Separable Effects for Causal Inference in the Presence of Competing Events

Abstract

In time-to-event settings, the presence of competing events complicates the definition of causal effects. Here we propose the new separable effects to study the causal effect of a treatment on an event of interest. The separable direct effect is the treatment effect on the event of interest not mediated by its effect on the competing event. The separable indirect effect is the treatment effect on the event of interest only through its effect on the competing event. Similar to Robins and Richardson’s extended graphical approach for mediation analysis, the separable effects can only be identified under the assumption that the treatment can be decomposed into two distinct components that exert their effects through distinct causal pathways. Unlike existing definitions of causal effects in the presence of competing events, our estimands do not require cross-world contrasts or hypothetical interventions to prevent death. As an illustration, we apply our approach to a randomized clinical trial on estrogen therapy in individuals with prostate cancer. Supplementary materials for this article are available online.

KEYWORDS:

• Competing risks
• Direct and indirect effects
• Failure time analysis
• Lifetime and survival analysis
• Separable effects

Supplementary Materials

The online supplementary materials contain the proofs of the identification formulas and simulation studies. Furthermore, we describe conditional independencies that imply the dismissible component conditions. Computer code in R is provided as separate files.

Additional information

Funding

This work was funded by NIH grant R37 AI102634. M.J.S. was also supported by an ASISA Fellowship and the Research Council of Norway, grant NFR239956/F20.