A competing risks model to estimate the risk of graft failure and patient death after kidney transplantation using continuous donor-recipient age combinations.

Graft failure and recipient death with functioning graft are important competing outcomes after kidney transplantation. Risk prediction models typically censor for the competing outcome thereby overestimating the cumulative incidence. The magnitude of this overestimation is not well described in real-world transplant data. This retrospective cohort study analyzed data from the European Collaborative Transplant Study (n = 125 250) and from the American Scientific Registry of Transplant Recipients (n = 190 258). Separate cause-specific hazard models using donor and recipient age as continuous predictors were developed for graft failure and recipient death. The hazard of graft failure increased quadratically with increasing donor age and decreased decaying with increasing recipient age. The hazard of recipient death increased linearly with increasing donor and recipient age. The cumulative incidence overestimation due to competing risk-censoring was largest in high-risk populations for both outcomes (old donors/recipients), sometimes amounting to 8.4 and 18.8 percentage points for graft failure and recipient death, respectively. In our illustrative model for posttransplant risk prediction, the absolute risk of graft failure and death is overestimated when censoring for the competing event, mainly in older donors and recipients. Prediction models for absolute risks should treat graft failure and death as competing events.

Contemporary prevalence and practice patterns of out-of-sequence kidney allocation.

Since 2021, the Organ Procurement and Transplantation Network has reported a nearly 10-fold rise in out-of-sequence (OOS) kidney allocation, generating concern and halting development of continuous distribution policies. We report contemporary (2022-2023) practice patterns in OOS allocation using Organ Procurement and Transplantation Network data. We examined in sequence vs OOS donors with multivariable logistic regression and skipped vs OOS-accepting recipients with conditional logistic regression. Nearly 20% of kidney placements were OOS, varying from 0% to 43% acsoss organ procurement organizations; the 5 highest OOS-organ procurement organizations accounted for 29% of all OOS. Of OOS kidneys, 33% were declined ≥100 times in the standard allocation sequence and 51% were declined by ≥10 centers before OOS allocation began; 4.5% were made without any in-sequence declines. Nearly, all OOS offers were open offers. OOS kidneys were more likely to be from female, Black, older, donation after cardiac death, hypertensive, diabetic, and elevated creatinine donors. Candidates receiving OOS kidneys were more likely female, Asian, and older than skipped candidates. Higher-volume centers and centers with more White, fewer Hispanic, and more educated waiting list patients underwent transplantation disproportionately with more OOS kidneys. These findings suggest that the current, highly variable, discretionary use of OOS might exacerbate disparities, yet the impact of OOS on organ utilization cannot be determined with data now collected.

Logistical burden of offers and allocation inefficiency in circle-based liver allocation.

Recent changes to liver allocation replaced donor service areas with circles as the geographic unit of allocation. Circle-based allocation might increase the number of transplantation centers and candidates required to place a liver, thereby increasing the logistical burden of making and responding to offers on organ procurement organizations and transplantation centers. Circle-based allocation might also increase distribution time and cold ischemia time (CIT), particularly in densely populated areas of the country, thereby decreasing allocation efficiency. Using Scientific Registry of Transplant Recipient data from 2019 to 2021, we evaluated the number of transplantation centers and candidates required to place livers in the precircles and postcircles eras, nationally and by donor region. Compared with the precircles era, livers were offered to more candidates (5 vs. 9; p < 0.001) and centers (3 vs. 5; p < 0.001) before being accepted; more centers were involved in the match run by offer number 50 (9 vs. 14; p < 0.001); CIT increased by 0.2 h (5.9 h vs. 6.1 h; p < 0.001); and distribution time increased by 2.0 h (30.6 h vs. 32.6 h; p < 0.001). Increased burden varied geographically by donor region; livers recovered in Region 9 were offered to many more candidates (4 vs. 12; p < 0.001) and centers (3 vs. 8; p < 0.001) before being accepted, resulting in the largest increase in CIT (5.4 h vs. 6.0 h; p < 0.001). Circle-based allocation is associated with increased logistical burdens that are geographically heterogeneous. Continuous distribution systems will have to be carefully designed to avoid exacerbating this problem.

Removing geographic boundaries from liver allocation: A method for designing continuous distribution scores.

