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Simpson's Paradox in Survival Models

By CLELIA DI SERIO, YOSEF RINOTT and 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. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.

DOI identifier: 10.1111/j.1467-9469.2008.00637.x
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