Compared with dialysis, kidney transplantation confers significant survival and quality of life benefits for children with ESRD, while offering time-sensitive opportunities for growth and psychosocial development.1 In the United States, the Organ Procurement and Transplantation Network (OPTN) has responsibility for allocating deceased donor organs for transplantation. Recognizing the unique benefits of transplantation for children, the OPTN implemented the “Share 35” policy in 2005. This policy gives a high priority to pediatric candidates (aged<18 years at listing) when allocating kidneys from local deceased donors aged<35 years.2 However, two features of the allocation system create substantial potential for geographic variation in pediatric waiting time for a deceased donor kidney transplant (DDKT). First, certain categories of adult candidates receive even higher priority than children. Second, kidneys are usually allocated to children and adults locally before being offered to children in other areas.2
Federal law and guidelines direct the OPTN to allocate organs in a way that is efficient and equitable. The National Organ Transplant Act also acknowledges the unique benefits of transplantation for pediatric patients.3,4 Despite this acknowledgment, at least three categories of adults may divert a high-quality kidney from pediatric candidates.2 An adult candidate for multiorgan transplantation (MOT) can get maximum priority for a kidney if that candidate has been designated to receive another organ from the same donor. Because of a lack of widely accepted clinical criteria for MOT, rates of MOT (e.g., liver-kidney transplantation) vary widely between centers.5 Second, an adult with antibodies against human leukocyte antigens (HLAs) can receive higher priority for a biologically compatible kidney allograft than pediatric candidates. Lastly, an adult who is a zero antigen mismatch with a donated kidney can take priority over a pediatric candidate.2
Although federal regulations stipulate that organ allocation should not depend on a candidate’s location, kidney allocation usually begins locally.4 The OPTN created a system of organ procurement organizations (OPOs) to work with transplant centers and local communities in performing deceased donor organ recovery.3 Each OPO serves a geographically defined donor service area (DSA). DSAs vary widely in size, population characteristics, and in the volume of donated organs.6 A kidney is usually offered first to transplant candidates in the DSA where it was procured before being offered to candidates elsewhere.
The aim of this study was to examine whether geographic variation in patient-level and DSA-level factors influences pediatric waiting time for DDKT. At the DSA level, we hypothesized that longer waiting time for DDKT would be associated with (1) lower ratios of high-quality kidneys to pediatric candidates and (2) higher rates of diversions of high-quality kidneys to adult candidates.
The cohort was composed of 3764 children listed for DDKT, 84% of whom received a kidney transplant during the observation period. The median time to DDKT was 284 days (interquartile range, 80–750).
As shown in Table 1, there were no significant differences in sex, blood type, history of prior transplant, dialysis at listing, or insurance status of pediatric candidates between the three categories of DSAs defined by waiting time. However, the areas with the longest time to DDKT had the highest percentage of Hispanic children, children who were ever inactive on the waiting list, and candidates not transplanted. Supplemental Appendix 1 shows cohort generation.
Characteristics of DSAs
Figure 1 shows variation in waiting time for DDKT across DSAs (range, 14–1313 days). DSAs with long waiting times were located in the Northeast, the Midwest, the Southwest, and the Northwest, but not the Southeast. Many DSAs with long waiting times were adjacent to areas with short waiting times.
Figure 2 shows that the ratio of pediatric-quality kidneys/candidate differed substantially between DSAs. As shown in Table 2, the ratios of pediatric kidneys/candidates were 5.9, 3.8, and 3.1 in DSAs with short, intermediate, and long waiting times, respectively (P<0.001).
Forty-three percent of pediatric-quality kidneys were diverted to adults and 29% were diverted locally. Minus the total number of diverted kidneys, the ratios of pediatric kidneys/candidates were 2.6, 2.3, and 1.7 in areas with short, intermediate, and long waiting times, respectively.
We observed small differences in the percentage of pediatric-quality kidneys diverted to adults between DSAs (Table 2). Figure 3 displays the positive correlation between waiting time for DDKT and the percentage of pediatric-quality kidneys diverted to adults across DSAs (Spearman correlation coefficient=0.26; P=0.06).
