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J Am Soc Nephrol 14:2967-2974, 2003
© 2003 American Society of Nephrology

CLINICAL SCIENCE

Nomogram for Predicting the Likelihood of Delayed Graft Function in Adult Cadaveric Renal Transplant Recipients

William D. Irish*, David A. McCollum{dagger}, Raymond J. Tesi{ddagger}, Art B. Owen§, Daniel C. Brennan||, Jane E. Bailly{ddagger} and Mark A. Schnitzler||

*Research Triangle Institute, Research Triangle Park, NC; {dagger}Cincinnati Transplant Institute, Cincinnati, OH; {ddagger}SangStat Medical Corporation, Fremont, CA; §Stanford University, Palo Alto, CA; and ||Washington University, St. Louis, MO, United States.

Correspondence to: Dr. William D. Irish, Research Triangle Institute, 3040 Cornwallis Road, Research Triangle Park, NC 27709. Phone: 919-541-6452; Fax: 919-541-7222;


   Abstract
Top
 Abstract
Introduction
 Patients and Methods
 Results
 Discussion
 References
 
ABSTRACT. Delayed graft function (DGF) is the need for dialysis in the first week after transplantation. Studied were risk factors for DGF in adult (age >=16 yr) cadaveric renal transplant recipients by means of a multivariable modeling procedure. Only donor and recipient factors known before transplantation were chosen so that the probabilities of DGF could be calculated before transplantation and appropriate preventative measures taken. Data on 19,706 recipients of cadaveric allografts were obtained from the United States Renal Data System registry (1995 to 1998). Graft losses within the first 24 h after surgery were excluded from the analysis (n = 89). Patients whose DGF information was missing or unknown (n = 2820) and patients missing one or more candidate predictors (n = 2951) were also excluded. By means of a multivariable logistic regression analysis, factors contributing to DGF in the remaining 13,846 patients were identified. After validating the logistic regression model, a nomogram was developed as a tool for identifying patients at risk for DGF. The incidence of DGF was 23.7%. Sixteen independent donor or recipient risk factors were found to predict DGF. A nomogram quantifying the relative contribution of each risk factor was created. This index can be used to calculate the risk of DGF for an individual by adding the points associated with each risk factor. The nomogram provides a useful tool for developing a pretransplantation index of the likelihood of DGF occurrence. With this index in hand, better informed treatment and allocation decisions can be made. E-mail: wirish@rti.org


   Introduction
Top
 Abstract
 Introduction
Patients and Methods
 Results
 Discussion
 References
 
Historically, acute rejection (AR) was the principal clinical challenge after renal transplantation and a primary determinant of transplantation outcome. With the introduction of modern immunosuppressive regimens, the frequency of AR episodes after cadaveric kidney transplantation has been reported at less than 20% (1,2). Increasing attention is being focused on a more common obstacle to successful renal transplantation: delayed graft function (DGF). DGF of a renal allograft has been recently cited to occur in approximately 25% of primary cadaveric renal transplantations in the United States (3), although the reported center-specific incidence ranges broadly. DGF occurs in the immediate posttransplantation period and results in oliguria requiring dialysis. Although the clinical severity of DGF varies, it is defined functionally as the need for dialysis in the first 7 d after transplantation (3–5).

The etiology of DGF is not well understood but is believed to have both immunologic and nonimmunologic components. Ischemia/reperfusion injury of an allograft during the transplantation procedure causes a cascade of molecular events, including the activation of endothelial adhesion molecules and cytokine release (6). Leukocyte adherence/diapedesis and lymphocyte activation cause apoptosis, inflammation, and tissue damage resulting in organ dysfunction (6,7). There is evidence that these immunologic events can upregulate immune response and may increase organ alloreactivity, resulting in a greater probability of AR (6,8).

The detrimental clinical effect of DGF after kidney transplantation is well documented (3–5,7). Although the precise contribution of DGF to graft loss is debated, many studies have identified DGF as a predisposing factor for AR and decreased graft survival. The exact relationship between DGF and AR is controversial. Several studies suggest that in the absence of AR, DGF has no effect on graft survival (9,10). Others have shown that DGF and AR independently portend poor graft survival in both children and adults (3–5,11–13). The independent contribution of DGF to graft outcome is important because it indicates that eliminating only AR will not assure optimal graft survival. In fact, although renal AR incidence has decreased dramatically over the past 10 yr, DGF rates have decreased from about 29% to 23% (14).

