Simpson's Paradox in Survival Models

Y. Rinott, C. Di Serio, M. SCARSINI

Scandinavian Journal of Statistics

September 2009, vol. 36, n°3

Departments: Economics & Decision Sciences

Keywords: Cox model, Detrimental covariate, Linear transformation model, Omitting covariates, Positive dependence, Proportional hazard, Proportional odds model, Protective covariate, Total positivity

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