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We show that selecting these edges is a challenging combinatorial problem, which is non-monotonic and non-submodular, in addition to being NP-hard

Improving Policy-Constrained Kidney Exchange via Pre-Screening

NIPS 2020, (2020)

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Abstract

In barter exchanges, participants swap goods with one another without exchanging money; exchanges are often facilitated by a central clearinghouse, with the goal of maximizing the aggregate quality (or number) of swaps. Barter exchanges are subject to many forms of uncertainty--in participant preferences, the feasibility and quality of ...More

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Introduction
  • The authors consider a multi-stage decision problem in which a decision-maker uses a fixed policy to solve a hard problem.
  • Failed transplants are especially troublesome in kidney exchange, due to the cycle and chain structures used: for example, suppose that a cyclical swap is planned between three patient/donor pairs; if any one of the planned transplants fails, none of the other transplants in that cycle can occur.
  • It is quite common for planned transplants to fail.
  • The United Network for Organ Sharing (UNOS1) estimates that in FY2019, about 85% of their planned kidney transplants failed [18]
Highlights
  • We consider a multi-stage decision problem in which a decision-maker uses a fixed policy to solve a hard problem
  • Failed transplants are especially troublesome in kidney exchange, due to the cycle and chain structures used: for example, suppose that a cyclical swap is planned between three patient/donor pairs; if any one of the planned transplants fails, none of the other transplants in that cycle can occur
  • We propose a Monte Carlo Tree Search algorithm and a simple greedy algorithm
  • Monte Carlo Tree Search for Edge Selection (MCTS): We propose a tree-search algorithm for single-stage edge selection, MCTS, based on Monte Carlo Tree Search (MCTS), with the Upper Confidence for Trees (UCT) algorithm [17]
  • Many planned kidney exchange transplants fail for a variety of reasons; these failures greatly reduce the number of transplants that an exchange can facilitate, and increase the waiting time for many patients in need of a kidney
  • A value of ∆MAX = 0 means that method X did not improve over the baseline, a value of ∆MAX = 1 means that X achieved an objective 100% greater than the baseline, and so on
  • We formalize a multi-stage optimization problem based on realistic assumptions about how transplants fail, and how exchanges match patients and donors; we emphasize that these important assumptions are not included in prior work. While this problem is challenging in theory, we show that it is much easier in practice–with computational experiments using both synthetic data and real data from the United Network for Organ Sharing
Methods
  • Edge selection, for the Simple and KPD edge distributions, respectively.
  • The authors draw two conclusions from these results: (1) MCTS and Greedy produce almost identical results, further suggesting that Greedy is nearly optimal in the setting; (2) in the setting, edge selection is effectively monotonic, as ∆MAX almost never decreases.
  • Figure 2d gives an example of non-monotonicity for both Greedy and Random: in some cases, querying edges can lead to a worse outcome than querying no edges
Results
  • A value of ∆MAX = 0 means that method X did not improve over the baseline, a value of ∆MAX = 1 means that X achieved an objective 100% greater than the baseline, and so on.
  • The authors generate three sets of 100 random graphs with N = 50, 75, and 100 vertices, and each with p = 0.01.
  • The authors find that pre-screening even a small number of potential transplants significantly increases the overall quality of the final match–by more than 100% of the original match weight
Conclusion
  • Conclusions and Future Research

    Directions

    Many planned kidney exchange transplants fail for a variety of reasons; these failures greatly reduce the number of transplants that an exchange can facilitate, and increase the waiting time for many patients in need of a kidney.
  • The authors formalize a multi-stage optimization problem based on realistic assumptions about how transplants fail, and how exchanges match patients and donors; the authors emphasize that these important assumptions are not included in prior work
  • While this problem is challenging in theory, the authors show that it is much easier in practice–with computational experiments using both synthetic data and real data from the United Network for Organ Sharing.
  • The authors find that pre-screening even a small number of potential transplants significantly increases the overall quality of the final match–by more than 100% of the original match weight
Summary
  • Introduction:

    The authors consider a multi-stage decision problem in which a decision-maker uses a fixed policy to solve a hard problem.
  • Failed transplants are especially troublesome in kidney exchange, due to the cycle and chain structures used: for example, suppose that a cyclical swap is planned between three patient/donor pairs; if any one of the planned transplants fails, none of the other transplants in that cycle can occur.
  • It is quite common for planned transplants to fail.
  • The United Network for Organ Sharing (UNOS1) estimates that in FY2019, about 85% of their planned kidney transplants failed [18]
  • Objectives:

