Pitfalls of statistical analysis and clinical interpretation of the estimates of patients with chronic kidney disease. Part II: Survival analysis

Survival analysis is one of the most widely used methods of statistical analysis. With an imaginary simplicity, this analysis has certain pitfalls. There are different approaches, each of which requires compliance with certain assumptions and a peculiar clinical interpretation. The risk of death can be analysed by directly measuring the relative risk or indirectly assessing it using an odds ratio. However, these estimates are cumulative, do not involve censored observations and do not take into account the time of observation and the impact of covariates. The most common methods of analysis in a case of censored observation are the Kaplan-Meier procedure (which is empirically estimate the probability of surviving a certain time - survival function) and the Nelson-Allen (which is estimate the cumulative hazard function). Both of these methods do not require a priori information about the shape of survival function, however, they allow to estimate the impact on survival (or risk) of only one categorical predictor, cannot correct covariates and are based on the assumption of uninformative censoring. The use of these methods in a case of competing risks gives a deliberately biased assessment of survival. The most widely used method of survival analysis in the presence of competing risks is a cause-specific Cox proportional hazards model. The use of this method is advisable when the researcher aims to study the causal relationship of various factors and a certain outcome. However, it is important to interpret the results of such analysis correctly: it allows to assess the risk of a particular event among patients who have lived to a certain time-point and have not undergone any of the competing events. Because competing events are ignored (censored), it is not possible to directly assess the impact of covariates on their frequency. An alternative may be the increasingly popular Fine and gray competing risks regression model. This method simulates the impact of covariates on the cumulative incidence function and can be applied when the aim of the researcher is not to study the etiological associations, but to estimate the probability of each of the events - i.e. an individual forecast. Thus, the survival analysis can be performed using different methods. Each of them is not universal, and was designed for specific purposes, has its advantages, disadvantages and limitations. The use of the optimal approach in each case will provide the most objective analysis.

анализ выживаемости, статистика, трансплантация почки, выживаемость реципиентов, лист ожидания, причинно-специфический риск, процедура Каплана-Мейера, модель пропорциональных рисков Кокса, регрессионная модель Файн и Грей, конкурирующий риск, survival analysis, statistics, kidney transplant, recipient’s survival rate, waiting list, cause-specific risk, Kaplan-Meier procedure, Cox proportional hazards model, Fine and Gray competing risk regression model

1. Erdoğan S., Gülhan O.T. Alternative Confidence Interval Methods Used in the Diagnostic Accuracy Studies. Comput Math Methods Med. 2016; 2016:7141050. DOI: 10.1155/2016/7141050.

2. du Prel J.B., Hommel G., Röhrig B. et al. Confidence interval or p-value?: part 4 of a series on evaluation of scientific publications. Dtsch Arztebl Int. 2009; 106(19):335-9. DOI: 10.3238/arztebl.2009.0335.

3. Braschel M.C., Svec I., Darlington G.A. et al. A comparison of confidence interval methods for the intraclass correlation coefficient in community-based cluster randomization trials with a binary outcome. Clin Trials. 2016; 13(2):180-7. DOI: 10.1177/1740774515606377.

4. Pulkstenis E., Robinson T.J. Goodness-of-fit tests for ordinal response regression models. Stat Med. 2004 Mar 30;23(6):999-1014.

5. Fagerland M.W., Hosmer D.W. A goodness-of-fit test for the proportional odds regression model. Stat Med. 2013 Jun 15;32(13):2235-49. DOI: 10.1002/sim.5645.

6. Carlin B.P., Hong H., Shamliyan T.A. et al. Case Study Comparing Bayesian and Frequentist Approaches for Multiple Treatment Comparisons. Rockville (MD): Agency for Healthcare Research and Quality (US); 2013. Report No.: 12(13)-EHC103-EF. AHRQ Methods for Effective Health Care.

7. Bennett M.M., Crowe B.J., Price K.L. el al. Comparison of Bayesian and frequentist meta-analytical approaches for analyzing time to event data. J Biopharm Stat. 2013;23(1):129-45. DOI: 10.1080/10543406.2013.737210.

8. Kaplan E.L., Meier P. Non-parametric estimation from incomplete observations. J Am Stat Assoc. 1958; 53(282):457-481

9. Hobbs B.P. On nonparametric hazard estimation. J Biom Biostat. 2015;6. pii: 232. DOI: 10.4172/2155-6180.1000232

10. Xian Liu. Survival Analysis: Models and Applications. John Wiley & Sons, 2012

11. Li Y., Schaubel D.E., He K. Matching methods for obtaining survival functions to estimate the effect of a time-dependent treatment. Stat Biosci. 2014; 6(1):105-126.

