

Year : 2012  Volume
: 23
 Issue : 4  Page : 693700 

Predicting longterm graft survival in adult kidney transplant recipients 

Brett W Pinsky^{1}, Krista L Lentine^{1}, Patrick R Ercole^{1}, Paolo R Salvalaggio^{2}, Thomas E Burroughs^{1}, Mark A Schnitzler^{1}
^{1} Center for Outcomes Research, Saint Louis University School of Medicine, St. Louis, MO, USA ^{2} Division of Transplant Surgery, University of Washington, Seattle, WA, USA
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Date of Web Publication  9Jul2012 




Abstract   
The ability to accurately predict a population's longterm survival has important implications for quantifying the benefits of transplantation. To identify a model that can accurately predict a kidney transplant population's longterm graft survival, we retrospectively studied the United Network of Organ Sharing data from 13,111 kidneyonly transplants completed in 1988 1989. Nineteenyear deathcensored graft survival (DCGS) projections were calculated and compared with the population's actual graft survival. The projection curves were created using a twopart estimation model that (1) fits a KaplanMeier survival curve immediately after transplant (Part A) and (2) uses truncated observational data to model a survival function for longterm projection (Part B). Projection curves were examined using varying amounts of time to fit both parts of the model. The accuracy of the projection curve was determined by examining whether predicted survival fell within the 95% confidence interval for the 19year KaplanMeier survival, and the sample size needed to detect the difference in projected versus observed survival in a clinical trial. The 19year DCGS was 40.7% (39.841.6%). Excellent predictability (41.3%) can be achieved when Part A is fit for three years and Part B is projected using two additional years of data. Using less than five total years of data tended to overestimate the population's longterm survival, accurate prediction of longterm DCGS is possible, but requires attention to the quantity data used in the projection method.
How to cite this article: Pinsky BW, Lentine KL, Ercole PR, Salvalaggio PR, Burroughs TE, Schnitzler MA. Predicting longterm graft survival in adult kidney transplant recipients. Saudi J Kidney Dis Transpl 2012;23:693700 
How to cite this URL: Pinsky BW, Lentine KL, Ercole PR, Salvalaggio PR, Burroughs TE, Schnitzler MA. Predicting longterm graft survival in adult kidney transplant recipients. Saudi J Kidney Dis Transpl [serial online] 2012 [cited 2020 Nov 26];23:693700. Available from: https://www.sjkdt.org/text.asp?2012/23/4/693/98112 
Introduction   
The ability to accurately predict future longterm allograft and patient survival after transplantation at a population level is important for both clinical and policy decisions. In the past, projections of longterm kidney survival have been used to suggest substantial increases in median graft survival in the period from 1988 to 1995. ^{[1]} However, subsequent comparison of these projections to the observed KaplanMeier survival fractions suggested overestimation, particularly for projections based on short durations of observed data. ^{[2]} The accuracy of any projection approach depends on two major factors: the duration of observed data used to model the form of the survival function and the length of time over which subsequent survival is projected. ^{[3]} Projecting survival after transplant is complicated by the increased risk of graft loss in the early peritransplant period. In this study, we applied a twopart projection method to predict longterm survival after kidney transplantation and used observed outcomes data to assess how varying model inputs impacted prediction accuracy.
Subjects and Methods   
Study population and outcome
This was a retrospective cohort study of data drawn from the Organ Procurement and Transplantation Network (OPTN) registry. ^{[7]} The Health Resources and Services Administration (HRSA), US Department of Health and Human Services, provides oversight to the activities of the OPTN contractor. We included adult (age >18 years), firsttime recipients of solitary kidney transplants in 19881989. This cohort was chosen because their longterm observed survival data are available, providing a standard against which to compare the accuracy of the predictions.
The primary outcome of interest was deathcensored graft failure. Graft failure was identified from the OPTN core files. Death events were identified by OPTN reporting and supplemented with the Social Security Death Master File.
Projection model
To minimize inaccuracies introduced by the early peritransplant hazard of graft loss, we constructed twopart survival projections. The first part of the projection (Part A) was fit directly to the KaplanMeier survival curve immediately after transplant. The second part of the projection (Part B) used truncated observed data to model a survival function. This estimated survival function was then employed to predict survival for an extended period beyond the truncation.
