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Simpson's Paradox in Survival Models

Author

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  • Marco Scarsini

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique, Dipartimento di Scienze Economiche e Aziendali - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

  • Yosef Rinott
  • Clelia Di Serio

Abstract

In the context of survival analysis it is possible that increasing the value of a covariate X has a beneficial effect on a failure time, but this effect is reversed when conditioning on any possible value of another covariate Y. When studying causal effects and influence of covariates on a failure time, this state of affairs appears paradoxical and raises questions about the real effect of X. Situations of this kind may be seen as a version of Simpson's paradox. In this paper, we study this phenomenon in terms of the linear transformation model. The introduction of a time variable makes the paradox more interesting and intricate: it may hold conditionally on a certain survival time, i.e. on an event of the type {T>t} for some but not all t, and it may hold only for some range of survival times.

Suggested Citation

  • Marco Scarsini & Yosef Rinott & Clelia Di Serio, 2009. "Simpson's Paradox in Survival Models," Post-Print hal-00464530, HAL.
    • Handle: RePEc:hal:journl:hal-00464530
    DOI: 10.1111/j.1467-9469.2008.00637.x
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    References listed on IDEAS

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    1. A. G. DiRienzo & S. W. Lagakos, 2001. "Effects of model misspecification on tests of no randomized treatment effect arising from Cox’s proportional hazards model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 745-757.
    2. Rinott Y. & Tam M., 2003. "Monotone Regrouping, Regression, and Simpsons Paradox," The American Statistician, American Statistical Association, vol. 57, pages 139-141, May.
    3. Marco Scarsini & Fabio Spizzichino, 1999. "Simpson-type paradoxes, dependence, and ageing," Post-Print hal-00540264, HAL.
    4. A. N. Pettitt, 1984. "Proportional Odds Models for Survival Data and Estimates Using Ranks," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(2), pages 169-175, June.
    5. Lu, Wenbin & Liang, Yu, 2006. "Empirical likelihood inference for linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1586-1599, August.
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    Cited by:

    1. P. Vellaisamy, 2017. "Collapsibility of some association measures and survival models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1155-1176, October.

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