12. Kenah E. Nonparametric survival analysis of infectious disease data. J R Stat Soc Series B Stat Methodol. 2013; 75(2):277-303.

13. Commenges D., Letenneur L., Joly P. el al. Modelling age-specific risk: application to dementia. Stat Med. 1998; 17(17):1973-88.

14. Bratt O., Drevin L., Akre O. el al. Family History and Probability of Prostate Cancer, Differentiated by Risk Category: A Nationwide Population-Based Study. J Natl Cancer Inst. 2016; 108(10). pii: djw110. DOI: 10.1093/jnci/djw110.

15. Røder M.A., Brasso K., Christensen I.J. el al. Survival after radical prostatectomy for clinically localised prostate cancer: a population-based study. BJU Int. 2014; 113(4):541-7. DOI: 10.1111/bju.12065.

16. Gavrilova N.S., Gavrilov L.A. Mortality Trajectories at Extreme Old Ages: A Comparative Study of Different Data Sources on U.S. Old-Age Mortality. Living 100 Monogr. 2014; 2014. pii: https://www.soa.org/Library/Monographs/Life/Living-To-100/2014/mono-li14-3a-gavrilova.pdf.

17. Ghosh D. Proportional hazards regression for cancer studies. Biometrics. 2008; 64(1):141-8.

18. Cleves М., Gould W.W., Marchenko Y.V. An Introduction to Survival Analysis Using Stata, Revised Third Edition. Stata Press, 2016

19. Зулькарнаев А.Б., Фоминых Н.М., Карданахишвили З.Б. Сосудистый доступ и выживаемость пациентов на гемодиализе: особенности причинно-следственной связи. Вестник трансплантологии и искусственных органов. 2019;21(2):49-58. DOI: 10.15825/1995-1191-2019-2-49-58

20. Saranya, Karthikeyan. A Comparison study of Kaplan Meier and NelsonAalen methods in survival analysis. International journal for research in emerging science and technology. 2(11): 34-38

21. Gaynor J.J., Ciancio G., Guerra G. et al. Lower tacrolimus trough levels are associated with subsequently higher acute rejection risk during the first 12 months after kidney transplantation. Transpl Int. 2016;29(2):216-26. DOI: 10.1111/tri.12699

22. Stel V.S., Dekker F.W., Tripepi G. et al. Survival analysis I: the Kaplan-Meier method. Nephron Clin Pract. 2011; 119(1):c83-8. DOI: 10.1159/000324758

23. Colosimo E., Ferreira F., Oliveira M. et al. Empirical comparisons between Kaplan-Meier and Nelson-Aalen survival function estimators. J. Stat. Comput. Simul. 2002; 72(4): 299-308. DOI: 10.1080/00949650212847

24. Wolbers M., Koller M.T., Stel V.S. et al. Competing risks analyses: objectives and approaches. Eur Heart J. 2014; 35(42):2936-41. DOI: 10.1093/eurheartj/ehu131

25. van Londen M., Aarts B.M., Deetman P.E. et al. Post-Transplant Hypophosphatemia and the Risk of Death-Censored Graft Failure and Mortality after Kidney Transplantation. Clin J Am Soc Nephrol. 2017;12(8):1301-1310. DOI: 10.2215/CJN.10270916

26. Eide I.A., Halden T.A.S., Hartmann A. et al. Associations Between Posttransplantation Diabetes Mellitus and Renal Graft Survival. Transplantation. 2017;101(6):1282-1289. DOI: 10.1097/TP.0000000000001259

27. Austin PC, Lee DS, Fine JP. Introduction to the Analysis of Survival Data in the Presence of Competing Risks. Circulation. 2016; 133(6):601-9. DOI: 10.1161/CIRCULATIONAHA.115.017719

28. Taber D.J., Gebregziabher M., Payne E.H. et al. Overall Graft Loss Versus Death-Censored Graft Loss: Unmasking the Magnitude of Racial Disparities in Outcomes Among US Kidney Transplant Recipients. Transplantation. 2017;101(2):402-410. DOI: 10.1097/TP.0000000000001119

