Data

All simulations run herein used historical SRTR data on candidate waitlists, registrations, status updates and organ arrivals from 2010 and 2011. Transportation distance and times were estimated at the donor hospital to candidate transplant center level, as in LSAM. The statistics reported are averages (and standard deviations where applicable) over 20 iterations of simulation for each run.

Scoretype

Beyond MELD scoring for candidates, allocation was also run using the Optimized Prediction of Mortality (OPOM) score developed previously by members of the team. OPOM utilizes machine learning Optimal Classification Tree models to predict any adult candidate’s (HCC and non-HCC) three-month waitlist mortality or removal using the STAR dataset. Notably, OPOM, when compared to MELD-based allocation, reduced mortality on average by 418 deaths every year in simulation analysis when using the current 11-district distribution policy. Furthermore, OPOM delivered substantially higher AUC values across all disease severity groups when compared to MELD and MELD-Na. Paper on OPOM forthcoming in American Journal of Transplantation:

Bertsimas D., Kung J., Wang Y., Trichakis N., Hirose R., Vagefi P. "Development and validation of an Optimized Prediction of Mortality (OPOM) for candidates awaiting liver transplantation." American Journal of Transplantation. November 2018.

Distribution Schemes

Distribution policies considered here fall into one of several schemes; differences lie in the way geographical location of a candidate relative to an incoming organ is prioritized in allocation. The schemes considered are:

Optimized Districts (OD): A revised regional grouping of the 58 DSAs into some number of broader districts, with allocation proceeding as in the current UNOS status quo (including Share35 and score boosting rules). Parameters: number of districts K, and assignments of the 58 DSAs into districts.

Acuity Circles (AC): Uses three distance-based circles (small, medium, large) around each donor hospital for prioritization within small bands of four MELD/PELD points for high urgency candidates (MELD/PELD > 28), and larger bands for low urgency candidates. Generalization of scenarios 3 and 4 tested in [2]. Status 1A and 1B candidates at centers within the large circle are offered first, then in expanding circles for each decreasing MELD/OPOM subgroup: 37+, 33-36, 29-33, X-29 (X being a parameter set in the model, typically 15 or 20). Candidates outside the large circle are offered next for status 1A, 1B and MELD/OPOM X+. Finally MELD/OPOM 6-X in expanding circles and outside the large circle. Sorting priority within each offer group by ABO compatibility points, decreasing MELD and listing time at current or lower MELD. Parameters: The radii of the three circles in nautical miles, and the threshold X between low/medium priority groups.

Broader 2-Circle (B2C): Similar to AC but with bigger MELD/OPOM bands used in the high-urgency regime. Generalization of scenario 5 tested in [2]. Status 1A and 1B candidates at centers within the large circle are offered first, followed by those within the medium circle with a MELD/OPOM X+ (X being a parameter set in the model, typically 29, 32 or 35). Candidates with MELD/OPOM of 15+ are offered next in expanding circles, followed by Status 1A/1B and MELD/OPOM 15+ outside the large circle. Finally, candidates with MELD/OPOM 6-14 are offered in expanding circles and outside the large circle. Sorting priority within each offer group by ABO compatibility points, decreasing MELD/OPOM and listing time at current or lower MELD/OPOM. Parameters: The radii of the three circles in nautical miles, and the threshold between medium/high priority groups.

Concentric Circles (CCD): A version of the concentric circle paradigm discussed in [3], with no MELD/OPOM bands. Two concentric circles (small, large) are defined around each donor hospital, with radii measured in nautical miles. Status 1A and 1B candidates at centers within the large circle are offered first, followed by all MELD/OPOM candidates in increasing circles, sorted by compatibility points, MELD/OPOM and wait time at current or lower MELD/OPOM. Status 1A, 1B and all MELD/OPOM candidates at centers outside the large circle in the same order. Parameters: The radii of the two circles in nautical miles.

Population Concentric Circles (CCP): Same as CCD, but circles around donor hospitals do not have a constant radius. Instead, they are based on population thresholds, their radius defined such that the historical candidate population in transplant centers within the circle exceeds the assigned threshold. Population in this case is defined as the average number of waitlisted candidates over 2007-2009. Parameters: The population thresholds for the two circles.

Continuous Scoring (CS): A version of the continuous scoring paradigm discussed in [3] with the aim of avoiding "cliffs" (geographic discontinuities). Status 1A and 1B candidates within a 600 nautical mile radius are offered first in increasing order of distance to the donor hospital, with additional allocation points awarded for blood type compatibility. Next all non-status 1A/1B candidates nationally are offered in decreasing order of a unified Score = (MELD/OPOM) - λ(Distance to donor hospital). Ties are broken by listing time at current or lower MELD/OPOM. Parameters: The tradeoff parameter λ.

Continuous Scoring (binned) (CSB): Same as above but the second component (Distance to donor hospital) is rounded to the nearest 50nm increment, to avoid small differences in priority score due to practically immaterial differences in candidate location. Parameters: The tradeoff parameter λ.

Reference Points

Certain reference points have been simulated for direct comparison to the various policies. These are:

• Current UNOS: The current 11-district UNOS policy.

• National Sharing: Organs are offered nationally solely on the basis of disease severity, i.e. in order of decreasing MELD/OPOM. Note this is essentially a continuous scoring (CS) policy with no weight on the distance component.

• One District: All DSAs belong to a single district. Note that the allocation rules stipulate that local candidates still get some priority over regional (in this case national) candidates in this setting.

• Gentry (K4 and K8): The 4- and 8-district solutions proposed by Gentry et al. in [1], under the OD paradigm.

• AC (250,500) Thresh = 15: Scenario 3 tested in [2], under the AC paradigm, with circle radii set to 150, 250, 500 miles and low/medium MELD threshold of 15. Also available is AC (250,500) Thresh = 20 with the low/medium MELD threshold set to 20.

• AC (300,600) Thresh = 15: Scenario 4 tested in [2], under the AC paradigm, with circle radii set to 150, 300, 600 miles and low/medium MELD threshold of 15. Also available is AC (300,600) Thresh = 20 with the low/medium MELD threshold set to 20.

• B2C (250,500) Thresh = 35: Scenario 5 tested in [2], under the B2C paradigm, with circle radii set to 150, 250, 500 miles and the medium/high MELD threshold set to 32. Also available are B2C (250,500) Thresh = 29 and B2C (250,500) Thresh = 32 with threshold set to 29 and 35 respectively.

• B2C (250,500) Thresh = 29+35: A variant on B2C with an additional high urgency MELD band; Status 1A and 1B within 500nm (large circle) are offered first and second, followed by MELD/OPOM 35+ within 500nm (large circle). Candidates with MELD 29-34 within 250nm (medium circle) follow and then allocation proceeds as in regular B2C.

[1] S. Gentry, E.K.H. Chow, A.B. Massie, and D.L. Segev. Gerrymandering for justice: redistricting U.S. liver allocation. Interfaces 45 (5): 462-80, September 2015.
[2] T. Weaver et al. SRTR Liver Simulated Allocation Model (LSAM) Analysis Report. Report. OPTN website, accessed November 2018.
[3] OPTN/UNOS Ad Hoc Committee on Geography. Frameworks for Organ Distribution. Report. OPTN website, accessed November 2018.