## Simpson’s Paradox for the Cox Model

Di Serio, Clelia and Rinott, Yosef and Scarsini, Marco (2007) *Simpson’s Paradox for the Cox Model.* [Discussion Paper]. p. 20. Discussion Paper Series (No. 441). (Submitted)

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Official URL: http://ratio.huji.ac.il/node/2097

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## Abstract/Index

In the context of survival analysis, we define a covariate X as protective (detrimental) for the failure time T if the conditional distribution of [T | X = x] is stochastically increasing (decreasing) as a function of x. In the presence of another covariate Y, there exist situations where [T | X = x, Y = y] is stochastically decreasing in x for each fixed y, but [T | X = x] is stochastically increasing. When studying causal effects and influence of covariates on a failure time, this state of affairs appears paradoxical and raises the question of whether X should be considered protective or detrimental. In a biomedical framework, for instance when X is a treatment dose, such a question has obvious practical importance. 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 well-known Cox model. More specifically, we analyze conditions on the parameters of the model and the type of dependence between X and Y required for the paradox to hold. Among other things, we show that the paradox may hold for residual failure times conditioned on T > t even when the covariates X and Y are independent. This is due to the fact that independent covariates may become dependent when conditioned on the failure time being larger than t.

Item Type: | Report / Paper (Discussion Paper) |
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Research documents and activity classification: | Working Papers > Non-Refereed Working Papers / of national relevance only |

Divisions: | Department of Business and Management |

Uncontrolled Keywords: | Detrimental Covariate; Protective Covariate; Proportional Hazard; Omitting Covariates; Positive Dependence; Total Positivity. |

MIUR Scientific Area: | Area 13 - Economics and Statistics > SECS-S/01 Statistics Area 13 - Economics and Statistics > SECS-P/05 Econometrics |

Deposited By: | Maria Teresa Nistico |

Deposited On: | 20 Dec 2010 11:51 |

Last Modified: | 23 Apr 2013 16:34 |

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