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.
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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