# The Risk of Transplant Failure With HLA Mismatch in First Adult Kidney Allografts From Deceased Donors

Background: Since the beginning of the technology, there has been active debate about the role of human leucocyte antigen (HLA) matching in kidney allograft survival. Recent studies have reported diminishing importance of HLA matching, which have, in turn, been challenged by reports that suggest the continuing importance of these loci. Given the controversies, we examined the effect of HLA compatibility on kidney allograft survival by studying all first adult kidney transplants in the United States from a deceased donor.

Methods: Using the United Network for Organ Sharing data, we identified first deceased donor kidney transplants between October 1, 1987, and December 31, 2013. Recipients were classified by their number of HLA mismatches. Cox multivariate regression analyses adjusting for recipient and donor transplant characteristics were performed to determine the impact of HLA compatibility on kidney allograft survival.

Results: Study cohort included 189 141 first adult kidney alone transplants, with a total of 994 558 years of kidney allograft follow-up time. Analyses adjusted for recipient and donor characteristics demonstrated a 13% higher risk (hazard ratio, 1.13; 95% confidence interval, 1.06-1.21) with 1 mismatch and a 64% higher risk (hazard ratio, 1.64, 95% confidence interval, 1.56-1.73) with 6 mismatches. Dividing the mismatch categories into 27 ordered permutations, and testing their 57 within mismatch category differences, demonstrated that all but 1 were equal, independent of locus.

Conclusions: A significant linear relationship of hazard ratios was associated with HLA mismatch and affects allograft survival even during the recent periods of increasing success in renal transplantation.

This largest, most contemporary analysis of HLA shows that HLA mismatching is associated with worse transplant outcomes, ordered by number of mismatches and without an independent effect of any specific locus, such as donor-recipient mismatching.

^{1} Phoenix Epidemiology and Clinical Research Branch, NIH, NIDDK, Phoenix, AZ.

^{2} Department of Transplantation Immunology, Institute of Immunology, University of Heidelberg, Heidelberg, Germany.

^{3} Mayo Clinic Hospital, Mayo Clinic, Phoenix, AZ.

^{4} Division of Nephrology, Mayo Clinic, Phoenix, AZ.

Received 13 July 2015. Revision received 12 November 2015.

Accepted 21 November 2015.

This work was supported in part by Health Resources and Services Administration contract 234-2005-370011C. The content is the responsibility of the authors alone and does not necessarily reflect the views or policies of the Department of Health and Human Services, nor does mention of trade names, commercial products, or organizations imply endorsement by the US Government.

The authors declare no conflict of interest.

R.C.W. is responsible for the design and performance of the statistical analysis, wrote the first draft, acts as corresponding author, and is responsible for the accuracy and integrity of the work. G.O. participated in the design of the analysis, revises the drafts, has final approval on the submission manuscript, and is responsible for the integrity of the work. C.M.G. participated in the design of the analysis and the creation of new variables and covariates, revises the drafts, has final approval on the submission of the article, and is responsible for the integrity of the work. E.J.W. participated in the design of the analysis, particularly the categories for induction and immunosuppression and covariates, revises the drafts, has final approval on the submission of the manuscript, and is responsible for the integrity of the work. H.C. provided the UNOS STAR files for the work, participated in the design of the analysis, particularly the categories for induction and immunosuppression and covariates, revises the drafts, has final approval on the submission of the article, and is responsible for the integrity of the work.

Correspondence: Robert C. Williams, PhD, NIH, NIDDK, PECRB 1550, East Indian School Road, Phoenix, AZ 85014. (williamsr@mail.nih.gov).

Supplemental digital content (SDC) is available for this article. Direct URL citations appear in the printed text, and links to the digital files are provided in the HTML text of this article on the journal's Web site (www.transplantjournal.com).

