Nomograms for Predicting Graft Function and Survival in Living Donor Kidney Transplantation Based on the UNOS Registry

Materials and Methods 

Data for a total of 20,085 living donor renal transplant cases were obtained from the UNOS registry for 2000 to 2003. Three nomograms were designed based on Organ Procurement and Transplantation Network data as of July 22, 2004. The first nomogram predicted 1-year eGFR (ml per minute per 1.73 m2) based on information known about donors and recipients at transplantation. The second nomogram predicted 5-year graft survival based on the same information. The third nomogram predicted 5-year graft survival taking into account additional information available by 6 months after transplantation. The predictor variables in the nomograms were selected after literature review of donor and recipient factors shown to be predictors of kidney transplantation outcomes.1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Pretransplant recipient variables included age, gender, BMI (kg/m2), race, cause of renal failure, induction therapy, and use of mycophenolate mofetil, sirolimus and/or calcineurin inhibitors. Pretransplant donor predictors included BMI (kg/m2), creatinine (mg/dl), HLA mismatch, age, gender, race, donor/recipient relationship and type of procurement procedure (open vs laparoscopic). For the 6-month posttransplant prediction of 5-year graft survival all of the pretransplant donor and recipient predictors were the same as previously noted. Additional predictors for this nomogram include delayed graft function, any treated rejection episode in 6 months and the 6-month eGFR (ml per minute per 1.73 m2).

Continuous data were summarized as the mean ± SD or median with range, and categorical data as proportions. The R software package version 2.5.1 (Bell Laboratories, Murray Hill, New Jersey) was used for the construction of the models. Nomograms were constructed using Cox or linear multivariable regression models, depending on the outcome variable.11 Ordinal and continuous variables were fit using restricted cubic splines to relax the linearity assumptions. No variable selection was performed statistically. Each variable was assigned a scale of points according to prognostic significance, which ranged from 0 to 100. The point values for individual cases added up to give a total points value. The total sum thus calculated was correlated to the predicted estimated GFR or 5-year graft survival probability of each individual case. All nomograms were internally validated with 10-fold cross-validation to correct for optimism. R-square, the coefficient determination, was calculated for the linear regression model that predicted a continuous outcome (1-year eGFR). The concordance index was used as a discrimination measure for the 2 time-to-event nomograms (5-year graft survival). The concordance index estimates the probability a patient who experiences an event first has a higher predicted probability of the event. It is scaled from 0.5 to 1 with a value of 0.5 indicating no predictive discrimination and a value of 1 indicating perfect separation of patients with different outcomes. Calibration plots were constructed for all nomograms by plotting the observed proportions against the predicted probabilities. They were assessed visually for all nomograms.

Results 

Descriptive statistics for recipient and donor characteristics in this cohort are shown in table 1. Data on a total of 20,085 live donor transplantations were available for analysis. As noted in table 1 data are missing for various demographic variables. For the construction of the nomograms missing values in all predictors were imputed using the MICE package in R. Mean age of donors and recipients at transplantation was 40 ± 11 and 46 ± 14 years, respectively, with 59% (11,806) of donors and 41% (8,320) of recipients being female. In terms of donor-recipient gender matching 35% (7,127) of the kidney transplantations involved a female donor and male recipient. African-Americans accounted for 14% (2,767) and 15% (2,976) of donors and recipients, respectively. The cause of end stage renal disease in the recipients was glomerulonephritis in 24% (4,779) and diabetes in 15% (3,062) of the patients. There were 3 or fewer HLA mismatches at the HLA-A, HLA-B and HLA-DR loci in 65% (12,887) of the transplants with a mean recipient/donor HLA mismatch of 3.02.