BACKGROUND: The Organ Procurement and Transplantation Network (OPTN) is eliminating geographic boundaries in liver allocation, in favor of continuous distribution. Continuous distribution allocates organs via a composite allocation score (CAS): a weighted sum of attributes like medical urgency, candidate biology, and placement efficiency. The opportunity this change represents, to include new variables and features for prioritizing candidates, will require lengthy and contentious discussions to establish community consensus. Continuous distribution could instead be implemented rapidly by computationally translating the allocation priorities for pediatric, status 1, and O/B blood type liver candidates that are presently implemented via geographic boundaries into points and weights in a CAS. METHODS: Using simulation with optimization, we designed a CAS that is minimally disruptive to existing prioritizations, and that eliminates geographic boundaries and minimizes waitlist deaths without harming vulnerable populations. RESULTS: Compared with Acuity Circles (AC) in a 3-year simulation, our optimized CAS decreased deaths from 7771.2 to 7678.8 while decreasing average (272.66 NM vs. 264.30 NM) and median (201.14 NM vs. 186.49 NM) travel distances. Our CAS increased travel only for high MELD and status 1 candidates (423.24 NM vs. 298.74 NM), and reduced travel for other candidates (198.98 NM vs. 250.09 NM); overall travel burden decreased. CONCLUSION: Our CAS reduced waitlist deaths by sending livers for high-MELD and status 1 candidates farther, while keeping livers for lower MELD candidates nearby. This advanced computational method can be applied again after wider discussions of adding new priorities conclude; our method designs score weightings to achieve any specified feasible allocation outcomes.

Life expectancy without a transplant for status 1A liver transplant candidates.

Status 1A liver transplant candidates are given the highest medical priority for the allocation of deceased donor livers. Organ Procurement and Transplantation Network (OPTN) policy requires physicians to certify that a candidate has a life expectancy without a transplant of less than 7 days for that candidate to be given status 1A. Additionally, candidates receiving status 1A must have one of six medical conditions listed in policy. Using Scientific Registry of Transplant Recipients data from all prevalent liver transplant candidates from 2010 to 2020, we used a bias-corrected Kaplan-Meier model to calculate the survival of status 1A candidates and to determine their life expectancy without a transplant. We found that status 1A candidates have a life expectancy without a transplant of 24 (95% CI 20-46) days-over three times longer than what policy requires for status 1A designation. We repeated the analysis for subgroups of status 1A candidates based on the medical conditions that grant status 1A. We found that none of these subgroups met the life expectancy requirement. Harmonizing OPTN policy with observed data would sustain the integrity of the allocation process.

MELD 3.0: The Model for End-Stage Liver Disease Updated for the Modern Era.

BACKGROUND & AIMS: The Model for End-Stage Liver Disease (MELD) has been established as a reliable indicator of short-term survival in patients with end-stage liver disease. The current version (MELDNa), consisting of the international normalized ratio and serum bilirubin, creatinine, and sodium, has been used to determine organ allocation priorities for liver transplantation in the United States. The objective was to optimize MELD further by taking into account additional variables and updating coefficients with contemporary data. METHODS: All candidates registered on the liver transplant wait list in the US national registry from January 2016 through December 2018 were included. Uni- and multivariable Cox models were developed to predict survival up to 90 days after wait list registration. Model fit was tested using the concordance statistic (C-statistic) and reclassification, and the Liver Simulated Allocation Model was used to estimate the impact of replacing MELDNa with the new model. RESULTS: The final multivariable model was characterized by (1) additional variables of female sex and serum albumin, (2) interactions between bilirubin and sodium and between albumin and creatinine, and (3) an upper bound for creatinine at 3.0 mg/dL. The final model (MELD 3.0) had better discrimination than MELDNa (C-statistic, 0.869 vs 0.862; P < .01). Importantly, MELD 3.0 correctly reclassified a net of 8.8% of decedents to a higher MELD tier, affording them a meaningfully higher chance of transplantation, particularly in women. In the Liver Simulated Allocation Model analysis, MELD 3.0 resulted in fewer wait list deaths compared to MELDNa (7788 vs 7850; P = .02). CONCLUSION: MELD 3.0 affords more accurate mortality prediction in general than MELDNa and addresses determinants of wait list outcomes, including the sex disparity.

