Future Developments

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


This final chapter introduces two open problems for future research. This might help find research topics for students and researchers.


Copula-graphic estimator Dependent truncation Left-truncation Log-rank test 


  1. Bakoyannis G, Touloumi G (2017) Impact of dependent left truncation in semiparametric competing risks methods: a simulation study. Commun Stat Simul Comput 46(3):2025–2042MathSciNetCrossRefzbMATHGoogle Scholar
  2. Chaieb LL, Rivest LP, Abdous B (2006) Estimating survival under a dependent truncation. Biometrika 93(3):655–669MathSciNetCrossRefzbMATHGoogle Scholar
  3. 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
  4. 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
  5. Emura T, Murotani K (2015) An algorithm for estimating survival under a copula-based dependent truncation model. Test 24(4):734–751MathSciNetCrossRefzbMATHGoogle Scholar
  6. Emura T, Pan CH (2017) Parametric likelihood inference and goodness-of-fit for dependently left-truncated data, a copula-based approach, Stat Pap,
  7. Emura T, Wang W (2010) Testing quasi-independence for truncation data. J Multivar Anal 101:223–239MathSciNetCrossRefzbMATHGoogle Scholar
  8. Emura T, Wang W (2012) Nonparametric maximum likelihood estimation for dependent truncation data based on copulas. J Multivar Anal 110:171–188MathSciNetCrossRefzbMATHGoogle Scholar
  9. Hyde J (1980) Survival analysis with incomplete observations. In: Miller RG, Efron B, Brown BW, Moses LE (eds) Biostatistics casebook. Wiley, New York, pp 31–46Google Scholar
  10. Klein JP, Moeschberger ML (2003) Survival analysis techniques for censored and truncated data. Springer, New YorkzbMATHGoogle Scholar
  11. Moradian H, Denis Larocque D, Bellavance F (2017). Survival forests for data with dependent censoring, Stat Methods Med Res,
  12. 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
  13. Rodríguez-Girondo M, Deelen J, Slagboom EP, Houwing-Duistermaat JJ (2016). Survival analysis with delayed entry in selected families with application to human longevity. Stat Methods Med Res,
  14. 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

Personalised recommendations