A causal framework for classical statistical estimands in failure time settings with competing events (1806.06136v3)

Abstract: In failure-time settings, a competing risk event is any event that makes it impossible for the event of interest to occur. For example, cardiovascular disease death is a competing event for prostate cancer death because an individual cannot die of prostate cancer once he has died of cardiovascular disease. Various statistical estimands have been defined as possible targets of inference in the classical competing risks literature. Many reviews have described these statistical estimands and their estimating procedures with recommendations about their use. However, this previous work has not used a formal framework for characterizing causal effects and their identifying conditions, which makes it difficult to interpret effect estimates and assess recommendations regarding analytic choices. Here we use a counterfactual framework to explicitly define each of these classical estimands. We clarify that, depending on whether competing events are defined as censoring events, contrasts of risks can define a total effect of the treatment on the event of interest, or a direct effect of the treatment on the event of interest not mediated through the competing event. In contrast, regardless of whether competing events are defined as censoring events, counterfactual hazard contrasts cannot generally be interpreted as causal effects. We illustrate how identifying assumptions for all of these counterfactual estimands can be represented in causal diagrams in which competing events are depicted as time-varying covariates. We present an application of these ideas to data from a randomized trial designed to estimate the effect of estrogen therapy on prostate cancer mortality.

A Causal Framework for Failure-Time Settings with Competing Events

This paper presents an in-depth exploration of causal inference related to failure-time settings with competing events. The authors advocate for a counterfactual framework to redefine classical statistical estimands, with specific emphasis on identifying causal effects and acknowledging censoring events. The statistical literature recognizes various estimands, such as marginal cumulative incidence and cause-specific cumulative incidence, but these have historically lacked formal causal definitions. This paper addresses such gaps, proposing a framework to elucidate causal interpretations, particularly in the presence of competing risks.

Key Contributions

• Causal Effect Definitions: The paper distinguishes between total and direct effects of treatment on the event of interest. It is noted that total effects encompass all causal pathways, including those mediated by competing events, whereas direct effects exclude mediation by competing events. This distinction highlights the necessity of specifying whether competing events are considered censoring events.
• Counterfactual Framework: Using a counterfactual construct, the paper defines risks and hazards in competing events settings. This approach introduces two counterfactual definitions for risks and three for hazards, providing a structured interpretation of these classical estimands in causal terms.
• Causal Diagrams: The authors emphasize the utility of causal diagrams for representing identifying assumptions. Competing events are illustrated as time-varying covariates, which assists in visualizing and evaluating assumptions in a rigorous manner.
• Data Analysis Application: An application of the methodologies to a randomized trial assessing estrogen therapy's impact on prostate cancer mortality demonstrates how these causal frameworks can be operationalized and analyzed using real-world data.

Numerical Results and Claims

The paper delivers several numerical results concerning the effects of estrogen therapy. These results underscore the protective total effects on prostate cancer mortality while indicating possible harmful effects on competing events, such as death from other causes. Such findings reveal the importance of considering both total and direct effects in making informed decisions regarding treatment impacts.

Implications and Future Directions

The proposed causal framework is crucial for refining interpretations of competing risks in failure-time settings. Practically, it facilitates more nuanced analyses of treatment effects, particularly when outcomes are affected by intermediate events that compete with the primary event of interest. Theoretically, it opens pathways for further methodological advancements, especially in formulating identifiable causal effects under complex scenarios with competing risks.

Looking forward, new effect definitions that circumvent the drawbacks of current approaches are vital. These developments will contribute to more robust evaluations of biological harm or benefit in treatment scenarios and offer practical guidance for researchers dealing with complex event data.

Conclusion

This paper is a significant step towards formalizing causal inference frameworks for failure-time settings with competing events. By focusing on counterfactual reasoning and causal diagrams, the authors effectively bridge the gap between classical statistical estimands and their causal interpretations. The proposed methodologies are comprehensive and offer critical insights applicable to both experimental and observational paper designs. διa