The Precise Relationship Between Model for End-Stage Liver Disease and Survival Without a Liver Transplant.

BACKGROUND AND AIMS: Scores from the Model for End-Stage Liver Disease (MELD), which are used to prioritize candidates for deceased donor livers, are widely acknowledged to be negatively correlated with the 90-day survival rate without a liver transplant. However, inconsistent and outdated estimates of survival probabilities by MELD preclude useful applications of the MELD score. APPROACH AND RESULTS: Using data from all prevalent liver waitlist candidates from 2016 to 2019, we estimated 3-day, 7-day, 14-day, 30-day, and 90-day without-transplant survival probabilities (with confidence intervals) for each MELD score and status 1A. We used an adjusted Kaplan-Meier model to avoid unrealistic assumptions and multiple observations per person instead of just the observation at listing. We found that 90-day without-transplant survival has improved over the last decade, with survival rates increasing >10% (in absolute terms) for some MELD scores. We demonstrated that MELD correctly prioritizes candidates in terms of without-transplant survival probability but that status 1A candidates' short-term without-transplant survival is higher than that of MELD 40 candidates and lower than that of MELD 39 candidates. Our primary result is the updated survival functions themselves. CONCLUSIONS: We calculated without-transplant survival probabilities for each MELD score (and status 1A). The survival function is an invaluable tool for many applications in liver transplantation: awarding of exception points, calculating the relative demand for deceased donor livers in different geographic areas, calibrating the pediatric end-stage liver disease score, and deciding whether to accept an offered liver.

Heterogeneous Circles for Liver Allocation.

BACKGROUND AND AIMS: In February 2020, the Organ Procurement and Transplantation Network replaced donor service area-based allocation of livers with acuity circles, a system based on three homogeneous circles around each donor hospital. This system has been criticized for neglecting to consider varying population density and proximity to coast and national borders. APPROACH AND RESULTS: Using Scientific Registry of Transplant Recipients data from July 2013 to June 2017, we designed heterogeneous circles to reduce both circle size and variation in liver supply/demand ratios across transplant centers. We weighted liver demand by Model for End-Stage Liver Disease (MELD)/Pediatric End-Stage Liver Disease (PELD) because higher MELD/PELD candidates are more likely to be transplanted. Transplant centers in the West had the largest circles; transplant centers in the Midwest and South had the smallest circles. Supply/demand ratios ranged from 0.471 to 0.655 livers per MELD-weighted incident candidate. Our heterogeneous circles had lower variation in supply/demand ratios than homogeneous circles of any radius between 150 and 1,000 nautical miles (nm). Homogeneous circles of 500 nm, the largest circle used in the acuity circles allocation system, had a variance in supply/demand ratios 16 times higher than our heterogeneous circles (0.0156 vs. 0.0009) and a range of supply/demand ratios 2.3 times higher than our heterogeneous circles (0.421 vs. 0.184). Our heterogeneous circles had a median (interquartile range) radius of only 326 (275-470) nm but reduced disparities in supply/demand ratios significantly by accounting for population density, national borders, and geographic variation of supply and demand. CONCLUSIONS: Large homogeneous circles create logistical burdens on transplant centers that do not need them, whereas small homogeneous circles increase geographic disparity. Using carefully designed heterogeneous circles can reduce geographic disparity in liver supply/demand ratios compared with homogeneous circles of radius ranging from 150 to 1,000 nm.

Heterogeneous donor circles for fair liver transplant allocation.

The United States (U.S.) Department of Health and Human Services is interested in increasing geographical equity in access to liver transplant. The geographical disparity in the U.S. is fundamentally an outcome of variation in the organ supply to patient demand (s/d) ratios across the country (which cannot be treated as a single unit due to its size). To design a fairer system, we develop a nonlinear integer programming model that allocates the organ supply in order to maximize the minimum s/d ratios across all transplant centers. We design circular donation regions that are able to address the issues raised in legal challenges to earlier organ distribution frameworks. This allows us to reformulate our model as a set-partitioning problem. Our policy can be viewed as a heterogeneous donor circle policy, where the integer program optimizes the radius of the circle around each donation location. Compared to the current policy, which has fixed radius circles around donation locations, the heterogeneous donor circle policy greatly improves both the worst s/d ratio and the range between the maximum and minimum s/d ratios. We found that with the fixed radius policy of 500 nautical miles (NM), the s/d ratio ranges from 0.37 to 0.84 at transplant centers, while with the heterogeneous circle policy capped at a maximum radius of 500 NM, the s/d ratio ranges from 0.55 to 0.60, closely matching the national s/d ratio average of 0.5983. Our model matches the supply and demand in a more equitable fashion than existing policies and has a significant potential to improve the liver transplantation landscape.

