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A Data Envelopment Analysis Approach for Assessing Fairness in Resource Allocation: Application to Kidney Exchange Programs

Ali Kaazempur-Mofrad, Xiaowu Dai

TL;DR

This work develops a conditional Data Envelopment Analysis framework to assess fairness in kidney allocation across three dimensions: Priority, Access, and Outcome. By localizing frontiers with covariates via a kernel and measuring efficiency with a hyperbolic DEA score, the authors produce a unified fairness metric, augmented by Reference Frontier Mapping and group-conditional conformal prediction for robust uncertainty quantification. Analyses on US UNOS data reveal nuanced disparities: longer wait times for some groups, donor-driven variations in organ quality, and differential graft-rejection risks, with distributional differences capturing equity concerns beyond average effects. The approach offers a diagnostic tool for policy evaluation and stress-tests allocation rules under realistic demographic and clinical heterogeneity, while outlining practical considerations for implementation and future extensions.

Abstract

Kidney exchange programs have substantially increased transplantation rates but also raise critical concerns about fairness in organ allocation. We propose a novel framework leveraging Data Envelopment Analysis (DEA) to evaluate multiple dimensions of fairness-Priority, Access, and Outcome-within a unified model. This approach captures complexities often missed in single-metric analyses. Using data from the United Network for Organ Sharing, we separately quantify fairness across these dimensions: Priority fairness through waitlist durations, Access fairness via the Living Kidney Donor Profile Index (LKDPI) scores, and Outcome fairness based on graft lifespan. We then apply our conditional DEA model with covariate adjustment to demonstrate significant disparities in kidney allocation efficiency across ethnic groups. To quantify uncertainty, we employ conformal prediction within a novel Reference Frontier Mapping (RFM) framework, yielding group-conditional prediction intervals with finite-sample coverage guarantees. Our findings show notable differences in efficiency distributions between ethnic groups. Our study provides a rigorous framework for evaluating fairness in complex resource allocation systems with resource scarcity and mutual compatibility constraints.

A Data Envelopment Analysis Approach for Assessing Fairness in Resource Allocation: Application to Kidney Exchange Programs

TL;DR

This work develops a conditional Data Envelopment Analysis framework to assess fairness in kidney allocation across three dimensions: Priority, Access, and Outcome. By localizing frontiers with covariates via a kernel and measuring efficiency with a hyperbolic DEA score, the authors produce a unified fairness metric, augmented by Reference Frontier Mapping and group-conditional conformal prediction for robust uncertainty quantification. Analyses on US UNOS data reveal nuanced disparities: longer wait times for some groups, donor-driven variations in organ quality, and differential graft-rejection risks, with distributional differences capturing equity concerns beyond average effects. The approach offers a diagnostic tool for policy evaluation and stress-tests allocation rules under realistic demographic and clinical heterogeneity, while outlining practical considerations for implementation and future extensions.

Abstract

Kidney exchange programs have substantially increased transplantation rates but also raise critical concerns about fairness in organ allocation. We propose a novel framework leveraging Data Envelopment Analysis (DEA) to evaluate multiple dimensions of fairness-Priority, Access, and Outcome-within a unified model. This approach captures complexities often missed in single-metric analyses. Using data from the United Network for Organ Sharing, we separately quantify fairness across these dimensions: Priority fairness through waitlist durations, Access fairness via the Living Kidney Donor Profile Index (LKDPI) scores, and Outcome fairness based on graft lifespan. We then apply our conditional DEA model with covariate adjustment to demonstrate significant disparities in kidney allocation efficiency across ethnic groups. To quantify uncertainty, we employ conformal prediction within a novel Reference Frontier Mapping (RFM) framework, yielding group-conditional prediction intervals with finite-sample coverage guarantees. Our findings show notable differences in efficiency distributions between ethnic groups. Our study provides a rigorous framework for evaluating fairness in complex resource allocation systems with resource scarcity and mutual compatibility constraints.
Paper Structure (14 sections, 2 theorems, 58 equations, 5 figures, 16 tables)

This paper contains 14 sections, 2 theorems, 58 equations, 5 figures, 16 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Fairness Criteria in Kidney Allocation
  4. Data Envelopment Analysis Framework
  5. Group-Conditional Uncertainty Quantification under Reference Frontier Mapping
  6. Preliminary Analyses and Fairness Criteria
  7. Exploratory Data Analysis
  8. Data Preprocessing: Resampling and Relative Measures
  9. Fairness Criteria Analysis
  10. DEA Estimation and Inference
  11. DEA Results
  12. Analysis of Efficiency Distributions
  13. Discussion and Implication for Practice
  14. Conclusion

Key Result

Theorem 1

Let $\mathcal{G}$ denote a set of groups, and let ${(X_i, Y_i, Z_i)}_{i=1}^n$ be i.i.d. samples from a joint distribution $\mathbb{P}_{X,Y,Z}$, where $X_i \in \mathbb{R}^p$, $Y_i \in \mathbb{R}^q$, and $Z_i \in \mathbb{R}^r$. Let $\mathcal{D}_\text{ref}$ be a fixed reference set used to compute cond where $\theta_{n+1} = \varphi_{\mathcal{T}_{Z_{n+1}}}(X_{n+1}, Y_{n+1})$ and $\alpha$ is the target

Figures (5)

  • Figure 1: Illustration of the conditional DEA framework for a single focal patient. Each panel plots one input (waitlist duration or LKDPI) against the output (graft lifespan). Small points represent all observations in the sample, and the focal patient is marked with a diamond. Filled circular points indicate the focal patient's local reference set, consisting of patients with similar covariate profiles $Z$. The solid curve represents the covariate-conditional efficiency frontier estimated from this local reference set; points marked along this curve correspond to observations lying on the frontier. The dashed curve shows the hyperbolic trajectory along which the focal patient's input–output pair is scaled by $\theta$ until it intersects the frontier at the conditional efficiency target $\theta_i(Z_i)=1$.
  • Figure 2: Comparison of the Distribution of Ethnic Groups in the 2019 Subset of the Imbalanced Data and the 2019 ESRD Prevalence in the U.S.
  • Figure 3: Cumulative Incidence Functions for Graft Rejection and Competing Risks by Ethnicity
  • Figure 4: Distribution of Relative Efficiency Scores by Ethnic Group.
  • Figure 5: Relative Efficiency Scores Across Different Proportion Scenarios

Theorems & Definitions (4)

  • Theorem 1
  • Theorem 2
  • proof
  • proof