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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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 wellknown 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) 

Research documents and activity classification:  Working Papers > NonRefereed 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 > SECSS/01 Statistics Area 13  Economics and Statistics > SECSP/05 Econometrics 
Deposited by:  Maria Teresa Nistico 
Date Deposited:  20 Dec 2010 10:51 
Last Modified:  22 Apr 2015 00:13 
URI:  http://eprints.luiss.it/id/eprint/863 
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