The OPTN collects followup information during the patient's yearly visits. Patients who died or lost their graft during the final year of the study will have had more followup time than surviving patients for whom final followup forms have not yet been submitted. Therefore, the survival of the population would drop effectively to 0 due to all surviving patients being censored at their final followup visit. To avoid such early reporting bias, we allowed maximum observation times to extend to 18 months before the end of the study (12/31/2007); thus, graft failures reported beyond the maximum allowed observation time were censored. Patients were following to one of the following endpoints: death or end of study period (06/30/2006).
To create Part A, we used the KaplanMeier method to calculate early graft survival. By using the KaplanMeier method, we can fit graft survival during the time immediately after transplant when patients are at a greater risk of graft loss. We fit Part A using different followup times to identify the ideal amount of time needed to appropriately model initial survival.
To create Part B, we fit a parametric survival model with a Weibull functional form using the end of Part A as the new index date. ^{[8]} The Weibull model relates the covariate parameters (β_{k} ) and model scale parameter (σ) to the survival function (S (t)) according to the equation S (t) = exp [[te ^{(β0 + β1 X1 +…βkXk)1/σ}]. Projection analyses were preformed examining the population as a whole and, therefore, we did not include covariates in the models.
Varying lengths of observed data were used to fit the survival function to assess impact on prediction accuracy, and then expected survival was projected to 19 years posttransplant. Because the Weibull function estimates survival from the end of Part A, we adjusted the estimates by multiplying by the survival fraction on the last day of Part A. All estimates were produced using SAS version 9.1 (SAS Institute Inc., Cary, NC, USA).
Evaluation of the projected model
The accuracy of predictions was quantified by comparison with the 19year completely observed deathcensored graft survival based on the KaplanMeier method (reference model). Predictive accuracy of the projected model was assessed based on two different metrics. First, the predicted 19year survival estimate was compared with the reference 19year survival. If the projected survival fraction was within the 95% confidence interval of the reference survival then we considered a model to have excellent predictability. In addition, we calculated the sample size needed to determine the difference in projected versus reference survival in a prospective clinical trial. Sample size calculations for the log rank test of differences in patient survival were performed with PASS for windows software (NCSS, Kaysville, UT, USA). If the calculated sample size needed to detect a significant difference was very large, specifically greater than 5000 patients, then we considered the projection model to have good predictability by this criterion. Predicted and reference survivals over time were also plotted together for comparison of prediction accuracy by visual inspection.
Results   
There were 13,111 kidney transplants from 1987 to 1989. The mean age of the population at transplant was 41 years. The majority of the transplants were from standard criteria deceased donors [Table 1]. The 19year KaplanMeier deathcensored graft survival estimate was 40.7%. The 95% confidence interval for the KaplanMeier estimate was 39.8% and 41.6%.
[Table 2] shows the projected survival estimates from the twopart models. Excellent predictability for 19year deathcensored graft survival was achieved with 15, ten, and five years as well as 182 days of total posttransplant followup. With 15 years of followup, excellent predictability was achieved with fitting Part A for 30, 60 or 90 days and using the rest of the 15 years to form the projection of Part B. With ten years of followup, excellent predictability was achieved with fitting Part A for 182, 270 or 365 days and using the rest of the ten years to form the projection of Part B. For five years of followup data, excellent predictability was only achieved when Part A was fit for three years and Part B was projected using two additional years of data. With only 182 days of followup, only 30 days produced an accurate estimate of 19year survival; however, this model was inaccurate over most of its course and converged with observed survival only late in the prediction.  Table 2: Projected deathcensored graft survival rate. Part A is the number of days the projection is exactly fit by applying the Kaplain Meier method to observed data. The total number of days over which survival is projected is shown in the lefthand column. The number of days used to calculate the Weibull equation (i.e., length of Part B) is total Day – Part A. Estimated 19year survival fraction is displayed within the table cells. For example, in the 60/1096 cell, the Weibull is calculated using the final 1036 days of followup) predicted survival is 64.0%. Reference deathcensored graft survival based on 19 years of complete observed data is 40.7% (95% CI: 39.8– 41.6%)
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[Table 3] illustrates the number of patients needed in a clinical trial to detect the difference between the actual and the predicted 19year survival. Good predictability was found using two, four, five, ten and 15 years of posttransplant followup. With ten and 15 years of posttransplant followup, good predictability was achieved in every model. For five years of followup data, good predictability was only achieved when Part A was fit for nine months or one, two or three years and Part B was projected using the remaining followup time. For four years of followup data, good predictability was only achieved when Part A was fit for two or three years and Part B was projected using the remaining followup time.  Table 3: Prospective sample sizes that would be required to detect observed differences between the projected 19year deathcensored graft survival and the reference 19year deathcensored graft surivial. The total number of days over which survival is projected is shown in the left hand column. The number of days used to calculate the Weibull equation (i.e., length of Part B) is total days – Part A. Estimated sample size to detect the difference between projected and observed survival is shown in the cells. Sample size was calcualted for log rank test of patient survival, assuming 80% power, an alfa of 0.05, 2 years of enrollment, 19 years of followup and a 20% dropout rate.