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With advances in surgical technique, knowledge about covariates that enhance kidney survival, and immune therapy, there has been a vigorous debate in the literature about the role of HLA in allograft survival.^{1-5} An analysis of 135 970 deceased donor transplants from 363 worldwide transplant centers comparing 2 decades (1985-1994, 1995-2004) showed that the number of HLA mismatches adversely influenced graft survival in both decades (relative risk per mismatch = 1.09 and 1.08, respectively, for both decades).^{6} More recent studies also support HLA matching as an important determinant of kidney allograft survival.^{7-10} However, an analysis of 33 433 deceased donor kidney transplants performed between 1994 and 1998 in the United States showed diminishing significance of HLA over that period.^{11} Similarly, Morales et al^{12} also suggested that HLA mismatch did not influence graft survival in a cohort of 2600 deceased donor kidney transplants in Spain. In addition, the change in allocation policy in the United States in 2005 to eliminate priority for HLA-B matching had no documented effect on graft survival.^{13} Current kidney allocation policy puts a premium on zero mismatch and does not account for the number of mismatches. Given the controversies surrounding the impact of HLA compatibility on kidney allograft survival, we examined all first adult kidney transplants in the United Network for Organ Sharing (UNOS) Standard Transplant Analysis and Research files database during years 1987 to 2013 to define a mathematical model that will allow us to quantify its effect.

## MATERIALS AND METHODS

This study was conducted using patient level data from the UNOS Standard Transplant Analysis and Research database. These data are collected by the Organ Procurement and Transplantation Network and other participating centers and laboratories using standard questionnaires and transmitted by the electronic transplant information application (UNet^{SM}). Their primary use is to transmit pretransplant and posttransplant data from transplant centers, histocompatibility laboratories, and organ procurement organizations.^{14} Data from first deceased donor kidney-only transplants in adults (age â‰¥18 years) stratified by UNOS region were included from October 1, 1987, to December 31, 2013 (**Table S1, SDC,** http://links.lww.com/TP/B245). Kidney allograft survival was censored at the last recorded examination or at death. Persons with a functioning kidney at death were included in the study. For living patients, kidney allograft failure date was determined by the start of renal replacement therapy.

### Variable Definitions

Table 1 defines the variables. To maximize the size of the sample, categorical variables were created with an unknown (U) value for missing or U values. Including the U category controls for possible bias from nonrandomly distributed missing data. The variables include recipient age in year quartiles (Q1, 18-40; Q2, >40-51; Q3, >51-60; and Q4, >60), donor age in year quartiles (Q1, â‰¤22; Q2, >22-38; Q3, >38-50; and Q4 > 50), era (from October 1, 1987, to December 31, 2013, divided into 5 equal periods: 1987-1993, 1994-1998, 1999-2003, 2004-2008, 2009-2013), sex (male, female), ethnicity (Hispanic, non-Hispanic white, non-Hispanic black, American Indian, Pacific Islander, Asian), cold ischemia time (â‰¤25 hours, >25 hours), panel-reactive antibody (â‰¤50%, >50%), education (high school or less, greater than high school, U), recipient body mass index (BMI) >30 (yes (Y), no (N), U), donor BMI greater than 30, (Y, N, U), recipient diabetes (Y, N, U), recipient working for income before transplant (Y, N, U), recipient drug treatment for chronic obstructive pulmonary disease at transplant (Y, N, U), recipient dialysis type (hemodialysis, peritoneal dialysis, no, U), drug induction therapy (divided into categorical variables based on the most common therapies: antithymocyte globulin, macomonab CD3, basiliximab, daclizumab, alemtuzumab, other drug, steroids only, no induction), immunosuppression maintenance therapies at discharge posttransplant derived from permutations of 6 groups of drugs as presented in **Table S2** (**SDC,** http://links.lww.com/TP/B245) and HLA mismatch (0, 1, 2, 3, 4, 5, 6). An additional categorical variable was created to contain the 27 permutations of mismatch at HLA-A, -B, and -DR with values 0, 1, and 2 at each locus. The locus-ordered triples are found in Table 3.