Table 1. Recipient and donor characteristics for living donor renal transplants from the UNOS registry

	Recipient characteristics (at transplant)
	No. female (%)	8,320 (41)
	Mean pt age ± SD	46±14
	Mean inches ht ± SD⁎	67.3±4.3
	Mean lbs wt ± SD⁎	173±41
	Mean kg/m2 BMI ± SD⁎	26.8±5.4
	Mean m2 BSA ± SD⁎	1.95±0.28
	No. race (%):†
	White	13,470 (67)
	Black	2,976 (15)
	Other	3,548 (18)
	No. primary diagnosis (%):‡
	Glomerulonephritis	4,779 (24)
	Diabetes	3,062 (15)
	Re-transplant	135 (0.68)
	Other	11,816 (60)
	Recipient/donor matching
	Mean HLA mismatch level ± SD§	3.02±1.7
	No. level (%):
	0	2,148 (11)
	1	1,262 (6.3)
	2	3,738 (19)
	3	5,739 (29)
	4	2,500 (13)
	5	2,956 (15)
	6	1,538 (7.7)
	Donor characteristics
	No. female (%)	11,806 (59)
	Mean pt age ± SD∥	40±11
	Mean inches ht ± SD¶	67.0±4.0
	Mean lbs wt ± SD¶	171±36
	Mean kg/m2 BMI ± SD¶	26.9±4.7
	Mean m2 BSA ± SD¶	1.93±0.24
	No. race (%):
	White	13,876 (69)
	Black	2,767 (14)
	Other	3,442 (17)
	Mean mg/dl creatinine ± SD⁎⁎	0.9±0.5
	No. donor procedure (%):††
	Laparoscopic	12,997 (65)
	Open	6,998 (35)
	Recipient posttransplant outcomes
	No. dialysis in first wk after transplant (%)‡‡	957 (4.8)
	Mean GFR (MDRD) 6 mos after transplant (ml/min/1.73 m2) ± SD§§	56.5±18
	No. treated for rejection within 1st 6 mos (%)∥∥	1,861 (13)
	No. grafts failed at last followup (%)	2,300 (11)

⁎ Data available for 19,175 patients. † Data available for 19,994 patients. ‡ Data available for 19,792 patients. § Data available for 19,881 patients. ∥ Data available for 20,078 patients. ¶ Data available for 16,846 patients. ⁎⁎ Data available for 18,805 patients. †† Data available for 19,995 patients. ‡‡ Data available for 20,083 patients. §§ Data available for 15,194 patients. ∥∥ Data available for 14,817 patients.

Nomograms with their calibration curves were created as shown in Figure 1, Figure 2, Figure 3. The nomogram predicting eGFR had an r-square value of 0.13 (fig. 1). Based on the internal calibration plot in figure 1, B it worked best when predicting eGFR values between 50 and 70 ml per minute per 1.73 m2. The nomograms predicting 5-year graft survival were also internally validated. The concordance index for the nomogram predicting 5-year graft survival using pretransplant information was 0.71 and for the nomogram predicting 5-year graft survival using additional data at 6 months after transplant was 0.78. Calibration plots suggest good accuracy for these nomograms.

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Figure 1. A, nomogram predicting 1-year eGFR based on pretransplant information. Instructions: first row (Points) is point assignment for each variable. Rows 2 to 19 represent variables included in model. For each donor-recipient pair each variable is assigned point value (uppermost scale, points). Vertical line is made between appropriate variable value and points line. Assigned points for all variables are summed and total is found in row 20 (Total Points). Once total is located vertical line is made between total points and final row 21 (1-Year predicted eGFR). W, white. B, black. O, other. D, diabetes. G, glomerulonephritis. R, re-transplant. B, calibration curve for internal validation. Broken line represents performance of ideal nomogram in which predicted outcome corresponds perfectly with actual ones. Solid line represents performance of constructed nomogram. Bootstrap corrected r-square of nomogram was 0.131.

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Figure 2. A, nomogram predicting 5-year graft survival probability based on pretransplant information. Instructions: first row (Points) is point assignment for each variable. Rows 2 to 19 represent variables included in model. For each donor-recipient pair each variable is assigned point value (uppermost scale, points). Vertical line is made between appropriate variable value and points line. Assigned points for all variables are summed and total is found in row 20 (Total Points). Once total is located vertical line is made between total points and final row 21 (5-Year Graft Survival Probability). W, white. B, black. O, other. D, diabetes. G, glomerulonephritis. R, re-transplant. B, calibration curve for internal validation. Diagonal line represents performance of ideal nomogram in which predicted outcome corresponds perfectly with actual ones. Line with vertical boxes represents performance of constructed nomogram. Vertical boxes indicate 95% confidence intervals based on bootstrapping analysis. Concordance index of nomogram was 0.71.

