Simpson's Paradox in Survival Models

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.