Results of Multivariable Cox Regression for the Outcome of Time to DDKT
As shown in Table 3, individual characteristics of young age (<5 years versus reference >11 years), prior transplant, having ever been inactive on the waiting list, and having an elevated panel reactive antibody (PRA) were significantly associated with lesser access to DDKT. A lower ratio of pediatric-quality kidneys to candidates was also strongly associated with lesser access to DDKT. Compared with the reference category of DSAs with a ratio of ≥5:1 kidneys/candidates, children in DSAs with a ratio of <2:1 kidneys/candidates had a much lower hazard ratio (HR) for undergoing DDKT (0.56; 95% confidence interval, 0.38 to 0.84; P<0.01). Children in DSAs with a ratio of kidneys/candidates between 2:1 and <3:1 had a lower HR for transplantation, which did not reach statistical significance (adjusted HR, 0.69; 95% confidence interval, 0.47 to 1.02; P=0.06).
A higher percentage of kidneys diverted to local adult recipients was not associated with access to DDKT (adjusted HR, 0.93 per each 10% additional diversion; P=0.38).
An analysis using a competing risks approach to live donor kidney transplantation showed similar results to the primary analysis. As shown in Supplemental Appendix 2, five additional multivariable analyses (one analysis restricted to type O candidates, one analysis excluding recipients aged<2 years, one analysis substituting total kidney diversions to adults for local kidney diversions to adults, one analysis excluding five DSAs with a policy variance related to waiting time calculation, and one analysis limited to never-inactive candidates) all showed similar results to those of the primary analysis. We also compared time to DDKT among children to the time to DDKT among adults. Median waiting times for adult kidney transplant candidates are presented in Supplemental Appendix 3. Using the outcome of waiting time until 25% of candidates underwent DDKT, we calculated a Spearman correlation coefficient of 0.32 (P=0.02).
This study is the first comprehensive analysis of national variation in waiting time to pediatric DDKT that examines the geographic effects of allocation policy. A novel finding is that candidates in DSAs with a smaller supply of pediatric-quality kidneys relative to the number of wait-listed pediatric patients have longer waiting times. The analysis confirms the importance of individual attributes such as younger age, prior transplant, elevated immunologic reactivity, and inactivity on the waiting list in prolonging waiting time to transplantation. Geographic disparities in timely access to a transplant raise substantial concerns about whether the current allocation system meets its mandate to provide equitable access to DDKT for children.
Children with ESRD have a finite opportunity for physical, cognitive, and social development that may be impaired by delays before transplantation.7 Median time to DDKT varied from 14 to 1313 days in different DSAs. Eighty percent of pediatric DDKT recipients were receiving dialysis by the time of transplantation. Dialysis raises the risks of death, infection, and cardiovascular events.8 As little as 6 months of dialysis may restrict children’s linear growth.9 Dialysis (versus kidney transplantation) is associated with reduced quality of life for patients and families.10 Children who are transplanted (versus those with CKD not receiving a kidney transplant) experience significant improvements in their intellectual and developmental functioning, which may have long-term benefits for survival into adulthood.11,12 In light of these benefits of transplantation, the National Organ Transplant Act directs the OPTN to “recognize the differences in health and in organ transplantation issues between children and adults throughout the system and adopt criteria, polices, and procedures that address the unique health care needs of children.”3
A smaller number of kidneys per pediatric candidate was strongly associated with longer waiting time to DDKT. However, even in DSAs with the longest waiting times, the ratio of pediatric-quality kidneys to candidates was >3:1. This ratio of pediatric-quality kidneys to candidates was 1.7:1 after accounting for diversions to adult recipients. There are several reasons why pediatric waiting times might be prolonged even with the apparent availability of >1 kidneys per patient. First, the transplant team may turn down a kidney for a particular candidate in order to wait for one with a better HLA match or due to the expectation that a potential live donor will complete the medical evaluation and enable live donor transplantation. Pediatric transplant candidates may also experience temporary periods of inactive status on the waiting list because of illness or psychosocial problems. In addition, some kidneys that we classified as pediatric quality may have had defects (e.g., abnormal renal vasculature) not reported in the dataset or captured by the kidney donor risk index (KDRI).
Improving timely and equitable access to DDKT for children, regardless of geographic residence, could be accomplished by increasing the organ supply or by making changes to organ allocation policy. Some DSAs may be able to augment organ donation rates through best practices related to working with the surrogates of potential donors.13,14 Geographic differences in organ donor registration and organ donation rates are large and not fully explained by demographics.6,15 Interventional studies have demonstrated successful approaches to encouraging organ donor registration and organ donation itself.16 These practices could improve the supply of pediatric-quality kidneys.
