Introduction to Survival Analysis

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


This chapter provides a concise introduction to survival analysis. We review the essential tools in survival analysis, such as the survival function, Kaplan–Meier estimator, hazard function, log-rank test, Cox regression, and likelihood-based inference.


Censoring Cox regression Independent censoring Kaplan–Meier estimator Log-rank test Overall survival Time-to-tumor progression 


  1. Andersen PK, Borgan O, Gill RD, Keiding N (1993) Statistical models based on counting processes. Springer, New YorkCrossRefzbMATHGoogle Scholar
  2. Collett D (2003) Modelling survival data in medical research, 2nd edn. CRC Press, LondonzbMATHGoogle Scholar
  3. Cox DR (1972) Regression models and life-tables (with discussion). J R Stat Soc Ser B Stat Methodol 34:187–220zbMATHGoogle 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, Chen HY, Matsui S, Chen YH (2018) Compound.Cox: univariate feature selection and compound covariate for predicting survival. CRANGoogle Scholar
  6. Fleming TR, Harrington DP (1991) Counting processes and survival analysis. WileyGoogle Scholar
  7. Gehan EA (1965) A generalized Wilcoxon test for comparing arbitrarily singly-censored samples. Biometrika 52:203–224MathSciNetCrossRefzbMATHGoogle Scholar
  8. Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data, 2nd edn. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  9. Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J Am Stat Assoc 53(282):457–481MathSciNetCrossRefzbMATHGoogle Scholar
  10. Klein JP, Moeschberger ML (2003) Survival analysis techniques for censored and truncated data. Springer, New YorkzbMATHGoogle Scholar
  11. Michiels S, Le Maître A, Buyse M, Burzykowski T, Maillard E, Bogaerts J, Pignon JP (2009) Surrogate endpoints for overall survival in locally advanced head and neck cancer: meta-analyses of individual patient data. Lancet Oncol 10(4):341–350CrossRefGoogle Scholar
  12. van der Vaart AW (1998) Asymptotic statistics. Cambridge series in statistics and probabilistic mathematics. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  13. van Houwelingen HC, Putter H (2011) Dynamic prediction in clinical survival analysis. CRC Press, New YorkzbMATHGoogle 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