### Statistical Methods

All analyses were conducted using SAS Institute software version 9.3.^{15,16} The primary explanatory variable was the number of HLA mismatches (0-mismatch reference). Cox proportional hazards regression analyses were performed to study the association of degree of HLA mismatch and time to kidney allograft failure. We initially constructed a reduced model adjusting for a set of minimal covariates (recipient characteristics including age, sex, and transplant era), and then constructed the full model adjusting for all the other recipient and donor covariates seen in Table 1. Each variable was tested for the proportional hazard assumption by ordinary least-squared regression of the Schoenfeld residuals on kidney survival time.^{15} The goodness of fit of the full proportional hazards model was tested with the cumulative sums of the martingale-based residuals.^{17,18} We sorted the 189 141 records by risk score and divided them into 100 groups while using the 100th group as reference. Then we calculated the expected number of events using the martingale residuals, the *z* score for each group, and then tested the fit of the z score distribution to a N(0,1) normal distribution. Equality of the hazard ratios [HRs] of the within mismatch category permutations was tested by creating index variables (0,1) for each triple, including the 26 variables in the full model of the Cox regression with at least 1 mismatch, and then comparing all permutations within a category 1 by 1 using the TEST option in the SAS PROC PHREG procedure.^{15} Adjustment of the *P* values in the 57 comparison tests, with a Ï‡^{2} distribution and 1 degree of freedom for each, was calculated by the sequential Holm-Bonferroni procedure.^{19}

On inspection, the hazard ratios appeared to increase in stepwise fashion from 1 to 6 so a linear model was fitted to the mismatches and the hazard ratios with the SAS procedure TRANSREG using the algorithm

where the variable mismatch has values 1 to 6 and param represents the parameter estimate for the respective value of mismatch in the Cox regression. Contingency (Ï‡^{2}) tables were performed by standard methods. Median survival times were calculated from Kaplan-Meier curves.

## RESULTS

### Study Cohort

Between October 1, 1987, and December 31, 2013, the data included 189 141 first kidney-alone transplant records in adults with complete data who received an organ from a deceased donor with a total of 994 558 years of kidney allograft follow-up time. Projected median survival times were estimated by Kaplan-Meier curves for the combined data and when stratified by HLA mismatch (**Figures S1** and **S2, SDC,** http://links.lww.com/TP/B245). There were 74 049 female recipients and 115 092 male recipients with a mean age at transplant of 49.8 years. In the cohort, 43 656 persons died with a functioning kidney. Table 1 presents the distribution of the variables stratified by number of HLA mismatches. Among donors, there were 75 520 women and 113 621 men with a mean age of 36.6 years. Non-Hispanic whites constituted the largest category of recipientsâ€”96 647â€”one and a half times the number of the next largest group, non-Hispanic blacksâ€”55 897. Recipients with a high school education or less were the majority in the sample, whereas 52 454 persons were educated past high school. Hemodialysis was the most common renal replacement therapy.

### Test of the Goodness-of-Fit for the Full Cox Multivariate Proportional Hazards Model

We first tested the proportional hazard assumption for each of the 17 variables by performing an ordinary least squared regression of the Schoenfeld residuals for the respective variable on kidney survival time (**Table S3, SDC,** http://links.lww.com/TP/B245). The Î² coefficient was never larger than 0.0001 and R^{2} did not exceed 0.0016. The large size of the sample for each regression, 41 987, created very small standard errors. Therefore, Î² was significantly greater than 0.0 for a number of variables but the low R^{2} demonstrated a lack of correlation between the 2 variables in each instance.

We then divided the 189 141 records into 100 groups and sorted them by risk score after which we calculated the expected number of events in each group by using the Martingale residuals (**Table S4, SDC,** http://links.lww.com/TP/B245). The test for the goodness-of-fit of the full proportional hazards model is how well the distribution of calculated *z* scores for the observed and expected number of events fits a normal distribution with mean of 0 and standard deviation of 1. The mean of the 99 *z* values was âˆ’0.04 and was not significantly different from 0.0 by *t* test (*P* = 0.75); the standard deviation is 1.13, which, when the 95% empirical confidence interval [CI] is estimated with the bootstrap (b = 1000), it includes 1.0 (0.98, 1.26); the tests for normalityâ€”Shapiro-Wilk (*P* = 0.49), Kolmogorov-Smirnov (*P* = 0.15), Cramer-von Mises (*P* = 0.25), and Anderson-Darling (*P* = 0.25)â€”do not reject the null hypothesis of a normal distribution, whereas the histogram appears normal (**Figure S3, SDC,** http://links.lww.com/TP/B245).

