Checking semiparametric transformation models with censored data

Li Chen, D. Y. Lin, Donglin Zeng

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


Semiparametric transformation models provide a very general framework for studying the effects of (possibly time-dependent) covariates on survival time and recurrent event times. Assessing the adequacy of these models is an important task because model misspecification affects the validity of inference and the accuracy of prediction. In this paper, we introduce appropriate time-dependent residuals for these models and consider the cumulative sums of the residuals. Under the assumed model, the cumulative sum processes converge weakly to zero-mean Gaussian processes whose distributions can be approximated through Monte Carlo simulation. These results enable one to assess, both graphically and numerically, how unusual the observed residual patterns are in reference to their null distributions. The residual patterns can also be used to determine the nature of model misspecification. Extensive simulation studies demonstrate that the proposed methods perform well in practical situations. Three medical studies are provided for illustrations.

Original languageEnglish
Pages (from-to)18-31
Number of pages14
Issue number1
StatePublished - Jan 2012


  • Goodness of fit
  • Martingale residuals
  • Model checking
  • Model misspecification
  • Model selection
  • Recurrent events
  • Survival data
  • Time-dependent covariate

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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