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All predictive curves using five years of posttransplant followup were plotted in [Figure 1]. When Part A was calculated using only a few months, the predictive model was more likely to overestimate longterm survival. However, the actual survival curve was matched very well when 1095 days (three years) of data were used to fit Part A. Fitting Part A with 730 days (two years) of data also fitted well.  Figure 1: Projected survival curves with 1826 total days of observed data. The legend indicates the amount of time used to define Part A.
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[Figure 2] highlights why only examining the 19year survival to evaluate the predictability of a model can be misleading. [Figure 2] shows the longterm survival curve plotted against the curve projected using 30 days for Part A and 182 days for the followup curve. Although closely matched at 19 years, the two curves were very dissimilar, with the predictive model underestimating survival for the majority of the observation time.  Figure 2: Comparisons of survival curves: Comparison of actual 19year survival to projection constructed using 30 days of observed data to exactly fit early survival and 182. While the curve is accurate at 19 years, this projection would be very inaccurate at any other timepoint along the survival curve.
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Discussion   
The ability to accurately predict the longterm deathcensored graft survival of a population has important clinical and treatment implications. In this analysis, we have shown that in a transplant population we can accurately predict 19year graft survival, but the accuracy depends on the quantity of observed data as well as direct use of early observed data to avoid inaccuracies from the early posttransplant hazard of graft loss. Survival was predicted to 19 years in order to capture the maximum amount of followup time allowed by the data.
Prior attempts to predict longterm kidney survival have been based on estimating halflives. ^{[1],[2]} In most cases, the previous models calculated the halflife using an estimated rather than an actual survival. This results in "an estimation of an estimation" and two separate places where bias can influence the predictive model. The predictive halflife models also did not adjust for the immediate risk of graft failure within the first six months after transplant. By not adjusting for the increased risk of graft loss in the first six months, the models cannot accurately predict the entire survival time. We observed that survival also drops slightly after three years posttransplant. Survival trends differ between six months and three years posttransplant and three to five years posttransplant. From six months to three years, patient survival drops 0.009% a day and patient survival drops 0.01% a day from three years to five years posttransplant. Both trend lines are shown to have a high correlation with the actual survival curve. The previous models did not take either survivalaltering factor into consideration; therefore, resulting in overestimations of survival.
One metric we used to assess the accuracy of our projection method was based on the sample size needed to detect the difference in projected versus observed survival in a trial. The sample size threshold defining good accuracy was 5000 patients. We chose this sample size threshold to highlight how impractical it would be to conduct a clinical trial over 19 years to distinguish a similar difference and, thus, have an adequately powered trial to improve on these predictions. Thus, we believe it is possible to make longterm survival predictions using the OPTN registry that are more accurate than could be obtained from longterm followup of any trial that has been performed in transplantation. Based on the final survival estimate, the twopart model also met criteria for accurate prediction using only 182 days of followup [Figure 2]. While the projected curve is accurate at 19 years, it is inaccurate over the course of the projection until that point. The trajectory of the predictive curve drastically underestimates survival for the majority of the followup, and then it appears to intersect the actual survival curve and overestimate survival at approximately 16years posttransplant. Therefore, we believe that the apparent accuracy of this projected model that is based on limited data reflects chance rather than a wellperforming prediction.