    The authors aim to select an edge set q ∈ E which maximizes the expected weight of the final matching.
  • Methods:

    Edge selection, for the Simple and KPD edge distributions, respectively.
  • The authors draw two conclusions from these results: (1) MCTS and Greedy produce almost identical results, further suggesting that Greedy is nearly optimal in the setting; (2) in the setting, edge selection is effectively monotonic, as ∆MAX almost never decreases.
  • Figure 2d gives an example of non-monotonicity for both Greedy and Random: in some cases, querying edges can lead to a worse outcome than querying no edges
  • Results:

    A value of ∆MAX = 0 means that method X did not improve over the baseline, a value of ∆MAX = 1 means that X achieved an objective 100% greater than the baseline, and so on.
  • The authors generate three sets of 100 random graphs with N = 50, 75, and 100 vertices, and each with p = 0.01.
  • The authors find that pre-screening even a small number of potential transplants significantly increases the overall quality of the final match–by more than 100% of the original match weight
  • Conclusion:

    Conclusions and Future Research

    Directions

    Many planned kidney exchange transplants fail for a variety of reasons; these failures greatly reduce the number of transplants that an exchange can facilitate, and increase the waiting time for many patients in need of a kidney.
  • The authors formalize a multi-stage optimization problem based on realistic assumptions about how transplants fail, and how exchanges match patients and donors; the authors emphasize that these important assumptions are not included in prior work
  • While this problem is challenging in theory, the authors show that it is much easier in practice–with computational experiments using both synthetic data and real data from the United Network for Organ Sharing.
  • The authors find that pre-screening even a small number of potential transplants significantly increases the overall quality of the final match–by more than 100% of the original match weight
Tables
  • Table1: left) shows the number of random graphs binned by %OPT, as well as the maximum %OPT over all graphs. For each N , Greedy returns an optimal solution for at least 90 of the 100 graphs; the maximum %OPT over all graphs is 2.8. Left: Optimality gap for Greedy, over 100 random graphs with p = 0.01 and various N , with edge budget Γ = 3; bottom row shows the maximum value of %OPT over all graphs. Right: Single-stage results on UNOS graphs using the variable IIAB edge budget (top rows), and the failure-aware method (bottom row). Columns PX indicates the Xth percentile of ∆MAX over all UNOS graphs. right) shows a comparison of all edge-selection methods–each using the variable edge budget of IIAB; the bottom row shows results for Fail-Aware. Both MCTS and Greedy achieve greater ∆MAX (in distribution) than both benchmark methods. This is expected in both cases: IIAB uses a heuristic to select edges to query, which does not consider the final matching weight—the objective of our edge selection problem; on the other hand, both MCTS and Greedy are designed to maximize this objective. We do not expect Fail-Aware to out-perform any edge selection methods, since Fail-Aware does not have access to information revealed after edge queries
  • Table2: Median normalized standard deviation of the bootstrap mean, over 200 bootstrap samples for each sample size N , binned by edge budget
  • Table3: Single-stage results on random graphs with the Simple edge distribution, using the variable IIAB edge budget (top rows), and the failure-aware method (bottom row). Columns PX indicates the Xth percentile of ∆MAX over all 30 random graphs, for graphs with N = 50, 75, and 100 vertices
Download tables as Excel
Funding
  • Curry, Dickerson, and McElfresh were supported in part by NSF CAREER Award IIS-1846237, DARPA GARD, DARPA SI3-CMD #S4761, DoD WHS Award #HQ003420F0035, NIH R01 Award NLM-013039-01, and a Google Faculty Research Award
  • Sandholm was supported in part by the National Science Foundation under grants IIS-1718457, IIS-1617590, IIS-1901403, and CCF-1733556, and the ARO under award W911NF-17-1-0082
Study subjects and analysis
potential transplants: 1000
Pre-screening transplants is costly, as it requires scarce time and resources. Furthermore, there are often many thousand potential transplants in any given exchange; selecting which transplants to screen is not easy. In this paper we investigate methods for selecting a limited number of transplants to pre-screen, in order to “guide” the matching algorithm to a better outcome

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