29. Cox D.R. Regression Models and Life-Tables. Journal of the Royal Statistical Society, Series B. 1972; 34(2): 187-220

30. Gao H., Liu Y., Zhang T. et al. Parametric proportional hazards model for mapping genomic imprinting of survival traits. J Appl Genet. 2013; 54(1):79-88. DOI: 10.1007/s13353-012-0120-2

31. Austin P.C., Lee D.S., Fine J.P. Introduction to the Analysis of Survival Data in the Presence of Competing Risks. Circulation. 2016; 133(6):601-9. DOI: 10.1161/CIRCULATIONAHA.115.017719

32. Cameron A.C., Trivedi P.K. Microeconometrics: Methods and Applications. Cambridge University Press, 2005

33. Austin P.C. Generating survival times to simulate Cox proportional hazards models with time-varying covariates. Stat Med. 2012; 31(29):3946-58. DOI: 10.1002/sim.5452

34. Tang Y., Chen J., Huang K. el al. The incidence, risk factors and in-hospital mortality of acute kidney injury in patients after abdominal aortic aneurysm repair surgery. BMC Nephrol. 2017; 18(1):184. DOI: 10.1186/s12882-017-0594-6.

35. Kaufmann K.B., Baar W., Silbach K. el al. Modifiable Risk Factors for Delayed Graft Function After Deceased Donor Kidney Transplantation. Prog Transplant. 2019: 1526924819855357. DOI: 10.1177/1526924819855357.

36. Rodríguez Castellanos F.E., Domínguez Quintana F., Soto Abraham V. el al. Classification of Acute Rejection Episodes in Kidney Transplantation: a Proposal Based on Factor Analysis. Iran J Kidney Dis. 2018; 12(2):123-131.

37. Almutary H., Douglas C., Bonner A. Multidimensional symptom clusters: an exploratory factor analysis in advanced chronic kidney disease. J Adv Nurs. 2016; 72(10):2389-400. DOI: 10.1111/jan.12997.

38. Oh J.H., Thor M., Olsson C. el al. A Factor Analysis Approach for Clustering Patient Reported Outcomes. Methods Inf Med. 2016; 55(5):431-439.

39. Zheng W., Chen L. Factor analysis of diabetic nephropathy in Chinese patients. Diabetes Metab Syndr. 2011; 5(3):130-6. DOI: 10.1016/j.dsx.2012.02.018.

40. Bouaoun L., Villar E., Ecochard R., Couchoud C. Excess risk of death increases with time from first dialysis for patients on the waiting list: implications for renal allograft allocation policy. Nephron Clin Pract. 2013; 124(1-2):99-105. DOI: 10.1159/000355549

41. OPTN.transplant.hrsa.gov [Internet]. OPTN policies (last updated 10/01/2019). 2019. Available at: https://optn.transplant.hrsa.gov/media/1200/optn_policies.pdf

42. Olivier J., May W.L., Bell M.L. Relative effect sizes for measures of risk. Communications in Statistics - Theory and Methods. 2017; 46(14): 6774-6781. DOI: 10.1080/03610926.2015.1134575

43. Brody T. Clinical Trials, 2nd ed. Study Design, Endpoints and Biomarkers, Drug Safety, and FDA and ICH Guidelines. Academic Press, 2016

44. Sedgwick P., Joekes K. Interpreting hazard ratios. BMJ. 2015;351:h4631 DOI: 10.1136/bmj.h4631

45. Sankoh A.J., Li H., D'Agostino R.B. Sr. Use of composite endpoints in clinical trials. Stat Med. 2014; 33(27):4709-14. DOI: 10.1002/sim.6205

46. Srinivas T.R., Ho B., Kang J. et al. Post hoc analyses: after the facts. Transplantation. 2015;99(1):17-20. DOI: 10.1097/TP.0000000000000581

47. Rauch G., Rauch B., Schüler S. et al. Opportunities and challenges of clinical trials in cardiology using composite primary endpoints. World J Cardiol. 2015; 7(1):1-5. DOI: 10.4330/wjc.v7.i1.1

48. Dong G., Li D., Ballerstedt S. et al. A generalized analytic solution to the win ratio to analyze a composite endpoint considering the clinical importance order among components. Pharm Stat. 2016;15(5):430-7. DOI: 10.1002/pst.1763

49. Sapir-Pichhadze R., Pintilie M., Tinckam K.J. et al. Survival Analysis in the Presence of Competing Risks: The Example of Waitlisted Kidney Transplant Candidates. Am J Transplant. 2016 Jul;16(7):1958-66. DOI: 10.1111/ajt.13717

