Regression analysis of discrete time survival data under heterogeneity

Xiaonan Xue, Ron Brookmeyer

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


This paper concerns the regression analysis of discrete time survival data for heterogeneous populations by means of frailty models. We express the survival time for each individual as a sequence of binary variables that indicate if the individual survived at each time point. The main result is that the likelihood for these indicators can be factored into contributions that involve the conditional survival probabilities integrated over the frailty distribution of the risk set (population-averaged). We then model these population-averaged conditional probabilities as a function of covariates. The result justifies the practice of treating the failure indicators as independent Bernoulli trials and fitting binary regression models for the conditional failure probabilities at each time point. However, we must interpret the regression coefficients as population-averaged rather than subject-specific parameters. We apply the method to the Framingham Heart Study on risk factors for cardiovascular disease.

Original languageEnglish (US)
Pages (from-to)1983-1993
Number of pages11
JournalStatistics in Medicine
Issue number17
StatePublished - Sep 15 1997
Externally publishedYes

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


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