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Simpson's Paradox in Survival Models

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  • CLELIA DI SERIO
  • YOSEF RINOTT
  • MARCO SCARSINI

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.

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  • Clelia Di Serio & Yosef Rinott & Marco Scarsini, 2009. "Simpson's Paradox in Survival Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 463-480, September.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:3:p:463-480
    DOI: 10.1111/j.1467-9469.2008.00637.x
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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. 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.
    4. Marco Scarsini & Fabio Spizzichino, 1999. "Simpson-type paradoxes, dependence, and ageing," Post-Print hal-00540264, HAL.
    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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    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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