### Impact of Number of HLA Mismatches on Kidney Allograft Survival

In the reduced model, which included age of the recipient, recipient sex, and transplant era as covariates (Figure 1, Table 2), HLA mismatch had a linear, adverse impact on kidney allograft survival with 1 mismatch having a 17% higher risk of allograft failure (HR, 1.17; 95% CI, 1.10-1.25) and those with 6 mismatches having almost twice the risk of allograft failure (HR, 1.98; 95% CI, 1.88-2.08). With additional adjustment for all the recipient and donor characteristics in the full model, the adverse impact of HLA mismatch on kidney allograft survival was attenuated but still present, with a 13% (HR, 1.13; 95% CI, 1.06-1.21) higher risk with 1 mismatch and a 64% (HR, 1.64; 95% CI, 1.56-1.73 ) higher risk with 6 mismatches (Table 2). A linear model was fitted to both sets of HRs and is seen in Figure 1: the reduced model has a Î² (slope) of 0.16 (95% CI, 0.15-0.17); the full model slope is 0.11 (95% CI, 0.09-0.12), implying that the impact of HLA mismatches is diminished by other variables, such as induction and maintenance immunosuppression.

To examine the individual effect of the 3 HLA loci independently, a categorical variable representing the 27 ordered triple permutations of mismatch at HLA-A, -B, and -DR was created and incorporated into the full Cox model with triple [0, 0, 0] as the reference (Table 3). All permutations were significantly different from the reference. However, triple [0, 0, 1] is only marginally significant. A general linear model was fitted to the 27 hazard ratios, weighted for the number of persons in each triple (Figure 2). The intercept was 1.04 (95% CI, 1.00-1.08) with a slope of 0.11 (95% CI, 0.09-0.12).

To test the equality of the effect of each permutation within mismatch categories 1 to 5, index variables were created for 26 triples with at least 1 mismatch and then incorporated into the full Cox Regression. There were 57 comparisons (**Table S5, SDC,** http://links.lww.com/TP/B245). After correction of the *P* values with the Holm-Bonferroni procedure, only 1 comparison in mismatch category 3 was statistically significant, triples [0, 1, 2] with HR = 1.57 (95% CI, 1.41-1.75) and [2, 1, 0] HR, 1.27 (95% CI, 1.18-1.36). The difference is between HLA-A and -DR, 0 mismatches at 1 locus and 2 mismatches at the other. The other 56 comparisons were not statistically significant after correction.

Table 4 presents the impact of each covariate on allograft failure in the full model. There is an array of significant small and large effects. When HRs of the 5-year transplant era variables are examined, it is apparent that the significant effect of HLA matching reported here takes place during a time of increasing survival of kidney allografts from 1987 to 2013. Recipient age showed a trend of increasing allograft survival by quartile, whereas donor age exhibited the opposite effect. Dividing the age of the recipient and donor into quartiles allowed us to elaborate on trends that have been reported in the literature for both strata. Table 2 illustrates that, as the recipient ages, the survival of the allograft increases in Q2 to Q4 with Q1 as the reference: 0.74, 0.65, and 0.61, all of them with *P* values less than 0.0001. Quartiles of donor age, however, demonstrate the opposite effect. The older the deceased donor, the poorer the outcome of the transplant: 1.11, 1.37, and 1.90, *P* < 0.0001 for each effect with the 95% CIs nonoverlapping. To test the interaction of the 2 variables, a new categorical variable with 16 levels was created and then incorporated into the full Cox regression with the combination of Q1 for recipient age and Q1 for donor age as the reference (Table 5).

## DISCUSSION

In a large cohort of adult US patients who received first kidney transplants from deceased donors, we observed significant linear adverse impact on allograft survival with each HLA mismatch. We also found that in mismatch categories 0, 1, and 2, it is the HLA difference that primarily determines allograft survival. In categories 3 to 6, however, the covariates, including induction and immunosuppression, have their main effects by lowering the slope of the fitted line to the HRs.

### Fit of the Cox Multivariate Proportional Hazards Model

With a Cox multivariate proportional hazard analysis that incorporates a very large sample and many covariates, such as we present here, it is very important to ascertain that the model is statistically appropriate. There is no relationship between the Schoenfeld residuals and the kidney survival time for 17 variables in the full model, which demonstrates that the proportional hazards assumption holds for each. Using Martingale residuals,^{17,18} we found that the observed and expected number of events, when incorporated into *z* variables, created the expected distribution for a well-specified proportional hazards model, that is, one with a mean of 0.0 and a standard deviation that approximates 1.0. This gives us confidence in our estimates of the hazard ratios and their 95% CIs.

