Pooling Donor Organs Without Leaving Regions Behind

Why a larger pool can still create losers

An organ may become available when no compatible patient is waiting locally, even though someone elsewhere could receive it. Combining regional waiting lists can capture opportunities that separate systems miss. But broader sharing also redistributes organs, potentially disadvantaging regions with relatively abundant donations and less demand.

In the theoretical preprint Dynamic Pooling and Regional Participation in Deceased-Donor Organ Allocation, Genta Okada studies this tension using a mathematical queueing model. The central distinction is between creating additional transplantation opportunities and redistributing existing ones. The paper argues that the additional opportunities can support mutually beneficial sharing, but an allocation rule focused only on total patient utility need not deliver that outcome.

The gains come from timing and uncertainty

The model follows patients and organs arriving randomly over time. Patients enter queues defined by their region and type. They may leave without transplantation, while an arriving organ must be allocated immediately or discarded. Different patient types can receive different utility values from transplantation.

Compatibility is deliberately simplified: for each arriving organ, every waiting patient independently has the same probability of being compatible. The main frontier and algorithmic results also assume a common rate of leaving the queue across patient classes.

Within this framework, pooling reduces losses caused by fluctuating arrivals and compatibility outcomes. Okada calls this mechanism dynamic risk pooling. It differs from simply moving organs from high-supply regions to high-demand ones: it makes use of organs that separate systems would have discarded.

The paper proves that, under its assumptions and with multiple regions, an allocation policy exists that strictly improves every region’s long-run average utility relative to operating independently. That independent-operation benchmark, called autarky, assumes each region already uses its own optimal local priority rule.

Efficiency alone does not protect participation

A utilitarian allocation rule maximizes total patient utility, prioritizing compatible patients according to their transplantation value. In asymmetric regions, however, high-value patients elsewhere can displace lower-value local patients sufficiently often to make a donation-rich region worse off than under autarky.

The proposed remedy is a participation constraint: each region must receive at least its autarky average utility. This protects a regional average, not necessarily every patient group within that region.

A numerical example makes the distinction concrete. With regional constraints, one patient class receives average utility of 0.1674, below its autarky value of 0.2645, even though its region meets its benchmark. Adding separate constraints for every class prevents those class-level losses in the example, but reduces total utilitarian welfare by a reported 4.4 percent compared with regional constraints alone.

Searching for workable priorities

Okada proposes the Constrained Pareto Frontier Search, or CPFS, algorithm to find approximately optimal outcomes subject to participation requirements.

The mathematical shortcut is a static priority ranking: each patient class receives a fixed index, and an arriving organ goes to the highest-ranked compatible waiting class. Under the paper’s assumptions, such rankings solve weighted welfare problems. Their utility outcomes can then be combined to construct constrained solutions without exhaustively listing every possible ranking.

The theorem bounds both the objective shortfall and the total constraint violation by a chosen accuracy tolerance. It is an approximate guarantee, not a claim that every numerical output satisfies every constraint exactly.

In a five-region, ten-class example, the paper reports that CPFS matched the exhaustive method’s objective to machine precision, taking 0.0204 seconds rather than 874.4862 seconds. These are results from the reported computational experiments, not evidence of operational deployment.

A data-informed illustration, not a policy forecast

A separate exercise uses 2023 U.S. kidney-transplant data to set arrival rates for eleven regions. In this simplified, single-patient-type calibration, modeled throughput rises from about 82.27 transplants per day under autarky to 84.39 under pooling, a 2.58 percent gain.

A region-blind shared-list benchmark achieves that throughput but leaves four regions below their autarky transplant probabilities. CPFS preserves the same total throughput while satisfying all regional constraints in the reported solution. In this one-type model, all pooled policies that allocate whenever a compatible patient exists have the same aggregate throughput; the challenge is distributing it.

These findings remain conditional. The compatibility parameter is assumed rather than independently estimated, and the paper explicitly presents the calibration as an illustration, not a quantitative evaluation of current U.S. allocation. Its single organ type, homogeneous compatibility and common departure rate are substantial simplifications.

Finally, participation guarantees concern long-run averages. They do not ensure that every region benefits over every finite window. The preprint therefore offers a benchmark for designing sharing incentives, not a ready-made clinical allocation system.