Alternatively, the OPTN could develop policy proposals to promote greater equity in the allocation of pediatric-quality kidneys to children. Although Share 35 reduced overall DDKT waiting times for children, the policy did not necessarily improve equitable access nor did it address geographic disparities.17 Two specific strategies could now be considered. First, the OPTN could alter how organs are geographically distributed. One way to accomplish broader sharing is to allocate high-quality kidneys to children locally and nationally before allocating kidneys to adults locally. Another novel approach was recently proposed by Gentry et al. for adult liver allocation. The authors implemented mathematical redistricting optimization techniques to identify geographic partitions that would optimize equitable organ distribution and minimize mortality on the waiting list.18 Analogous redistricting approaches such as those proposed by Gentry et al. to redistrict the OPTN regional boundaries could reduce geographic disparities in waiting time for pediatric kidney transplantation. Notably, efforts to improve access to high-quality kidneys to children could improve efficiency because children have the greatest potential life-years after transplantation.19
Potential problems due to broader geographic organ sharing of kidney allografts must also be considered. One disadvantage is the potential for longer cold ischemia time, which increases the risk of delayed graft function. On the other hand, high-quality organs are likely to be accepted rapidly, limiting ischemia time. Innovations in organ preservation and rapid transportation could also mitigate the effects of broader sharing on organ outcomes. Another potential disadvantage is that lowering pediatric waiting time in certain regions could reduce the incentive for live kidney donation. Lower rates of living donation have been observed since the institution of Share 35, although the reasons for this finding remain unclear.20,21 If these proposed policies were implemented, rates of live kidney donation should be carefully assessed. An additional challenge is that proposals to revise organ allocation might differentially affect pediatric versus adult kidney transplant candidates. For example, we found that estimates of waiting time to kidney transplantation for pediatric versus adult candidates were only modestly (albeit statistically significantly) correlated. Therefore, the evaluation of organ allocation proposals should consider outcomes among both pediatric and adult populations.
A second specific approach to improving equitable access to pediatric kidney transplantation could be implemented within each DSA. The OPTN could consider increasing pediatric priority above some adult groups (e.g., MOT recipients) that currently have greater priority for kidney allografts than pediatric candidates.2 We found that 43% of high-quality kidneys were diverted to adults overall and 29% were diverted locally. However, this analysis uncovered limited support for the hypothesis that variation in the rate of diversions of kidneys to adults is an important cause of variation in pediatric waiting times. In univariate analysis, 27% of pediatric-quality kidneys were diverted locally in DSAs with short waiting times, whereas 31% were diverted in DSAs with long waiting times. In multivariable Cox regression, the association between these diversions and waiting time was not statistically significant.
To improve transparency, families of pediatric candidates should be educated about variation in waiting times for DDKT. In some cases, families in DSAs with long waiting times may consider traveling to list their children at centers with shorter waiting times.22 This approach, however, is not likely to be feasible for many individuals. First, distance from a center is an important barrier to transplant23; further travel would add burdens to families with a sick child. Second, travel and listing at multiple centers is costly and would provide advantages for families with greater resources, thus undermining equitable access.
We acknowledge this study’s limitations. Transplant access is likely to be reduced by comorbidities, acute illnesses, or psychosocial issues that temporarily preclude transplant readiness and are incompletely captured in this dataset. We do not have information about refusals of organ offers. Another confounder, PRA, was missing for a substantial minority of transplant candidates. However, most pediatric patients do not have anti-HLA antibodies and we have no reason to suspect that PRA elevations would cluster in certain geographic areas. Transplant centers may also exert judgment as to the timing of adding pediatric patients to the waiting list. On the other hand, the percentage of patients on dialysis at wait-listing was not significantly different across categories of DSA defined by waiting time.
In conclusion, this national study shows that large geographic variation in waiting times for pediatric DDKT is highly associated with local supply and demand factors. Long waiting times for pediatric kidney transplantation in some DSAs may contradict a federal directive to address the unique needs of children and suggests that broader geographic sharing of kidneys for children should be considered.
We performed a retrospective cohort study of pediatric (aged<18 years at wait-listing) kidney transplant candidates using data provided by the Scientific Registry of Transplant Recipients (SRTR). The SRTR includes data on all donors, wait-listed candidates, and transplant recipients in the United States, submitted by the members of the OPTN, and has been described elsewhere.24 The US Department of Health and Human Services Health Resources and Services Administration provides oversight to the activities of OPTN and SRTR contractors. This study was approved by the University of Pennsylvania Institutional Review Board.