50. Chopra B., Sureshkumar K.K. Changing organ allocation policy for kidney transplantation in the United States. World J Transplant. 2015; 5(2):38-43. DOI: 10.5500/wjt.v5.i2.38

51. Hahn A.B., Mackey M., Constantino D. et al. The new kidney allocation system does not equally advantage all very high cPRA candidates - A single center analysis. Hum Immunol. 2017; 78(1):37-40. DOI: 10.1016/j.humimm.2016.10.010

52. Monchaud C., Marin B., Estenne M. et al. Consensus conference on a composite endpoint for clinical trials on immunosuppressive drugs in lung transplantation. Transplantation. 2014;98(12):1331-8. DOI: 10.1097/TP.0000000000000235

53. Weldegiorgis M., de Zeeuw D., Heerspink H.J. Renal end points in clinical trials of kidney disease. Curr Opin Nephrol Hypertens. 2015; 24(3):284-9. DOI: 10.1097/MNH.0000000000000118.

54. White C.A., Siegal D., Akbari A. el al. Use of kidney function end points in kidney transplant trials: a systematic review. Am J Kidney Dis. 2010; 56(6):1140-57. DOI: 10.1053/j.ajkd.2010.08.015.

55. Weldegiorgis M., de Zeeuw D., Dwyer J.P. el al. Is Chronic Dialysis the Right Hard Renal End Point To Evaluate Renoprotective Drug Effects? Clin J Am Soc Nephrol. 2017; 12(10):1595-1600. DOI: 10.2215/CJN.09590916.

56. Fine J.P., Gray R.J. A proportional hazards model for the subdistribution of a competing risk. J Am Stat Assoc. 1999;94(446):496-509

57. Andersen P.K., Geskus R.B., de Witte T. et al. Competing risks in epidemiology: possibilities and pitfalls. Int J Epidemiol. 2012 Jun;41(3):861-70. DOI: 10.1093/ije/dyr213

58. Ватазин А.В., Зулькарнаев А.Б., Степанов В.А. Анализ выживаемости пациентов в листе ожидания трансплантации почки с позиции конкурирующих рисков. Вестник трансплантологии и искусственных органов. 2019;21(1):35-4 DOI: 10.15825/1995-1191-2019-1-35-455.

59. Arce C.M., Lenihan C.R., Montez-Rath M.E. et al. Comparison of longer-term outcomes after kidney transplantation between Hispanic and non-Hispanic whites in the United States. Am J Transplant. 2015;15(2):499-507. DOI: 10.1111/ajt.13043

60. Arce C.M., Goldstein B.A., Mitani A.A. et al. Differences in access to kidney transplantation between Hispanic and non-Hispanic whites by geographic location in the United States. Clin J Am Soc Nephrol. 2013;8(12):2149-57. DOI: 10.2215/CJN.01560213

61. Kim H., An J.N., Kim D.K. et al. Elderly Peritoneal Dialysis Compared with Elderly Hemodialysis Patients and Younger Peritoneal Dialysis Patients: Competing Risk Analysis of a Korean Prospective Cohort Study. PLoS One. 2015;10(6):e0131393. DOI: 10.1371/journal.pone.0131393

62. Sapir-Pichhadze R., Pintilie M., Tinckam K. el al. Survival Analysis in the Presence of Competing Risks: The Example of Waitlisted Kidney Transplant Candidates. Am J Transplant. 2016; 16(7):1958-66. DOI: 10.1111/ajt.13717.

63. van Geloven N., le Cessie S., Dekker F.W. el al. Transplant as a competing risk in the analysis of dialysis patients. Nephrol Dial Transplant. 2017; 32(suppl_2):ii53-ii59. DOI: 10.1093/ndt/gfx012.

64. Noordzij M., Leffondré K., van Stralen K.J. el al. When do we need competing risks methods for survival analysis in nephrology? Nephrol Dial Transplant. 2013; 28(11):2670-7. DOI: 10.1093/ndt/gft355.

65. Kiberd B.A., Tennankore K.K. Lifetime risks of kidney donation: a medical decision analysis. BMJ Open. 2017; 7(8):e016490. DOI: 10.1136/bmjopen-2017-016490.

66. Naik A.S., Sakhuja A., Cibrik D.M. el al. The Impact of Obesity on Allograft Failure After Kidney Transplantation: A Competing Risks Analysis. Transplantation. 2016; 100(9):1963-9. DOI: 10.1097/TP.0000000000000983.