DGF also has a substantial economic cost that is the result of prolonged patient hospitalization and the increased cost of patient management (dialysis, diagnostic radiology, needle core biopsies, immunosuppressive drug monitoring) (10,15–17). In a retrospective study, 34 (20%) of 170 patients developed DGF (16). The hospital stays for these patients averaged 10 d longer than those of patients with early graft function (16). Given the financial penalty attached to grafts with delayed versus immediate function, interventions that reduce the incidence or prevent development of DGF should be cost-effective.

Over the past decade, the criteria for acceptable donor kidneys have expanded to accommodate a rising demand for transplantation. High-risk donors include those younger than 5 yr or older than 55 yr, donors with significant comorbidities such as hypertension, vascular disease, or diabetes mellitus, and nonheart-beating donors (18,19). The use of higher-risk donors undoubtedly provides life-saving organs to critically ill patients. However, there has been a commensurate increase in the incidence of DGF in renal transplantation with the use of marginal donors (20). Clearly, a balance must be struck by minimizing the occurrence of DGF without rejecting marginal donor organs with reasonable prognoses for survival. One approach is to target patients at risk for DGF and administer appropriate preventative interventions. In a recent study of 241 patients, a donor scoring system was developed on the basis of seven donor variables to assist in the allocation of marginal organs (21). In the study presented here, we used the data available from more than 13,846 adult cadaveric renal transplant recipients recorded in the United States Renal Data System (USRDS) to develop an index, or nomogram, that quantifies the likelihood of DGF after renal transplantation by using both donor and recipient factors known before transplantation. This nomogram can be used to determine optimal allocation strategies and direct interventions to prevent or ameliorate DGF.


   Patients and Methods
Top
 Abstract
 Introduction
 Patients and Methods
Results
 Discussion
 References
 
Potential risk factors for DGF (defined as the necessity for dialysis within the first 7 days after renal transplantation) included donor and recipient factors known before transplantation and common to all transplantation centers. Donor variables included age, gender, primary cause of death, history of hypertension, duration of cold ischemia time (CIT; h), terminal serum creatinine (mg/dl), and nonheart-beating donor. Recipient variables included age, race, gender, primary indication for renal transplantation, the presence or absence of multiple organ transplant (kidney and nonkidney organ), previous transplantation or blood transfusion, preemptive transplantation, the titer of serum panel-reactive antibody (peak PRA), and the extent of HLA matching.

CIT was defined as the time elapsed from aortic cross-clamping in the donor to portal or arterial revascularization in the recipient. The extent of HLA matching was based on the total number of mismatches at the HLA-A, -B, and -DR loci. Mismatches were calculated by a serologic equivalency algorithm developed by the United Network for Organ Sharing. Pretransplantation blood transfusion was defined as the number of blood components (red blood cells, fresh frozen plasma, and/or platelets) transfused before the transplantation operation.

Study Population
Data on 19,706 adult (aged >=16 yr) recipients of cadaveric renal allografts over a 4-yr transplantation period (1995 to 1998) were obtained from the USRDS registry (22). The USRDS is a national data system that collects, analyzes, and distributes information about end-stage renal disease and renal transplantation. There were 89 (<1%) patients whose grafts failed within 24 h of the transplantation operation. These patients were excluded from further analysis. Also excluded were 2820 patients (14.3%) in whom DGF could not be determined and 2951 patients (15.0%) missing at least one candidate predictor. The study population therefore consisted of 13,846 adult renal transplant recipients.

Statistical Analyses
Continuous data are presented as the mean ± SD or median and range, and categorical data as proportions. Risk factors for DGF were studied by a multivariable binary logistic regression modeling technique (23–25). Because the uncritical application of modeling techniques can result in models that poorly fit the data set or inaccurately predict outcomes on new subjects, measures of model adequacy were obtained (23,25). These included measures on lack of fit (additivity and linearity assumptions) and predictive accuracy.

To test the assumption that the quantitative covariates (e.g., donor age) are linearly related to the log-odds of response in the binary logistic regression model, we used generalized additive models (GAM) (24). GAM are flexible statistical methods that can be used to identify and characterize the effect of potential prognostic factors on an outcome variable. These methods extend the traditional linear statistical models (e.g., multiple linear regression). They can be applied in a setting where a linear or generalized linear model is typically used. These settings include standard continuous response regression, categorical or ordinal categorical response date, count data, survival data, and time series (24). Graphical representations of the GAM, often termed "action profiles," were used to investigate the functional form of these quantitative covariates (i.e., nonlinear trends, discrete effects).

