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The distribution of unobserved heterogeneity in competing risks models

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  • Yang Lu

    (University of Paris-13, Sorbonne Paris Cité, CEPN, UMR-CNRS 7234)

Abstract

We show that in a large class of proportional hazard competing risks models, the distribution of the bivariate frailty among survivors converges to a limiting distribution. This generalizes the result of Abbring and van den Berg (Biometrika 94(1):87–99, 2007), who show that in a single spell duration model, the frailty distribution converges to the gamma distribution. The resulting limiting distribution has an interpretation in terms of partition of a gamma distribution, and allows for both positive and negative correlation between the survival variables. This result provides a natural and flexible specification for the frailty in competing risks models.

Suggested Citation

  • Yang Lu, 2020. "The distribution of unobserved heterogeneity in competing risks models," Statistical Papers, Springer, vol. 61(2), pages 681-696, April.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:2:d:10.1007_s00362-017-0956-y
    DOI: 10.1007/s00362-017-0956-y
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    References listed on IDEAS

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    1. David Hanagal, 2009. "Weibull extension of bivariate exponential regression model with different frailty distributions," Statistical Papers, Springer, vol. 50(1), pages 29-49, January.
    2. Jaap H. Abbring & Gerard J. Van Den Berg, 2007. "The unobserved heterogeneity distribution in duration analysis," Biometrika, Biometrika Trust, vol. 94(1), pages 87-99.
    3. Jaap H. Abbring & Gerard J. Van Den Berg, 2003. "The identifiability of the mixed proportional hazards competing risks model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 701-710, August.
    4. Guillaume Horny, 2009. "Inference in mixed proportional hazard models with K random effects," Statistical Papers, Springer, vol. 50(3), pages 481-499, June.
    5. Yongheng Deng & John M. Quigley & Robert Van Order, 2000. "Mortgage Terminations, Heterogeneity and the Exercise of Mortgage Options," Econometrica, Econometric Society, vol. 68(2), pages 275-308, March.
    6. Omey, E. & Willekens, E., 1989. "Abelian and Tauberian theorems for the Laplace transform of functions in several variables," Journal of Multivariate Analysis, Elsevier, vol. 30(2), pages 292-306, August.
    7. Baker, Michael & Melino, Angelo, 2000. "Duration dependence and nonparametric heterogeneity: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 96(2), pages 357-393, June.
    8. Lancaster, Tony, 1979. "Econometric Methods for the Duration of Unemployment," Econometrica, Econometric Society, vol. 47(4), pages 939-956, July.
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