Deaths were ascertained through center reports and linkage to the Social Security Death Master File. The primary outcome was time to DDKT.
Patients were wait-listed for DDKT between September 28, 2005, and September 30, 2010, and were followed until March 1, 2012. Patients were censored for death, delisting, live donor transplant, or transplant in another DSA. The initial date was chosen to assess a period after implementation of the Share-35 policy. We excluded pediatric candidates who were wait-listed for MOT, were never active on the waiting list, or underwent live donor kidney transplantation without being wait-listed for DDKT. Listings for patients who were candidates in multiple DSAs were counted distinctly.
Kaplan–Meier estimates for waiting time to DDKT were calculated for each DSA. Each DSA was categorized as having a short (0–180 days), intermediate (181–270 days), or long (>270 days) waiting time. These cutpoints were selected to achieve a similar number of DSAs in each category and before hypothesis testing.
We defined pediatric-quality kidneys as follows: (1) donated by individuals aged<35 years who did not have hepatitis C virus, diabetes, hypertension, cardiac death, or social/behavioral risk factors for HIV, and (2) transplanted.19,25 We examined the KDRI, an estimate of allograft failure risk based on donor attributes of age, race, diabetes, hypertension, serum creatinine, height, weight, hepatitis C virus, and cause of death.26 The KDRI for all of these pediatric-quality kidneys was <1. We also examined the distribution of KDRI scores for kidneys actually used in pediatric transplantation during the study period. Over 95% had KDRI<1.
To calculate the supply of pediatric-quality kidneys in each DSA, we summed the number of these kidneys procured in each DSA and transplanted during the observation period. We calculated the percentage of these kidneys “diverted” through allocation to local adult (aged≥18 years) recipients who had either a high (>80) PRA, underwent MOT, or had a zero antigen mismatch to that kidney.2
Analyses were conducted using Stata software (version 12.0; Stata Corporation, College Station, TX). Two-sided tests of hypotheses were conducted. A P value<0.05 was the criterion for statistical significance. We used ANOVA to compare means of normally distributed variables and chi-squared tests to compare categorical variables across DSA waiting time categories. The association between continuous variables was assessed using Spearman correlations, with tests for zero correlation. We fit multivariable Cox regression models for the outcome of DDKT. On the basis of prior literature and clinical experience, we adjusted for the following variables: age category (<2, 2–5, 6–10, and 11–17 years), sex, blood type, race/ethnicity as defined by the OPTN (white, African American, Hispanic, other), prior transplant (yes/no), insurance type (private/other), candidate PRA (defined by OPTN convention as <20, 20–79, and >79–100), whether the patient was ever inactive on the waiting list (yes/no), and ESRD cause.27–29
DSA-level covariates (the primary exposure) included the ratio of pediatric-quality kidneys/pediatric candidates (a categorical variable empirically defined as <2:1, 2:1–<3:1, 3:1–<4:1, 4:1–<5:1, and ≥5:1) and the percentage of these kidneys that were locally diverted to adults. Robust SEMs were calculated to adjust for the lack of independence between individuals in the same DSA.30,31
We performed a number of secondary analyses. First, we treated live donor kidney transplantation as a competing risk. To address the confounding effects of allocation according to blood type, we performed an analysis restricted to type O candidates.2 We also performed an analysis excluding candidates aged<2 years, who may be transplanted only in centers with sufficient expertise. Furthermore, we performed an analysis in which we excluded patients who were ever inactive during the study period.
We also performed an analysis in which we examined total pediatric-quality kidney diversions from the pediatric pool (local and nonlocal). In our primary analyses, we adjusted only for local diversions to adults within the same DSA because OPTN policy requires some diversions out of the DSA to be “paid back.” The recipient’s DSA later supplies a kidney to the procuring DSA, which might mitigate the effect of the initial diversion on pediatric waiting time.
An additional analysis excluded five DSAs with a policy variance allowing waiting time to commence when dialysis or waiting list registration occurs, whichever is earlier.
