A Nonasymptotic Approach to Analyzing Kidney Exchange Graphs
Bibliographic record
Abstract
We propose a novel methodology to study kidney exchange. Using a random graph model of kidney exchange, we propose a nonasymptotic approach to quantifying the effectiveness of transplant chains in reducing the number of unmatched highly sensitized patients. Our approach is based on a two-phase random walk procedure where random walks are used to allocate chains, followed by allocation in cycles. The benefit of random walks is that they preserve the probabilistic structure of residual graphs, greatly facilitating analysis. Our approach allows us to analytically show the benefit of chains, as opposed to transplantation in cycles only, in nonasymptotic (medium-sized) graphs. We also derive useful analytical bounds that illustrate the performance of our proposed allocation procedure and more general kidney allocation procedures. Our results complement previous findings from analytical results in large (limit) graphs and empirical results based on data from fielded kidney exchanges demonstrating the benefits of chains. Moreover, our analysis sheds light on the relative importance of chains versus cycles in kidney allocation. In particular, our results show prioritizing chains over easy-to-transplant cycles, as opposed to prioritizing those cycles over chains, improves performance and provides analytical bounds on the associated benefits. A detailed simulation study numerically verifies our main results and provides additional insights. The online appendix is available at https://doi.org/10.1287/opre.2017.1717 .
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".