Setting the Scene

  • Takeshi Emura
  • Yi-Hau Chen
Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)


This first chapter presents the purpose of the book. We first illustrate the issues of dependent censoring arising from medical research. We then explain several benefits of investigating dependent censoring. We finally illustrate how copula-based methods have been grown through the literature of survival analysis.


Censoring Competing risk Cox regression Endpoint Informative dropout Multivariate survival analysis Overall survival 


  1. Braekers R, Veraverbeke N (2005) A copula-graphic estimator for the conditional survival function under dependent censoring. Can J Stat 33:429–447MathSciNetCrossRefzbMATHGoogle Scholar
  2. Burzykowski T, Molenberghs G, Buyse M (eds) (2005) The evaluation of surrogate endpoints. Springer, New YorkzbMATHGoogle Scholar
  3. Burzykowski T, Molenberghs G, Buyse M, Geys H, Renard D (2001) Validation of surrogate end points in multiple randomized clinical trials with failure time end points. Appl Stat 50(4):405–422MathSciNetzbMATHGoogle Scholar
  4. Chen YH (2010) Semiparametric marginal regression analysis for dependent competing risks under an assumed copula. J R Stat Soc Ser B Stat Methodol 72:235–251MathSciNetCrossRefGoogle Scholar
  5. Chen YH (2012) Maximum likelihood analysis of semicompeting risks data with semiparametric regression models. Lifetime Data Anal 18:36–57Google Scholar
  6. Clayton DG (1978) A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65(1):141–151MathSciNetCrossRefzbMATHGoogle Scholar
  7. Collett D (2015) Modelling survival data in medical research, 3rd edn. CRC Press, LondonGoogle Scholar
  8. Cox DR (1972) Regression models and life-tables (with discussion). J R Stat Soc Ser B Stat Methodol 34:187–220zbMATHGoogle Scholar
  9. de Uña-Álvarez J, Veraverbeke N (2013) Generalized copula-graphic estimator. TEST 22(2):343–360MathSciNetCrossRefzbMATHGoogle Scholar
  10. de Uña-Álvarez J, Veraverbeke N (2017) Copula-graphic estimation with left-truncated and right-censored data. Statistics 51(2):387–403MathSciNetCrossRefzbMATHGoogle Scholar
  11. Durante F, Sempi C (2015) Principles of copula theory. CRC Press, LondonCrossRefzbMATHGoogle Scholar
  12. Emura T, Chen YH (2016) Gene selection for survival data under dependent censoring, a copula-based approach. Stat Methods Med Res 25(6):2840–2857MathSciNetCrossRefGoogle Scholar
  13. Emura T, Lin CW, Wang W (2010) A goodness-of-fit test for Archimedean copula models in the presence of right censoring. Comput Stat Data Anal 54:3033–3043MathSciNetCrossRefzbMATHGoogle Scholar
  14. Emura T, Nakatochi M, Murotani K, Rondeau V (2017a) A joint frailty-copula model between tumour progression and death for meta-analysis. Stat Methods Med Res 26(6):2649–2666MathSciNetCrossRefGoogle Scholar
  15. Emura T, Nakatochi M, Matsui S, Michimae H, Rondeau V (2017b) Personalized dynamic prediction of death according to tumour progression and high-dimensional genetic factors: meta-analysis with a joint model. Stat Methods Med Res. Scholar
  16. Emura T, Michimae H (2017) A copula-based inference to piecewise exponential models under dependent censoring, with application to time to metamorphosis of salamander larvae. Environ Ecol Stat 24(1):151–173MathSciNetCrossRefGoogle Scholar
  17. Escarela G, Carrière JF (2003) Fitting competing risks with an assumed copula. Stat Methods Med Res 12(4):333–349MathSciNetCrossRefzbMATHGoogle Scholar
  18. Fine JP, Jiang H, Chappell R (2001) On semi-competing risks data. Biometrika 88:907–920MathSciNetCrossRefzbMATHGoogle Scholar
  19. Genest C, MacKay J (1986) The joy of copulas: bivariate distributions with uniform marginals. Am Stat 40(4):280–283MathSciNetGoogle Scholar