As a post hoc analysis, we compared waiting time to DDKT between children and adults. However, in five DSAs, <50% of adults received a DDKT during the observation period. For this reason, using the Kaplan–Meier method, we also estimated the time until 25% of candidates underwent kidney transplantation and calculated the Spearman correlation coefficient between pediatric and adult waiting times. Patients were censored for death, delisting, live donor transplant, or transplant in another DSA.
A small minority of recipients had missing data on relevant variables, except for PRA, which was missing among 41% (n=1635). In primary analyses, we created a separate category for missingness for categorical values with >1% missing data. We performed sensitivity analyses in which extreme values were assigned to individuals with missing data. Lastly, we performed a secondary analysis using multiple imputation for missing PRA values. The primary associations of interest between DSA attributes and the outcome were consistent with primary analyses and not shown.
This work was supported by grants from the National Institutes of Health National Institute of Diabetes and Digestive and Kidney Diseases (K23-DK078688 to P.P.R. and K23-DK083529 to S.A.).
P.P.R. and S.A. are members of OPTN committees that develop and review transplant policy in the United States. This study is their own work and does not necessarily represent the views of the OPTN.
The data reported here have been supplied by the Minneapolis Medical Research Foundation as the contractor for the SRTR. The interpretation and reporting of these data are the responsibility of the authors and in no way should be seen as an official policy of or interpretation by the SRTR or the US Government.
Preliminary results related to this work were presented at the 2013 American Transplant Congress, May 18–22, 2013, in Seattle, WA.
Published online ahead of print. Publication date available at www.jasn.org.
This article contains supplemental material online at http://jasn.asnjournals.org/lookup/suppl/doi:10.1681/ASN.2013070684/-/DCSupplemental.
1. Greenbaum LA, Warady BA, Furth SL: Current advances in chronic kidney disease in children: Growth, cardiovascular, and neurocognitive risk factors. Semin Nephrol 29: 425–434, 2009
2. Smith JM, Biggins SW, Haselby DG, Kim WR, Wedd J, Lamb K, Thompson B, Segev DL, Gustafson S, Kandaswamy R, Stock PG, Matas AJ, Samana CJ, Sleeman EF, Stewart D, Harper A, Edwards E, Snyder JJ, Kasiske BL, Israni AK: Kidney, pancreas and liver allocation and distribution in the United States. Am J Transplant 12: 3191–3212, 2012
3. National Organ Transplantation Act (NOTA), 42 USC §273 et seq, 1984
4. US Department of Health and Human Services: Organ Procurement and Transplantation Network Final Rule. 42 CFR part 121, 1999
5. Nadim MK, Sung RS, Davis CL, Andreoni KA, Biggins SW, Danovitch GM, Feng S, Friedewald JJ, Hong JC, Kellum JA, Kim WR, Lake JR, Melton LB, Pomfret EA, Saab S, Genyk YS: Simultaneous liver-kidney transplantation summit: Current state and future directions. Am J Transplant 12: 2901–2908, 2012
6. Ojo AO, Pietroski RE, O’Connor K, McGowan JJ, Dickinson DM: Quantifying organ donation rates by donation service area. Am J Transplant 5: 958–966, 2005
7. Groothoff JW, Grootenhuis M, Dommerholt A, Gruppen MP, Offringa M, Heymans HS: Impaired cognition and schooling in adults with end stage renal disease since childhood. Arch Dis Child 87: 380–385, 2002
8. McDonald SP, Craig JCAustralian and New Zealand Paediatric Nephrology Association: Long-term survival of children with end-stage renal disease. N Engl J Med 350: 2654–2662, 2004
9. Gorman G, Frankenfield D, Fivush B, Neu A: Linear growth in pediatric hemodialysis patients. Pediatr Nephrol 23: 123–127, 2008
10. Neul SK, Minard CG, Currier H, Goldstein SL: Health-related quality of life functioning over a 2-year period in children with end-stage renal disease. Pediatr Nephrol 28: 285–293, 2013
11. Icard P, Hooper SR, Gipson DS, Ferris ME: Cognitive improvement in children with CKD after transplant. Pediatr Transplant 14: 887–890, 2010