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Figure 3. A, nomogram predicting 5-year graft survival based on information at before transplant and 6 months after transplant. Instructions: first row (Points) is point assignment for each variable. Rows 2 to 22 represent variables included in model. For each donor-recipient pair each variable is assigned point value (uppermost scale, points). Vertical line is made between appropriate variable value and points line. Assigned points for all variables are summed and total is found in row 23 (Total Points). Once total is located vertical line is made between total points and final row 24 (5-Year Graft Survival Probability). W, white. B, black. O, other. D, diabetes. G, glomerulonephritis. R, re-transplant. B, calibration curve for internal validation. Diagonal line represents performance of ideal nomogram in which predicted outcome corresponds perfectly with actual ones. Line with vertical boxes represents performance of constructed nomogram. Vertical boxes indicate 95% confidence intervals based on bootstrapping analysis. Concordance index of this nomogram was 0.784.

Discussion 

Using a large database (UNOS registry) we developed and internally validated 3 nomograms. The calibration plot for the first nomogram (1-year eGFR) indicated the best correlation of predicted and actual GFR over the range of 50 to 70 ml per minute per m2. The r-square value of 0.13 suggests a modest ability to predict this continuous outcome. While this r-square is low in absolute value, to our knowledge there are currently no other available tools to predict eGFR. This initial prototype will require refinement to enhance its predictive capability. The nomogram for pretransplant prediction of 5-year graft survival worked well with a concordance index of 0.71. This performance is comparable to the widely used and validated nomograms predicting oncological outcomes of kidney cancer and sarcoma with concordance indexes of 0.74 and 0.77, respectively.12, 13 The dynamic nomogram, predicting 5-year graft survival with additional measures from the first 6 months, performed even better than the pretransplant nomogram with an improved concordance index of 0.78.

A nomogram is an objective tool that uses an algorithm or mathematical formula to predict the probability of an outcome, optimized for predictive accuracy.11, 14 Nomograms have been shown to outperform clinicians in predicting oncological outcomes and may be of benefit in certain decision making settings.12, 13, 14 Nomograms can reconcile the multitude of donor and recipient parameters that impact transplant outcome and permit transplant physicians to better counsel their patients. In the context of multiple suitable donors clinicians can select the donor-recipient pair for transplantation that maximizes the expected function and survival of the allograft. Donor-recipient combinations with predicted suboptimal outcomes can be avoided or the recipient and donor can be informed appropriately. For paired donation programs outcome parity may be built into an optimized matching algorithm. In the absence of multiple donors the availability of objective prognostic information may better guide individualization of posttransplant care. For example, closer followup, targeted immunosuppressive tailoring, or more aggressive treatment of modifiable risk factors can be implemented for patients at greater risk for suboptimal graft function or survival. Lastly nomograms can be used by researchers in clinical trial designs for stratification of study subjects into high or low risk groups.

We selected 1-year graft function as determined by eGFR and graft survival at 5 years to be the predicted end points of our study. One-year graft function not only provided an idea of baseline graft function, but it was also reported to be a surrogate marker for kidney allograft longevity15 and for cardiovascular death after transplantation.16 An evidence-based approach was used to select predictor variables for the nomograms by including donor and recipient factors that have been shown in published studies to have an impact on kidney transplantation outcomes.1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Pretransplant increased donor age, small donor size with large recipient size, female donor gender and HLA mismatch have a negative impact on posttransplant graft function.2, 3, 4, 5, 6 The cause of renal failure (diabetes) and organ procurement technique remain under investigation as possible factors influencing graft function.1, 8 The impact of different immunosuppression regimens influencing graft function is equivocal with some evidence that using depleting antibodies may be better than nondepleting antibodies in preventing rejection.9 In addition, newer maintainence drugs such as mycophenolate mofetil and sirolimus may be associated with lower rates of rejection and chronic allograft nephropathy compared to azathioprine and calcineurin inhibitors.9 We included all the previously mentioned variables in the development of the nomogram. In turn, the nomograms weigh each individual factor's contribution to the specifically predicted end point. The choice of factors was not based on preliminary univariate or multivariate analysis of the UNOS data set, but rather on their importance to the individual outcome as judged by the authors' review of published literature. Such a strategy has been reported to avoid many of the problems associated with uncritical application of multivariable regression models to studies of clinical outcomes such as a poorly fit data set and overfitted models.11

