Assessing gamma frailty models for clustered failure time data

Joanna H. Shih, Thomas A. Louis

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


Proportional hazards frailty models use a random effect, so called frailty, to construct association for clustered failure time data. It is customary to assume that the random frailty follows a gamma distribution. In this paper, we propose a graphical method for assessing adequacy of the proportional hazards frailty models. In particular, we focus on the assessment of the gamma distribution assumption for the frailties. We calculate the average of the posterior expected frailties at several followup time points and compare it at these time points to 1, the known mean frailty. Large discrepancies indicate lack of fit. To aid in assessing the goodness of fit, we derive and estimate the standard error of the mean of the posterior expected frailties at each time point examined. We give an example to illustrate the proposed methodology and perform sensitivity analysis by simulations.

Original languageEnglish (US)
Pages (from-to)205-220
Number of pages16
JournalLifetime Data Analysis
Issue number2
StatePublished - Jun 1 1995
Externally publishedYes


  • Clustered failure times
  • gamma frailties
  • posterior
  • proportional hazards

ASJC Scopus subject areas

  • Applied Mathematics


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