Pure and hybrid causal effects on variables associated with an incident event

This article is concerned with the assessment of the causal effect of a treatment on a variable that is defined only in the subset of patients who experience a specific event. In this case, the treatment can affect the variable directly, as well as indirectly through its effect on the occurrence and severity of the event. In this article we describe the pure (direct) and hybrid (direct and indirect) causal effects and methods typically used to assess them. When the treatment has a strong effect on the occurrence of the event, we found no method with adequate properties to address the pure causal effect; this remains an intractable statistical problem with no clear solution. Among the valid methods for assessment of the hybrid causal effect, power depends greatly on whether the treatment effect is primarily on the occurrence of the event or on the variable of interest.