To illustrate the usefulness of the pretransplant nomograms table 2 shows hypothetical sample data for a kidney transplantation candidate with 2 potential living donors that can be entered into the nomograms. Donor surgical technique, recipient variables and immunosuppression regimen were the same for donor 1 and donor 2. Despite the greater level of HLA mismatch between the recipient and donor 2 compared to donor 1, the nomogram predicts nearly equivalent 5-year survival probability for both donors (90%, or recipient + donor 1—0.92 and recipient + donor 2—0.89). However, the renal function nomogram predicts a higher 1-year eGFR in the recipient with a kidney from donor 2 (63 mg/dl) compared to donor 1 (52 mg/dl). This is likely due to the greater renal dose from a larger size male donor 2. Donor 2 may well be a better choice with better recipient function at 1 year and equivalent graft survival despite a 1 haplotype mismatch. Although a simplified example, it illustrates how these tools could be helpful in modeling graft outcome, thus aiding in patient counseling and treatment.

Table 2. Characteristics of a kidney transplant recipient with 2 potential living donors

		Recipient	Donor 1	Donor 2
	Age	32	41	28
	Gender	Male	Female	Male
	Race	White	White	White
	Ht (inches)	72	61	74
	Wt (lbs)	200	120	240
	BMI (kg/m2)	27.9	22.7	30.8
	BSA (m2)	2.11	1.52	2.35
	Serum creatinine (mg/dl)		0.9	0.9
	Nephrectomy type		Laparoscopic	Laparoscopic
	Recipient/donor HLA mismatch level		0	3
	Cause of renal failure	Glomerulonephritis
	Depleting antibodies	No
	IL2 antibodies	Yes
	Azathioprine	No
	Mycophenolate	Yes
	Rapamycin	No
	Calcineurin inhibitor	Yes

Our work is consistent with the transplant physician community efforts to develop better predictive tools. Brennan et al derived an equation that predicts the risk of suboptimal 1-year graft function using living related donor-recipient data from the Scientific Registry of Transplant Recipients.17 Their prediction equation was developed using only demographic donor (age, gender and size) and recipient (age, gender, race and size) factors in addition to the donor-recipient relationship. The equation predicts the chances of a 1-year creatinine less than 1.5 mg/dl. Long-term outcome was not predicted by the equation. More recently Akl et al developed a nomogram similar to ours to predict 5-year graft survival after living donor kidney transplantation using data from a single center.18 Compared to these prediction models the nomograms developed in this study take this effort a step further by using a greater number of variables including early posttransplant information for better predictability and by attempting to predict specific outcome measures of renal function (expressed on continuous scale) in addition to long-term graft survival.

Caveats exist regarding the use of these nomograms to predict outcomes in de novo transplant cases. Recently a nomogram developed using data from the United States Renal Data System to predict delayed graft function was found to lack clinical correlation when applied to a single center with markedly differing donor and recipient characteristics.19, 20 Therefore, care is needed when drawing generalizations from predictive tools based on large registry data applied to unique smaller populations. Another limitation of the nomograms is that drawing lines and adding points on Figure 1, Figure 2, Figure 3 can be cumbersome. Therefore, Internet software for their implementation is currently under development, similar to other nomograms that have worked well for predicting cancer and other outcomes (http://www.nomograms.org and http://clinicriskcalculators.org).12, 13, 14

A theoretical concern is the potential for abuse of the nomograms when they are used to select potential donors because recipients may be encouraged to shop around for the best possible donor. This can result in increasing the cost and length of time required for donor evaluations. The reality may be that few recipients have the luxury of multiple donors. Ultimately transplant physicians should retain clinical judgment with the help of these nomograms to counsel their patients because there are other factors such as patient compliance which can impact outcomes but are difficult to characterize.

Conclusions 

We have developed and internally validated a set of nomograms to predict renal function and graft survival in the setting of living donor kidney transplantation. These models can help to optimize the selection of living kidney donors. The prognostic information these models provide can help improve patient care.