Martingale-based residuals for survival models

Terry M. Therneau, Patricia M. Grambsch, Thomas R. Fleming

Research output: Contribution to journalArticlepeer-review

698 Scopus citations


Graphical methods based on the analysis of residuals are considered for the setting of the highly-used Cox (1972) regression model and for the Andersen-Gill (1982) generalization of that model. We start with a class of martingale-based residuals as proposed by Barlow & Prentice (1988). These residuals and/or their transforms are useful for investigating the functional form of a covariate, the proportional hazards assumption, the leverage of each subject upon the estimates of ß, and the lack of model fit to a given subject.

Original languageEnglish (US)
Pages (from-to)147-160
Number of pages14
Issue number1
StatePublished - Mar 1990


  • Cox regression
  • Deviance
  • Influence function
  • Martingale
  • Outlier detection
  • Proportional hazards
  • Regression diagnostic
  • Residual

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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