# Separable Effects for Causal Inference in the Presence of Competing Events

## TL;DR

This paper introduces separable effects to clarify causal relationships in time-to-event studies with competing risks, enabling more precise effect estimation without cross-world assumptions.

## Contribution

It proposes a novel framework for defining and identifying causal effects in the presence of competing events, avoiding cross-world contrasts and hypothetical interventions.

## Key findings

- Separable effects can be identified under the assumption of treatment decomposition.
- Application to prostate cancer trial demonstrates practical utility.
- Distinct causal pathways for treatment effects are elucidated.

## 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.