A Cautionary Note on Extended Kaplan-Meier Curves for Time-varying Covariates.

The Kaplan-Meier curve is a standard statistical tool that is used in cohort studies to illustrate how survival during follow-up depends on time-fixed covariates that are measured at baseline. For time-varying covariates, an extended Kaplan-Meier curve has been proposed that is constructed by letting subjects move across risk sets as their covariate levels change during follow-up. It has been claimed, but not proven, that, under a particular independence assumption, this extended Kaplan-Meier curve has a causal interpretation as representing a hypothetical cohort whose covariate values remain constant during follow-up. In this note, we show that, in the absence of confounding, this claim is indeed correct. However, we argue that the causal implications of this independence assumptions are highly unrealistic, and that a causal interpretation of the extended Kaplan-Meier curve is therefore typically unwarranted.