A recently published article in the American Journal of Transplantation by Wolfe et al argues that models using lifeyears following transplant (LYFT) are optimal for predicting longterm survival for organ allocation. ^{[4]} In 2007, the OPTN Annual Report suggested that LYFT should be calculated by examining the median lifetime. ^{[5]} This method is simple to calculate, and in 2007 allowed for LYFT to be calculated within 15 years in 72% of the lifetimes without the need of any projection methods. However, as patient survival continues to improve, ^{[6]} we would expect an increase in the percent of lifetimes that can be calculated using the median method without the need for an accurate projection method.
MeierKreische et al have asserted that it is difficult to predict longterm graft survival based on early outcomes, and feel that the median lifetime estimates are often misleading. ^{[2]} They suggest a method to calculate LYFT using aggregate survival experience as an area under a survival curve at a fixed time point (i.e., 10 years). ^{[2]} This method underestimates the LYFT in patients with expected longterm survival benefit (i.e., a young transplant population). ^{[5]} Using the twopart model, LYFT could be calculated out to 19 years accurately therefore lessening the underestimation of LYFT in a population that is expected to have a longterm survival benefit. We believe that the accuracy of prediction varies with the methodological approach and that limitations can be overcome. A key finding of our analysis is that attempting to predict survival based on too little followup information can lead to an overestimation of survival. However, we have also shown that it is possible to predict with great accuracy survival 19 years into the future using only five years of observed data.
LYFT is being considered as a method for guiding deceased donor kidney allocation. Given that longterm survival estimates are needed to calculate LYFT, using the twopart method for calculating longterm survival will provide more accurate LYFT estimates. More accurate LYFT estimates will help allocation committees feel more comfortable making their difficult decisions.
The ability to accurately predict the longterm survival of a population has important implications for prediction, for quantifying the benefits of transplantation and possibly for estimating the longterm implications of treatment practices. We have shown that it is possible to produce a 19year survival projection within 1% of the actual 19year survival. To accurately predict longterm survival, a minimum of five years worth of followup data should be used. Direct use of early observed data to minimize inaccuracies from early graft loss hazards before beginning the projection also improves accuracy.
Acknowledgments   
The data reported here have been supplied by the United Network for Organ Sharing as the contractor for the OPTN. The interpretation and reporting of these data are the responsibility of the authors and should in no way be seen as representing official policy of or interpretation by the OPTN, the U.S. Government or the National Institutes of Health.
Dr. Lentine received support from a grant from the National Institute of Diabetes Digestive and Kidney Diseases (NIDDK), K08DK073036. Dr. Schnitzler received support from a grant from the NIDDK, P30DK079333.
References   
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3.  Henderson R, Jones M, Stare J. Accuracy of point predictions in survival analysis. Stat Med 2001;20:3083. [PUBMED] [FULLTEXT] 
4.  Wolfe RA, McCullough KP, Leichtman AB. Predictability of survival models for waiting list and transplant patients: calculating LYFT. Am J Transplant 2009;9:1523. [PUBMED] [FULLTEXT] 
5.  2007 Annual Report of the U.S. Organ Procurement and Transplantation Network and the Scientific Registry of Transplant Recipients: Transplant Data 19972006. Health Resources and Services Administration, Healthcare Systems Bureau, Division of Transplantation, Rockville, MD. 
6.  2008 Annual Report of the U.S. Organ Procurement and Transplantation Network and the Scientific Registry of Transplant Recipients: Transplant Data 19982007. U.S. Department of Health and Human Services, Health Resources and Services Administration, Healthcare Systems Bureau, Division of Transplantation, Rockville, MD. Available from: http://www.ustransplant.org/annual_reports/curr ent/509d_ki.pdf [Last Accessed on 2010 Mar 17]. 
7.  Organ Procurement and Transplant Network. About OPTN Data. Available from: http://optn.transplant.hrsa.gov/data/. [Last Accessed on 2010 Jan 4]. 
8.  Weibull W. A Statistical Distribution Function of Wide Applicability. J Appl Mech 1951; 18:293. 
Correspondence Address: Brett W Pinsky Center for Outcomes Research, Saint Louis University School of Medicine, St. Louis, MO, 63368 USA
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DOI: 10.4103/13192442.98112
[Figure 1], [Figure 2]
[Table 1], [Table 2], [Table 3] 











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