### The Risk of Kidney Failure Is Linear With HLA Mismatch

A significant linear relationship was observed among the 6 values of the HLA mismatch and kidney allograft failure (Table 2, Figure 1) in both the reduced and full model Cox regressions. The magnitude of the slope of the line can be used to gauge the strength of HLA mismatches in kidney allograft failure; as the steepness of the slope increases, the risk attributed to HLA mismatch on allograft failure increases. In addition, comparing the slopes of the reduced and full models quantifies the effects of the additional covariates in the full model. In the reduced model, including only recipient age, sex, and transplantation era as covariates, the HR for kidney allograft failure increases by 0.16 for every unit of HLA mismatch. The full model, with the additional ethnic, clinical, induction, and immunosuppression covariates, reduces the HR for kidney allograft failure slope to 0.11 (Figure 1).

The 2 lines in Figure 1 reveal a great deal about the biology of HLA in the survival of adult, first kidney allografts from deceased donors.

First, the significant linear fit suggests that even when adjusted, the effect of HLA matching is still strong and additive; that is, each additional mismatch has the same effect in reducing the survival of the allograft. This observation runs counter to the dogma that holds HLA-DR and its mismatches to be more important than those at HLA-A and HLA-B. To test this, we divided the mismatch categories into their respective permutations and created triples of mismatch in HLA-A, -B, and -DR order and tested these in the full Cox regression (Table 3). The linear effect implies equality for all mismatches within a mismatch category independent of locus. We tested this hypothesis by creating index variables for each triple, incorporating 26 of these in the full Cox regression, and then testing all combinations of paired differences between triples in the same mismatch category. Only one of the comparisons was significant after correction for multiple tests, which is about what one would expect at random when performing 57 tests with a *P* value of 0.05. This strongly suggests that, within mismatch category, the effect of the mismatch is identical for each locus combination, which is what we predicted with the linear relationships presented in Figure 1. Further confirmation for equality of mismatch triples within category is found in Figure 2. When the 27 hazard ratios are incorporated into a linear regression, weighted by the number of observations in each triple, the identical line results for the full model in Figure 1 with a slope of 0.11 (*P* < 0.0001).

Secondly, the 2 fitted lines in Figure 1 reveal the relative weights of HLA mismatching and the moderating effects of additional variables. For mismatch categories 1 and 2, the 2 observed HRs, for the reduced and full models, are nearly identical, and their CIs overlap (Table 2) which suggests that it is primarily the HLA difference that contributes to the increase in risk of kidney allograft failure. In mismatch categories 3 to 6, the CIs do not overlap. It is here, in the larger mismatch categories, that the clinical covariates, induction and immunosuppression, have their largest effects in kidney allograft survival. This is illustrated in Figure 1 by the lower slope of the line.

Third, although the covariates moderate the effects of HLA mismatches, they do not remove them. The highly significant linear fit of the full Cox regression model remains. This reinforces the importance of HLA matching in kidney allograft transplantation, particularly in mismatch categories 1 and 2, in which modifying covariates have the smallest effect, and strongly implies that the policies that determine kidney allocation should appropriately weight HLA matching.

### Covariates Reflect Known Effects on Kidney Survival

Recipient ethnicity also affects allograft survival. The hazard ratios of non-Hispanic Blacks and Asians were 1.62 and 0.81, respectively. It has been reported that persons of African heritage in the United States have poorer kidney allograft survival than patients from other ethnic groups. There is much speculation as to the etiology of these differences.^{10,20-22} One cause that has been suggested is the difficulty of non-Hispanic black recipients to receive well-matched donor organs. Our data suggest that, in addition to the demonstrated effect of HLA, there are other important factors at play. Table 1 does show that the reference group (non-Hispanic whites) has better HLA matching when compared with non-Hispanic blacks. However, it is also true when comparing the reference with persons of Asian ancestry that Asians have more HLA mismatches in categories 4 to 6. With a similar pattern of HLA mismatch and contrasting outcomes, there must be additional determinants to explain this disparity in allograft survival.

These data testify to the success of the transplant community in increasing the survival of kidney allografts from 1987 to 2013. The transplant era variable showed a steady decrease in the HRs for the last 4 measured time intervals from 0.80, 0.67, 0.50, to 0.37. Therefore, despite the overall improvement in allograft survival in recent years, HLA mismatch remains a significant factor.