In the logistic regression model, the effects of the predictors are assumed to be additive (i.e., lack interaction). Interactions were tested and described by adding cross-product terms to the model. Only two-way interactions were tested. Because the potential number of cross-product terms may be large, factors tested for additivity were specified before examining the data. These included previous transplantations by peak PRA, recipient race by recipient/donor gender match, peak PRA by previous blood transfusion, extent of HLA matching by recipient race, and age of the recipient by primary renal disease. The likelihood ratio statistic was used to test the global null hypothesis that the two-way interaction effects are equal to zero (23).

The predictive accuracy of the model was assessed by a concordance c index. The c index estimates the probability of concordance between predicted and observed responses. A value of 0.5 indicates no predictive discrimination and a value of one indicates perfect separation of patients with different outcomes. To obtain an unbiased estimate of the c index, an external validation process was performed using data from the Scientific Renal Transplant Registry (SRTR). Data were obtained for transplantations performed in the United States between 1999 and 2002. The predictive accuracy of the model was graphically displayed by the receiver operating characteristic (ROC) curve, whereby the c index is identical to the area under the ROC curve (25,26). The ROC curve is a plot of sensitivity versus 1 - specificity for different threshold probabilities of DGF. The threshold probabilities are arbitrary cutpoints used to classify patients as DGF and non-DGF. Sensitivity is defined as the probability of the model predicting a patient will have DGF, given the patient has DGF. The specificity is defined as the probability of the model predicting a patient will not have DGF, given that the patient does not have DGF.

After externally validating the logistic regression model, a nomogram was developed as a tool for identifying patients at risk for developing DGF. The nomogram provides a graphical representation of the effect of each covariate in the model. The nomogram can be used to calculate the risk of DGF for an individual patient by adding the points associated with each risk factor.

All statistical modeling procedures were performed by SAS for Windows software, except for the generalized additive regression analysis. This was performed by S-Plus for Windows software with the S-Plus GAM function (24).


   Results
Top
 Abstract
 Introduction
 Patients and Methods
 Results
Discussion
 References
 
Donor and Recipient Characteristics
Data on 13,846 transplantations were available for analysis. Recipient and donor characteristics are presented in Table 1. The mean age of the recipient at time of transplantation was 45.7 ± 12.8 yr, 25.5% were black, and 60.7% were men. In 27.5% of the recipients, the primary indication for renal transplantation was diabetes and for 17.6% was hypertension. Nearly 11% were recipients of multiple-organ transplants, and 13.9% had undergone previous transplantation. More than 90% were on dialysis before transplantation. The mean peak PRA was 14.2 ± 25.3%. There were 1122 six-antigen mismatches (8.1%) at the HLA-A, -B, and -DR loci (mean ± SD, 3.29 ± 1.71).


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  		Table 1. Recipient and donor characteristics at time of transplantation
 
The mean age of the donor was 34.1 ± 16.9 yr, and 60.0% were men. The most frequent cause of death was head trauma (51.9%), followed by cerebrovascular/stroke (36.9%) and anoxia (8.8%). Sixteen percent (16.0%) of the donors had a history of hypertension. In 1.1% of the donors, the heart was not beating. The mean terminal serum creatinine was 1.23 ± 1.94 mg/dl. The mean duration of CIT was 20.4 ± 8.5 h.

Model Development
The action profile for donor age and for CIT are presented in Figure 1 and Figure 2, respectively. The plots suggest a piecewise linear relationship for donor age and a linear relationship for CIT. For donor age, the risk of DGF increases linearly after approximately 13 yr of age, but remains relatively constant for donor ages less than 13 yr. The wide confidence interval for small and large values of donor age (age <13 yr and age >70 yr) indicates the variability of the donor age effect for these ranges of values. Similarly, the wide confidence interval for large values of CIT (CIT > 40 h) indicates the variability of CIT effect for values greater than 40 h. These areas of high variability correspond to the rarity of patients with low and high values of the respective covariates.



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  		Figure 1. Action profiles for donor age (yr). The dashed lines above and below the curves represent twice the standard errors of the estimated curve. Donor age displays no significant relationship with DGF risk until age 13. Beyond age 13 a linear relationship is apparent.

 


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  		Figure 2. Action profile for cold ischemia time (h). The dashed lines above and below the curves represent twice the standard errors of the estimated curve. Although CIT shows a slightly kinked relationship with DGF risk, the curve does not significantly differ from linearity.

 
The likelihood ratio {chi}2 statistic was used to test the additivity assumption. None of the two-way interactions defined a priori was significantly associated with DGF (likelihood ratio statistic, 14.533; P = 0.409 with 14 degrees of freedom). However, an a posteriori test for additivity was performed, again by the likelihood ratio {chi}2 statistic. Two-way interactions were found to be significant: pretransplantation dialysis by race and pretransplantation dialysis by single-organ transplant.

