tell the weights/priorities of different feasible transplants/patients; the feasibility/ compatibility information between all patients in the pool and all donors. • We developed (with NEPKE) an interface protocol which converts donor/patient data into the above text files (see the NEPKE presentation). APD also has an excellent interface for converting patient/donor information to compatibility information (see the APD presentation). 24

25. Optimization engine generates the optimized matching (see the following slides) based on several different criteria, including only 2-way, only 2&3-way, 2&3&4-way exchanges etc. • Output is written in comma, separated text files. • Automatically, NEPKE interface converts this information to displayable SECURE web-based files. • For example the whole NEPKE program is run in a single server (see the NEPKE program for details) • The relevant codes for the optimization program are written in a fast mathematical software MATLAB. • APD is working on to move every stage to a single server (see the APD presentation) • The end-user does not need to buy MATLAB license when the MATLAB-based engine is deployed. It is executable in PC-Windows environment. 25

26. Pros and Cons - MATLAB+CPLEX • Pros: • Different objectives can easily be used, that is: we have FLEXIBILITY: as the objectives/constraints change these can be implemented with minimal cost. • 2&3&…&k-way exchanges can be allowed instead of just 2-way exchanges • Testing, policy analysis, and simulations of new objectives can easily be done in the sophisticated MATLAB environment • Superb for regional exchange programs • Ideal for research and developing mathematical software • Cons: • For large exchange programs it can be somewhat slower to run • With 3-way and longer exchanges, it may be difficult to run exchanges for a national program larger than 800 patients. • We asked Tuomas Sandholm and his teamto develop a software based on Roth, Sonmez, Unver (2007 AER) paper and our APD-specific software that can handle more patients, even longer exchange cycles (see Tuomas’ presentation). 26

27. Examples of Some Flexible Objectives that can be Handled by UNOS through Our Approach inspired by our NEPKE and APD experiences 27

28. Example 1: Transplant Weighted Matching, and Exchange Cycle Weighted Matching(inspired by the APD practices) • Each patient is given an option about which compatible donors will be unacceptable based on • whether his own paired-donor will have to travel a long distance, • whether the assigned donor age is too high, • whether the BMI of the assigned donor is too high • etc. • Also suppose: • Region 1 wants to use list exchange option for the patients who cannot be matched otherwise in an optimal matching. • Region 2 wants to use never-ending donor chains such that the “outstanding” donor’s blood type should not be AB. • Region 3 does not want its patients to participate in a 3-way or larger exchange. 28

29. Optimized Weighted Matching Engine • determines the weights for each feasible transplant, based on • the constraints of the patients, • the age, and other properties of the possible transplant • the distance of travel • the age difference between the patient and donor, etc. determines feasible “exchange cycles” based on regional preferences and constraints, and forms weights for • each feasible EXCHANGE CYCLE, NON-DIRECTED DONOR CHAIN by summing up the weights determined for each individual transplant • for each LIST EXCHANGE CHAIN by summing up the weights and prioritizing such exchanges such that they can only be chosen if the list exchange patient is not part of a cycle chosen above. 29

30. Optimized Weighted Matching Engine (continued) • finally, produces 1 or more matching options based-on either • (Objective 1) maximizing the weights determined • (Objective 2) maximizing the number of transplants, without the list exchange option, and choosing the highest weighted matching out of this, and then matching the remaining willing pairs that can be matched in list exchange chains, • (Objectives 3&4) Each exchange cycle can also be weighted for the probability of NOT having false negative cross-match, then the probability-weighted sum of weights is maximized using one of the above criteria, etc. • In APD, currently, list exchange is not used, only maximizing the total number of matches based on weights (Objective 2) is what is employed. Also regions are not given choices as suggested above. But these can easily be incorporated to the system. 30

31. How? • The medical data and personal preferences are converted to a compatibility matrix of 0’s and 1’s telling which patient is compatible with which donor. • An ND donor is represented as a donor- virtual patient pair, whose virtual patient is compatible with every other donor. • A list-exchange pair is represented twice first as a normal pair, second as a pair whose patient is compatible with all donors • CONSTRAINT 2: Region 2 wants to have its own NDDs to be used in cycles ending with non-AB blood type donor. • Then in the above process, we simply do not make the virtual patient of the region 2 NDDs compatible with AB type donors.

32. How, weights and cycles? • Weights are determined according to the policy formula and assigned to each transplant (i.e. 1 if we want to maximize the number of transplants, etc.) • Feasible Paired /NDD/ List Exchange cycles are determined (either all of them at the same time -- as our software does -- or some relevant ones are determined at each time -- as Tuomas’ software does – to save memory).

33. How, other constraints? • CONSTRAINT 1: Region 1 wants to implement LIST exchange unless it cannot match its patients otherwise: • Exchange cycles determined in the previous stage will also contain some list exchange chains. Each such list exchange chain (or cycle) is further weighted by 1/n, where n is the number of total patients (this will make certain that such cycles are chosen only if nothing else is possible). • CONSTRAINT 3: Region 3 wants to withhold from 3-way exchanges. • Eliminate all 3-way cycles that include a patient from Region 3, i.e., assign each of them a negative weight, or remove them from the list of feasible exchanges.

34. How, optimization? • Now, • we have weights for each exchange cycle, and • we know which patient participates in which exchange cycle. • Using CPLEX, maximize the sum of weights of exchange cycles subject to the constraint that one patient can AT MOST participate in one exchange. • This is a binary integer program, why? • The chosen exchanges is represented by 1’s and the unchosen exchanges are represented by 0 in the determined solution.

35. Why honor regional preferences and constraints? • TO ENSURE PARTICPATION: • If Region 2’s NDD’s may be used in chains ending with AB blood types, Region 2 may not send these to the national system and can match them internally. • If Region 3 may not list its patients in the national program with the fear that they will participate in 3-way exchanges. • If 3-way exchanges are abolished, Regions 1 and 2 may not participate, feeling that the maximum set of advantages may not be reached.

36. Why honor (continued)? • These, in turn, may cause less number of transplants to be done nationally with respect to full participation. • This also discourages other regions against participation, since gains from national exchange goes down, and the costs (transportation costs for example) exceed benefits.

37. Example 2: Priority Matching, andMixed Priority and Weighted Matching (inspired by the NEPKE practices) • Suppose the National exchange program wants to “prioritize” patients instead of assigning “weights” to transplants with respect to the patient’s • age (children first) • previous donating status (previous kidney donors have higher priority) • PRA (higher priority patients have higher priority) • Etc… • NEPKE currently employs the basic version of a mixed priority and weighted matching mechanism 37

38. Optimized Mixed Priority and Weighted Matching: • Every personal and regional constraint/preference of the previous example can be handled as in Example 1. • The program software determines • maximum number of priority 1 patients that can be matched simultaneously • : maximum number of priority k patients who can be matched and do not conflict with the pre-determined matching of the higher priority patients After a pre-determined priority level, the objective can be converted into maximizing the number/sum of weights etc of transplants for the remaining patients as in Example 1. NEPKE has 5 levels of priority for patients (see the NEPKE presentation) 38

39. Conclusions Clearinghouses have to be designed to attract wide and full participation. Integer programming formulations that can do this are now flexible and fast, scalable and evolvable. Optimization criteria need to be chosen carefully, and with wide consultation and consensus. Simplicity may be a virtue in reaching consensus 39

40. Software implements policy • It should be flexible enough to • Encourage full participation • Allow options to be studied “offline” • Allow future changes in policy to be implemented • Inflexible software today will constrain policy in the future.