Correcting the sex disparity in MELD-Na.

MELD-Na appears to disadvantage women awaiting liver transplant by underestimating their mortality rate. Fixing this problem involves: (1) estimating the magnitude of this disadvantage separately for each MELD-Na, (2) designing a correction for each MELD-Na, and (3) evaluating corrections to MELD-Na using simulated allocation. Using Kaplan-Meier modeling, we calculated 90-day without-transplant survival for men and women, separately at each MELD-Na. For most scores between 15 and 35, without-transplant survival was higher for men by 0-5 percentage points. We tested two proposed corrections to MELD-Na (MELD-Na-MDRD and MELD-GRAIL-Na), and one correction we developed (MELD-Na-Shift) to target the differences we quantified in survival across the MELD-Na spectrum. In terms of without-transplant survival, MELD-Na-MDRD overcorrected sex differences while MELD-GRAIL-Na and MELD-Na-Shift eliminated them. Estimating the impact of implementing these corrections with the liver simulated allocation model, we found that MELD-Na-Shift alone eliminated sex disparity in transplant rates (p = 0.4044) and mortality rates (p = 0.7070); transplant rates and mortality rates were overcorrected by MELD-Na-MDRD (p = 0.0025, p = 0.0006) and MELD-GRAIL-Na (p = 0.0079, p = 0.0005). We designed a corrected MELD-Na that eliminates sex disparities in without-transplant survival, but allocation changes directing smaller livers to shorter candidates may also be needed to equalize women's access to liver transplant.

Allocating kidneys in optimized heterogeneous circles.

Recently, the Organ Procurement and Transplant Network approved a plan to allocate kidneys within 250-nm circles around donor hospitals. These homogeneous circles might not substantially reduce geographic differences in transplant rates because deceased donor kidney supply and demand differ across the country. Using Scientific Registry of Transplant Recipients data from 2016-2019, we used an integer program to design unique, heterogeneous circles with sizes between 100 and 500 nm that reduced supply/demand ratio variation across transplant centers. We weighted demand according to wait time because candidates who have waited longer have higher priority. We compared supply/demand ratios and average travel distance of kidneys, using heterogeneous circles and 250 and 500-nm fixed-distance homogeneous circles. We found that 40% of circles could be 250 nm or smaller, while reducing supply/demand ratio variation more than homogeneous circles. Supply/demand ratios across centers for heterogeneous circles ranged from 0.06 to 0.13 kidneys per wait-year, compared to 0.04 to 0.47 and 0.05 to 0.15 kidneys per wait-year for 250-nm and 500-nm homogeneous circles, respectively. The average travel distance for kidneys using heterogeneous, and 250-nm and 500-nm fixed-distance circles was 173 nm, 134 nm, and 269 nm, respectively. Heterogeneous circles reduce geographic disparity compared to homogeneous circles, while maintaining reasonable travel distances.

Liver simulated allocation model does not effectively predict organ offer decisions for pediatric liver transplant candidates.

The SRTR maintains the liver-simulated allocation model (LSAM), a tool for estimating the impact of changes to liver allocation policy. Integral to LSAM is a model that predicts the decision to accept or decline a liver for transplant. LSAM implicitly assumes these decisions are made identically for adult and pediatric liver transplant (LT) candidates, which has not been previously validated. We applied LSAM's decision-making models to SRTR offer data from 2013 to 2016 to determine its efficacy for adult (≥18) and pediatric (<18) LT candidates, and pediatric subpopulations-teenagers (≥12 to <18), children (≥2 to <12), and infants (<2)-using the area under the receiver operating characteristic (ROC) curve (AUC). For nonstatus 1A candidates, all pediatric subgroups had higher rates of offer acceptance than adults. For non-1A candidates, LSAM's model performed substantially worse for pediatric candidates than adults (AUC 0.815 vs. 0.922); model performance decreased with age (AUC 0.898, 0.806, 0.783 for teenagers, children, and infants, respectively). For status 1A candidates, LSAM also performed worse for pediatric than adult candidates (AUC 0.711 vs. 0.779), especially for infants (AUC 0.618). To ensure pediatric candidates are not unpredictably or negatively impacted by allocation policy changes, we must explicitly account for pediatric-specific decision making in LSAM.