The results of the final model are presented in Table 2. There were 16 donor or recipient variables and 2 two-way interactions that were found to be significantly associated with DGF. The most significant was a history of pretransplantation dialysis, followed by use of a nonheart-beating donor and recipient of a single organ transplant. However, the relative effect of pretransplantation dialysis is modified by the effect of recipient race and single organ transplant. For example, black recipients who received preemptive transplants are nearly three times more likely to develop DGF than nonblack recipients who received preemptive transplants (odds ratio [OR], 2.807). This is in contrast to black versus nonblack recipients who received pretransplantation dialysis (OR, 1.383). However, the OR for single versus multiple-organ transplant is 1.005 among patients who received preemptive transplantation, whereas the OR is 2.208 among patients who received pretransplantation dialysis.


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  		Table 2. Results of the multivariable logistic regression analysis of delayed graft functiona
 
Validation
We used the final model to develop an ROC curve that used data on 20,684 kidney transplants performed in the United States between 1999 and 2002 provided to us by the SRTR (Figure 3). The ROC curve lies above the line of unity signifying the predictive accuracy of the model. The c index (or area under the ROC curve) is 0.70, which indicates a high degree of discrimination. It is interesting to note that the results of this external validation, which used data not included in the model estimation procedure, were nearly identical to the results of an internal validation (c index = 0.71), by using the data used for model estimation. This suggests that little has changed in the determinants of DGF between the late 1990s and early 2000s.



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  		Figure 3. Predictive accuracy of the delayed graft function (DGF) model-receiver operating characteristic (ROC) curve. The predictive accuracy of the DGF model was validated by use of data from cadaveric renal transplant recipients drawn from the Scientific Renal Transplant Registry (SRTR). The ROC curve shows considerable ability of the index to correctly classify DGF at varying levels of risk. The concordance c statistic value for the validation of the model in these data was 0.70.

 
Nomogram
The 16 donor or recipient variables were then used to develop a functional nomogram for predicting the likelihood of DGF (Figure 4). Specific points relative to the effect on DGF were assigned to the 11 categorical variables. A point scale was used to assign points to the five continuous variables. The points were derived from a direct transformation of the parameter estimates presented in Table 2. These estimates were rescaled or normalized so that 1 h of CIT equals one point. Of the continuous variables, donor age, CIT, and donor serum creatinine accrue the most points, with peak PRA and HLA contributing relatively little toward the likelihood of developing DGF. A point score of approximately 120 correlates with the current average rate of DGF of approximately 25%. A point score of about 145 predicts a 50% chance of DGF. To put the nomogram into clinical perspective, most cadaveric recipients will have received pretransplantation dialysis (40 points), had an average CIT of 20 h (20 points), had a donor of 50 yr of age (16 points), an HLA mismatch of 3 (6 points), and received a transfusion before transplantation (4 points). If there are no additional penalties, the recipient would be considered to be at low risk, with a total of 86 points, or approximately a 10% risk of developing DGF. This value is comparable to the 6% rate of DGF found in recipients of living donor grafts (14).



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  		Figure 4. Nomogram for estimating the risk of delayed graft function (DGF) in adult renal transplant recipients. HLAmm, HLA mismatch; S. Cr., serum creatinine; PRA, panel-reactive antibody; CIT, cold ischemia time; RR, recipient race; PID, pretransplantation dialysis; DCOD, donor cause of death; SOT, single-organ transplant.

 

   Discussion
Top
 Abstract
 Introduction
 Patients and Methods
 Results
 Discussion
References
 
Increasing attention is focused on resource allocation in the health care system. The quantification of risk factors relative to resource use will become imperative as resources decline in managed health care organizations. Resource allocation in solid organ transplants is more complicated than in many other areas of medicine because of the requirement for a scarce resource, the transplanted organ, and the high cost of each procedure. Renal transplants differ from heart and liver transplants because an effective therapy, dialysis, is widely available and is the standard of care for end-stage renal disease. Therefore, patients and health care providers have to make choices to optimize both the efficacy and safety of patient management.

Risk assessment is increasingly used in the medical community as a tool to inform protocol decisions and resource allocation. DGF deals a double blow by incurring both clinical and economic penalties and therefore merits a formal risk analysis. Many donor- and recipient-specific risk factors for DGF in renal transplantation have previously been identified, including both immunologic (e.g. poor HLA matching, peak PRA, absence of T cell antibody induction therapy, female donor gender) and nonimmunologic (donor age >=50 yr, cause of death, prolonged CIT, African American recipient ethnicity, body mass index, recipient hypotension) origin (4,11,13,20,27). The recent development of a donor scoring system that was based on a small cohort of patients attempted to quantify some of these risks to determine early (day 30) graft function and assist in marginal donor allocation (21). The nomogram developed in the study presented here represents an additional contribution to risk analysis by quantifying a large number of risk factors, each of which demonstrated predictive discrimination and independently correlated with DGF. We have shown that by using this nomogram, the risk of DGF can be predicted with a high degree of certainty by using only information available at the time of transplantation.