12. Goldstein SL, Graham N, Burwinkle T, Warady B, Farrah R, Varni JW: Health-related quality of life in pediatric patients with ESRD. Pediatr Nephrol 21: 846–850, 2006
13. Ashby VB, Kalbfleisch JD, Wolfe RA, Lin MJ, Port FK, Leichtman AB: Geographic variability in access to primary kidney transplantation in the United States, 1996-2005. Am J Transplant 7: 1412–1423, 2007
14. Mathur AK, Ashby VB, Sands RL, Wolfe RA: Geographic variation in end-stage renal disease incidence and access to deceased donor kidney transplantation. Am J Transplant 10: 1069–1080, 2010
15. Rosenblum AM, Li AH, Roels L, Stewart B, Prakash V, Beitel J, Young K, Shemie S, Nickerson P, Garg AX: Worldwide variability in deceased organ donation registries. Transpl Int 25: 801–811, 2012
16. Schold JD, Segev DL: Increasing the pool of deceased donor organs for kidney transplantation. Nat Rev Nephrol 8: 325–331, 2012
17. Amaral S, Patzer RE, Kutner N, McClellan W: Racial disparities in access to pediatric kidney transplantation since share 35. J Am Soc Nephrol 23: 1069–1077, 2012
18. Gentry SE, Massie AB, Cheek SW, Lentine KL, Chow EH, Wickliffe CE, Dzebashvili N, Salvalaggio PR, Schnitzler MA, Axelrod DA, Segev DL: Addressing geographic disparities in liver transplantation through redistricting. Am J Transplant 13: 2052–2058, 2013
19. Levine MH, Reese PP, Wood A, Baluarte JH, Huverserian A, Naji A, Abt PL: Inferior allograft outcomes in adolescent recipients of renal transplants from ideal deceased donors. Ann Surg 255: 556–564, 2012
20. Abraham EC, Wilson AC, Goebel J: Current kidney allocation rules and their impact on a pediatric transplant center. Am J Transplant 9: 404–408, 2009
21. Agarwal S, Oak N, Siddique J, Harland RC, Abbo ED: Changes in pediatric renal transplantation after implementation of the revised deceased donor kidney allocation policy. Am J Transplant 9: 1237–1242, 2009
22. Axelrod DA, Dzebisashvili N, Schnitzler MA, Salvalaggio PR, Segev DL, Gentry SE, Tuttle-Newhall J, Lentine KL: The interplay of socioeconomic status, distance to center, and interdonor service area travel on kidney transplant access and outcomes. Clin J Am Soc Nephrol 5: 2276–2288, 2010
23. Samuel SM, Hemmelgarn B, Nettel-Aguirre A, Foster B, Soo A, Alexander RT, Tonelli MPediatric Renal Outcomes Canada Group: Association between residence location and likelihood of transplantation among pediatric dialysis patients. Pediatr Transplant 16: 735–741, 2012
24. Leppke S, Leighton T, Zaun D, Chen SC, Skeans M, Israni AK, Snyder JJ, Kasiske BLScientific Registry of Transplant Recipients: Collecting, analyzing, and reporting data on transplantation in the United States. Transplant Rev (Orlando) 27: 50–56, 2013
25. Centers for Disease Control and Prevention: Guidelines for preventing transmission of human immunodeficiency virus through transplantation of human tissue and organs. MMWR Recomm Rep 43: 1–17, 1994
26. Rao PS, Schaubel DE, Guidinger MK, Andreoni KA, Wolfe RA, Merion RM, Port FK, Sung RS: A comprehensive risk quantification score for deceased donor kidneys: The kidney donor risk index. Transplantation 88: 231–236, 2009
27. Grams ME, Massie AB, Schold JD, Chen BP, Segev DL: Trends in the inactive kidney transplant waitlist and implications for candidate survival. Am J Transplant 13: 1012–1018, 2013
28. Patzer RE, Amaral S, Klein M, Kutner N, Perryman JP, Gazmararian JA, McClellan WM: Racial disparities in pediatric access to kidney transplantation: Does socioeconomic status play a role? Am J Transplant 12: 369–378, 2012
29. Furth SL, Garg PP, Neu AM, Hwang W, Fivush BA, Powe NR: Racial differences in access to the kidney transplant waiting list for children and adolescents with end-stage renal disease. Pediatrics 106: 756–761, 2000
30. Lin DY, Wei LJ: The robust inference for the Cox proportional hazards model. J Am Stat Assoc 84: 1074–1078, 1989
31. Cleves M: Analysis of multiple failure-time survival data. Stata resources and support, 2009. Available at: http://www.stata.com/support/faqs/statistics/multiple-failure-time-data
. Accessed November 7, 2013