  20. Hsu L, Prentice RL (1996) On assessing the strength of dependency between failure time variates. Biometrika 83:491–506MathSciNetCrossRefzbMATHGoogle Scholar
  21. Joe H (2014) Dependence modeling with copulas. CRC Press, LondonzbMATHGoogle Scholar
  22. Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data, 2nd edn. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  23. Moradian H, Denis Larocque D, Bellavance F (2017) Survival forests for data with dependent censoring. Stat Methods Med Res. Scholar
  24. Nelsen RB (2006) An introduction to copulas, 2nd edn. Springer, New YorkzbMATHGoogle Scholar
  25. Oakes D (1982) A model for association in bivariate survival data. J R Stat Soc Ser B Stat Methodol 414–422Google Scholar
  26. Oakes D (1989) Bivariate survival models induced by frailties. J Am Stat Assoc 84:487–493MathSciNetCrossRefzbMATHGoogle Scholar
  27. Oba K, Paoletti X, Alberts S et al (2013) Disease-free survival as a surrogate for overall survival in adjuvant trials of gastric cancer: a meta-analysis. J Natl Cancer Inst 105(21):1600–1607CrossRefGoogle Scholar
  28. Peng M, Xiang L, Wang S (2018) Semiparametric regression analysis of clustered survival data with semi-competing risks. Comput Stat Data Anal 124:53–70Google Scholar
  29. Rivest LP, Wells MT (2001) A martingale approach to the copula-graphic estimator for the survival function under dependent censoring. J Multivar Anal 79:138–155MathSciNetCrossRefzbMATHGoogle Scholar
  30. Schepsmeier U, Stöber J (2014) Derivatives and Fisher information of bivariate copulas. Stat Pap 55(2):525–542MathSciNetCrossRefzbMATHGoogle Scholar
  31. Shih JH, Louis TA (1995). Inferences on the association parameter in copula models for bivariate survival data. Biometrics: 1384–99Google Scholar
  32. Shih JH (1998) A goodness-of-fit test for association in a bivariate survival model. Biometrika 85(1):189–200MathSciNetCrossRefzbMATHGoogle Scholar
  33. Siannis F, Copas J, Lu G (2005) Sensitivity analysis for informative censoring in parametric survival models. Biostatistics 6(1):77–91CrossRefzbMATHGoogle Scholar
  34. Sklar A (1959) Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de L’Université de Paris. 8:229–231zbMATHGoogle Scholar
  35. Staplin ND (2012) Informative censoring in transplantation statistics. Doctoral thesis, University of Southampton, School of MathematicsGoogle Scholar
  36. Staplin ND, Kimber AC, Collett D, Roderick PJ (2015) Dependent censoring in piecewise exponential survival models. Statist Methods Med Res 24(3):325–341MathSciNetCrossRefGoogle Scholar
  37. Sugimoto T, Hamasaki T, Evans SR (2017) Sizing clinical trials when comparing bivariate time-to-event outcomes. Stat Med 36(9):1363–1382MathSciNetCrossRefGoogle Scholar
  38. Tsiatis A (1975) A nonidentifiability aspect of the problem of competing risks. Proc Natl Acad Sci 72(1):20–22MathSciNetCrossRefzbMATHGoogle Scholar
  39. Wang W (2003) Estimating the association parameter for copula models under dependent censoring. J R Stat Soc Series B Stat Methodol 65(1):257–273MathSciNetCrossRefzbMATHGoogle Scholar
  40. Weiß G (2011) Copula parameter estimation by maximum-likelihood and minimum-distance estimators: a simulation study. Comput Stat 26:31–54MathSciNetCrossRefzbMATHGoogle Scholar
  41. Zheng M, Klein JP (1995) Estimates of marginal survival for dependent competing risks based on an assumed copula. Biometrika 82(1):127–138MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Takeshi Emura
    • 1
  • Yi-Hau Chen
    • 2
  1. 1.Graduate Institute of StatisticsNational Central UniversityTaoyuanTaiwan
  2. 2.Institute of Statistical ScienceAcademia SinicaTaipeiTaiwan

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