MELD is MELD is MELD? Transplant center-level variation in waitlist mortality for candidates with the same biological MELD.

Recently, model for end-stage liver disease (MELD)-based liver allocation in the United States has been questioned based on concerns that waitlist mortality for a given biologic MELD (bMELD), calculated using laboratory values alone, might be higher at certain centers in certain locations across the country. Therefore, we aimed to quantify the center-level variation in bMELD-predicted mortality risk. Using Scientific Registry of Transplant Recipients (SRTR) data from January 2015 to December 2019, we modeled mortality risk in 33 260 adult, first-time waitlisted candidates from 120 centers using multilevel Poisson regression, adjusting for sex, and time-varying age and bMELD. We calculated a "MELD correction factor" using each center's random intercept and bMELD coefficient. A MELD correction factor of +1 means that center's candidates have a higher-than-average bMELD-predicted mortality risk equivalent to 1 bMELD point. We found that the "MELD correction factor" median (IQR) was 0.03 (-0.47, 0.52), indicating almost no center-level variation. The number of centers with "MELD correction factors" within ±0.5 points, and between ±0.5-± 1, ±1.0-±1.5, and ±1.5-±2.0 points was 62, 41, 13, and 4, respectively. No centers had waitlisted candidates with a higher-than-average bMELD-predicted mortality risk beyond ±2 bMELD points. Given that bMELD similarly predicts waitlist mortality at centers across the country, our results support continued MELD-based prioritization of waitlisted candidates irrespective of center.

Restructuring the Organ Procurement and Transplantation Network contract to achieve policy coherence and infrastructure excellence.

The Organ Procurement and Transplantation Network (OPTN) went up for competitive bid again this year, yet this contract has been held by only 1 entity since its inception. The OPTN's scope has grown steadily, and it now embraces several disparate missions: to operate the computing and coordination infrastructure that maintains waitlists and makes organ offers in priority order, to regulate transplant centers and organ procurement organizations, to follow and protect living donors, and to decide organ allocation policy in concert with the many voices of the transplant community. The contracting process and performance work statement continue to discourage both innovative approaches to the OPTN and competitive bids outside of United Network for Organ Sharing (UNOS), with evaluation criteria that either disqualify or strongly disadvantage new applicants. The performance work statement also emphasizes bureaucratic tasks while obligating the OPTN contractor to the specific committee structure that has impeded decision-making and tended to preserve the status quo in controversial matters. Finally, the UNOS computing infrastructure is antiquated and requires months to years to implement small changes. Restructuring the OPTN contract to separate the information technology requirements from the policy/regulatory responsibilities might allow more nimble and effective specialty contractors to offer their capabilities in service of the national transplant enterprise.

Geographic disparities in lung transplant rates.

In November 2017, in response to a lawsuit from a New York City lung transplant candidate, an emergency change to the lung allocation policy eliminated the donation service area (DSA) as the first geographic tier of allocation. The lawsuit claimed that DSA borders are arbitrary and that allocation should be based on medical priority. We investigated whether deceased-donor lung transplant (LT) rates differed substantially between DSAs in the United States before the policy change. We estimated LT rates per active person-year using multilevel Poisson regression and empirical Bayes methods. We found that the median incidence rate ratio (MIRR) of transplant rates between DSAs was 2.05, meaning a candidate could be expected to double their LT rate by changing their DSA. This can be compared directly to a 1.54-fold increase in LT rate that we found associated with an increase in lung allocation score (LAS) category from 38-42 to 42-50. Changing a candidate's DSA would have had a greater impact on the candidate's LT rate than changing LAS categories from 38-42 to 42-50. In summary, we found that the DSA of listing was a major determinant of LT rate for candidates across the country before the emergency lung allocation change.