A recent article presented a similar scoring system for risk of DGF developed from a two-center study of 241 patients (21). The focus of this study was to identify characteristics of the donor that affected the risk of DGF. The number of factors accounted for in this study was hindered by the donor-directed focus combined with the small size of the study population. The work presented here expands on this greatly: we use a much larger patient population with a varied recipient/donor case mix. The objective was to identify risk factors for DGF known at transplantation regardless of source and common to all transplantation centers. As such, our model presents a relatively rich set of donor and recipient factors predicting DGF risk.

There are limitations to our study. Most prominently, the risk factors studied were limited to data available in the USRDS registry. Notable exclusions that may influence DGF risk include recipient body mass index and type of dialysis, and additional expanded criteria characteristics of the donor. Clearly the clinician may have additional information available to modify his or her assessment of a patient’s risk of developing DGF. Furthermore, our model was estimated by using data from the late 1990s. Although our model validation used data as recent as 2002, it is certainly possibly that the risk of DGF will change over time. In addition, future research may augment the results presented here to include additional information and adjust the model if the risks of DGF change over time.

Predicting a patient’s risk of developing DGF only has utility if interventions can be made to alter that risk. Once the risk of DGF is quantified, the clinician has three options: treat DGF when it occurs; abandon the transplantation; or make modifications to the transplantation protocol that decrease the risk. Current medical practice has adopted the first option and routinely treats DGF only once it is diagnosed. Unfortunately, this may confer too little clinical benefit, too late. Abandoning the transplantation is not practical given the current and growing disparity between the number of patients waiting for a transplant and the number of available donor organs.

Option 3, modifying the transplantation protocol, can be explored in three ways. First, the clinician may be able to control CIT, which significantly contributes to the risk of DGF in the current model. We have also previously shown the importance of CIT in the cost of transplantation (28). Limiting DGF by swift, efficient organ allocations and emergent implantation can have many benefits. Second, the risk of DGF can be lowered by selecting a recipient who will contribute fewer points to the risk score. For instance, eliminating a patient with diabetes (5 points) with a PRA of 60% (10 points) who is receiving his second transplant (10 points) will decrease the risk score by 25 points, which will lower the risk of DGF by 10% to 40%. It is noteworthy that organ allocation in the United States is currently based on criteria that have little (HLA mismatch) or no (e.g., waiting list time) effect on the risk of DGF. The nomogram will have greatest empirical value as a tool for patient management rather than as a means of excluding marginal donors or high-risk recipients.

The third and most flexible way to intervene when there is a high risk of DGF is to modify the transplantation protocol to limit ischemia/reperfusion injury. Strategies include choice of organ preservation solution, maintenance of an adequate intravascular volume, use of osmotic diuretics, use of the vasodilators verapamil and dopamine, and delaying nephrotoxic agents such as calcineurin inhibitors. The identification of patients who would most likely benefit from these or other interventions is the most practical application of the DGF index. By use of this algorithm, the optimal transplantation protocol in terms of potency, convenience, and cost can be adapted for the individual patient.

The renal transplantation community is now challenged to approach DGF with the same intensity given AR. Although AR incidence has not been eliminated, it has decreased dramatically in the last decade. We believe similar improvements in the incidence of DGF will result in better immunologic (improved graft survival) and physiologic (better renal function) outcomes. Pretransplantation prediction of DGF via the nomogram can substantially affect this goal by informing patient and organ management decisions.


   Acknowledgments
 
Data reported here have been supplied by the USRDS. The interpretation and reporting of these data are the responsibility of the authors and in no way should be seen as an official policy or interpretation of the U.S. government. Data reported here from the Scientific Renal Transplant Registry (SRTR) have been supplied by United Network for Organ Sharing and URREA under contract with HHS. The authors alone are responsible for reporting and interpreting of these data. Supported in part by a grant from the National Institute of Diabetes, Digestive, and Kidney Diseases (K25-DK-02916).


   References
Top
 Abstract
 Introduction
 Patients and Methods
 Results
 Discussion
 References
 

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Received for publication September 18, 2002. Accepted for publication August 16, 2003.




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