Use of log−log survival function in modeling time-covariate interactions in Cox regression

Mizanur R. Khondoker, M. Ataharul Islam

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Plotting of log−log survival functions against time for different categories or combinations of categories of covariates is perhaps the easiest and most commonly used graphical tool for checking proportional hazards (PH) assumption. One problem in the utilization of the technique is that the covariates need to be categorical or made categorical through appropriate grouping of the continuous covariates. Subjectivity in the decision making on the basis of eye-judgment of the plots and frequent inconclusiveness arising in situations where the number of categories and/or covariates gets larger are among other limitations of this technique. This paper proposes a non-graphical (numerical) test of the PH assumption that makes use of log−log survival function. The test enables checking proportionality for categorical as well as continuous covariates and overcomes the other limitations of the graphical method. Observed power and size of the test are compared to some other tests of its kind through simulation experiments. Simulations demonstrate that the proposed test is more powerful than some of the most sensitive tests in the literature in a wide range of survival situations. An example of the test is given using the widely used gastric cancer data.
Original languageEnglish
Pages (from-to)1968-1973
Number of pages6
JournalJournal of Statistical Planning and Inference
Issue number6
Early online date23 Sep 2008
Publication statusPublished - 1 Jun 2009


  • Hazard functions
  • Proportional hazards
  • Partial likelihood
  • Log−log survival function
  • Censoring
  • Score test

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