Accelerating kidney allocation: Simultaneously expiring offers.

Using nonideal kidneys for transplant quickly might reduce the discard rate of kidney transplants. We studied changing kidney allocation to eliminate sequential offers, instead making offers to multiple centers for all nonlocally allocated kidneys, so that multiple centers must accept or decline within the same 1 hour. If more than 1 center accepted an offer, the kidney would go to the highest-priority accepting candidate. Using 2010 Kidney-Pancreas Simulated Allocation Model-Scientific Registry for Transplant Recipients data, we simulated the allocation of 12 933 kidneys, excluding locally allocated and zero-mismatch kidneys. We assumed that each hour of delay decreased the probability of acceptance by 5% and that kidneys would be discarded after 20 hours of offers beyond the local level. We simulated offering kidneys simultaneously to small, medium-size, and large batches of centers. Increasing the batch size increased the percentage of kidneys accepted and shortened allocation times. Going from small to large batches increased the number of kidneys accepted from 10 085 (92%) to 10 802 (98%) for low-Kidney Donor Risk Index kidneys and from 1257 (65%) to 1737 (89%) for high-Kidney Donor Risk Index kidneys. The average number of offers that a center received each week was 10.1 for small batches and 16.8 for large batches. Simultaneously expiring offers might allow faster allocation and decrease the number of discards, while still maintaining an acceptable screening burden.

Geographic disparity in kidney transplantation under KAS.

The Kidney Allocation System fundamentally altered kidney allocation, causing a substantial increase in regional and national sharing that we hypothesized might impact geographic disparities. We measured geographic disparity in deceased donor kidney transplant (DDKT) rate under KAS (6/1/2015-12/1/2016), and compared that with pre-KAS (6/1/2013-12/3/2014). We modeled DSA-level DDKT rates with multilevel Poisson regression, adjusting for allocation factors under KAS. Using the model we calculated a novel, improved metric of geographic disparity: the median incidence rate ratio (MIRR) of transplant rate, a measure of DSA-level variation that accounts for patient casemix and is robust to outlier values. Under KAS, MIRR was 1.75 1.811.86 for adults, meaning that similar candidates across different DSAs have a median 1.81-fold difference in DDKT rate. The impact of geography was greater than the impact of factors emphasized by KAS: having an EPTS score ≤20% was associated with a 1.40-fold increase (IRR = 1.35 1.401.45 , P < .01) and a three-year dialysis vintage was associated with a 1.57-fold increase (IRR = 1.56 1.571.59 , P < .001) in transplant rate. For pediatric candidates, MIRR was even more pronounced, at 1.66 1.922.27 . There was no change in geographic disparities with KAS (P = .3). Despite extensive changes to kidney allocation under KAS, geography remains a primary determinant of access to DDKT.

Turn down for what? Patient outcomes associated with declining increased infectious risk kidneys.

Transplant candidates who accept a kidney labeled increased risk for disease transmission (IRD) accept a low risk of window period infection, yet those who decline must wait for another offer that might harbor other risks or never even come. To characterize survival benefit of accepting IRD kidneys, we used 2010-2014 Scientific Registry of Transplant Recipients data to identify 104 998 adult transplant candidates who were offered IRD kidneys that were eventually accepted by someone; the median (interquartile range) Kidney Donor Profile Index (KDPI) of these kidneys was 30 (16-49). We followed patients from the offer decision until death or end-of-study. After 5 years, only 31.0% of candidates who declined IRDs later received non-IRD deceased donor kidney transplants; the median KDPI of these non-IRD kidneys was 52, compared to 21 of the IRDs they had declined. After a brief risk period in the first 30 days following IRD acceptance (adjusted hazard ratio [aHR] accept vs decline: 1.22 2.063.49 , P = .008) (absolute mortality 0.8% vs. 0.4%), those who accepted IRDs were at 33% lower risk of death 1-6 months postdecision (aHR 0.50 0.670.90 , P = .006), and at 48% lower risk of death beyond 6 months postdecision (aHR 0.46 0.520.58 , P < .001). Accepting an IRD kidney was associated with substantial long-term survival benefit; providers should consider this benefit when counseling patients on IRD offer acceptance.