Important variables along with HLA mismatch in kidney allocation are the ages of recipient and donor. These 2 trends in survival, in the opposite direction, immediately raise the question of their interaction.^{23-25} In a subset of the UNOS data set, it has been reported that the beneficial effect of recipient age buffers the deleterious effect of donor age and that older recipients do well with older allografts.^{26} To investigate this in our larger data set, we created an interaction variable with 16 categories while using recipient Q1 with a donor Q1 as the reference (Table 5). For a recipient in the first quarter of age, there is an increasingly worse outcome with the increasing age of the donor with hazard ratios for Q2 to Q4 of 1.09, 1.27, and 1.61. Although the effect of better allograft survival is evident in recipient age quartiles Q2 to Q4, there is a trend within each for worse allograft survival with the increasing age of the deceased donor. For each quartile of recipient age, an allograft from the donor Q4 age group overwhelms the beneficial effect of recipient age and had its worst effect on survival when given to a young recipient. A balance point of the 2 opposite trends in the ages of recipient and donor comes in combination Q2 of the recipient and Q3 of the donor for which the hazard ratio is not significantly different from 1.0 when compared with the reference.

### Strengths of the Study

(1) We test the appropriateness of the Cox multivariate proportional hazards model for our data and demonstrate that it is properly specified.

(2) We have 189 141 allografts and 994 557 years of survival time in the Cox model with many important covariates.

(3) We found that the hazard ratios are significantly linear for HLA mismatches. Each has the same effect, irrespective of locus, and the effect on survival is additive. This runs counter to the accepted opinion that HLA-DR is the most important. When one looks at all of the data, the effect on survival is the same for each 1 increment of mismatch.

(4) Now that we have demonstrated a linear relationship to the hazard ratios, we can use the lines, their slopes, to measure the difference between the reduced and full Cox models. This is a mathematical measure of the improvement in survival that is achieved by adding covariates, such as induction and immunosuppression at discharge.

(5) In addition to mismatch category 0, we show that categories 1 and 2 are similar in that it is primarily HLA that plays the role in allograft survival. This has major implications for the allocation of kidneys and also for the clinical approach that is taken for induction and immunosuppression.

(6) Our sample size increases the power of the analysis and narrows the confidence limits of known and published significant covariate effects, such as the increasing survival of allograft with recipient age and the decreasing survival with donor age. We also further refine the interaction of the age variables.

(7) There is novelty, we believe, in our construction of the categories for immunosuppression at the time of discharge and our employment of this and the induction variable in the Cox model.

### Weaknesses of the Study

A weakness is the inclusion of immunosuppression and maintenance therapy only at discharge. A consideration of a time-dependent covariate that takes into consideration the duration of therapy and change in therapies would be desirable. However, the current state of the data does not allow the construction of such a model.

A potential further weakness is the inclusion of missing values in a subset of categorical variables in the full Cox model. Variables recipient age, donor age, recipient sex, 5-year intervals, ethnicity, induction, immunosuppression, and HLA mismatch have no missing values. Therefore, the reduced model had none. Nine additional covariates in the full Cox model have an U value (**Table S6, SDC,** http://links.lww.com/TP/B245). By including the missing values, we are assuming that the distribution of data among the missing cohort would be the same as those observed in the nonmissing one. There is no way to demonstrate this in practice; including the missing values can produce biased estimates of the hazard ratios. However, we are dealing in very large numbers, a total of 189 141 transplants, and the idea that the missing strata approximate the structure of the large number of nonmissing values is not an unreasonable one. For instance, 5 of the U values, cold ischemia time, peak panel-reactive antibody, recipient education level, recipient BMI, and drug treatment for chronic obstructive pulmonary disease, have hazard ratios not significantly different from the reference (**Table S6, SDC,** http://links.lww.com/TP/B245). The remaining 4 variables have HRs that mirror to some extent one of the nonmissing categories. We take comfort in the fact that our HRs for the nonmissing values in the covariates are similar in trend and magnitude for those that have occurred in the literature, which suggests that if there is bias, it is not large.

## CONCLUSIONS

A significant linear relationship of hazard ratios was associated with HLA mismatch and affects allograft survival even during the recent periods of increasing success in renal transplantation. These data also reinforce the importance of optimizing HLA matching to further improve survival in renal allografts in the future.

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