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.