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Random Effects Cox Models: A Poisson Modelling Approach


  • Renjun Ma

    () (Faculty of Medicine, University of Ottawa)

  • Daniel Krewski

    (School of Mathematics and Statistics, Carleton University, and Faculty of Medicine, University of Ottawa)

  • Richard T. Burnett

    (Faculty of Medicine, University of Ottawa, and Environmental Health Directorate, Health Canada)


We propose a Poisson modelling approach to random effects Cox proportional hazards models. Specifically we describe methods of statistical inference for a class of random effects Cox models which accommodate a wide range of nested random effects distributions. The orthodox BLUP approach to random effects Poisson modeling techniques enables us to study this new class of models as a single class, rather than as a collection of unrelated models. The explicit expressions for the random effects given by our approach facilitate incorporation of relatively large number of random effects. An important feature of this approach is that the principal results depend only on the first and second moments of the unobserved random effects. The application of proposed methods is illustrated through the reanalysis of data on the time to failure (tumour onset) in an animal carcinogen esis experiment previously reported by Mantel and Ciminera (1979).

Suggested Citation

  • Renjun Ma & Daniel Krewski & Richard T. Burnett, 2000. "Random Effects Cox Models: A Poisson Modelling Approach," RePAd Working Paper Series lrsp-TRS338, Département des sciences administratives, UQO.
  • Handle: RePEc:pqs:wpaper:0012005

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    More about this item


    Cox model; BLUP; estimating equation; frailty; generalized linear models; random effects; Tweedie exponential dispersion model;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General


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