Abstract
In competing event settings, a counterfactual contrast of cause-specific cumulative incidences quantifies the total causal effect of a treatment on the event of interest. However, effects of treatment on the competing event may indirectly contribute to this total effect, complicating its interpretation. We previously proposed the separable effects to define direct and indirect effects of the treatment on the event of interest. This definition was given in a simple setting, where the treatment was decomposed into two components acting along two separate causal pathways. Here we generalize the notion of separable effects, allowing for interpretation, identification and estimation in a wide variety of settings. We propose and discuss a definition of separable effects that is applicable to general time-varying structures, where the separable effects can still be meaningfully interpreted as effects of modified treatments, even when they cannot be regarded as direct and indirect effects. For these settings we derive weaker conditions for identification of separable effects in studies where decomposed, or otherwise modified, treatments are not yet available; in particular, these conditions allow for time-varying common causes of the event of interest, the competing events and loss to follow-up. We also propose semi-parametric weighted estimators that are straightforward to implement. We stress that unlike previous definitions of direct and indirect effects, the separable effects can be subject to empirical scrutiny in future studies.
Highlights
Researchers are often interested in treatment effects on an event of interest that is subject to competing events, that is, events that make it impossible for the event of interest to subsequently occur
We recently proposed the separable effects for causal inference in competing event settings (Stensrud et al 2020), inspired by Robins and Richardson’s extended graphical approach to mediation analysis (Robins and Richardson 2010; Didelez 2018; Robins et al 2020)
As in the previous example of blood pressure therapy and kidney injury, the AY separable effect of statin therapy on type 2 diabetes risk evaluated at aD = 1 may be of particular clinical interest, quantifying the effect of assignment to the original statin therapy containing both components versus a modified treatment that removes the component possibly leading to weight gain
Summary
Researchers are often interested in treatment effects on an event of interest that is subject to competing events, that is, events that make it impossible for the event of interest to subsequently occur. Other estimands that have been considered for causal inference in the face of competing events that do have a causal interpretation include the controlled direct effects (Robins and Greenland 1992; Young et al 2020) and pure (natural) effects (Robins and Greenland 1992; Pearl 2009) These estimands refer to treatment effects under unspecified interventions on the competing events; in the example on blood pressure therapy, we would need to consider an intervention that “eliminates” death from all causes. Identification of pure (natural) effects relies on counterfactual assumptions across different “worlds” that are untestable, even in principle (Robins and Richardson 2010) To address these problems, we recently proposed the separable effects for causal inference in competing event settings (Stensrud et al 2020), inspired by Robins and Richardson’s extended graphical approach to mediation analysis (Robins and Richardson 2010; Didelez 2018; Robins et al 2020).
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