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Causal treatment effect decompositions with time-to-event outcomes under competing events

This paper proposes a novel four-way causal decomposition of treatment effects on time-to-event outcomes in the presence of competing events, utilizing cross-world estimands to disentangle distinct mechanisms and provide causally interpretable insights validated through two randomized trials.

Original authors: Mikko Valtanen, Tommi Härkänen, Jenni Lehtisalo, Tiia Ngandu, Miia Kivipelto, Kari Auranen

Published 2026-05-20

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CC BY 4.0

Original authors: Mikko Valtanen, Tommi Härkänen, Jenni Lehtisalo, Tiia Ngandu, Miia Kivipelto, Kari Auranen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to judge how well a new medicine works to prevent a specific illness, let's call it "The Target." But there's a problem: patients might die from something else first, let's call it "The Competitor."

If a patient dies from "The Competitor," they can't get "The Target." This makes it very hard to tell if the medicine actually helped prevent "The Target," or if it just changed the timing of other events.

This paper proposes a new way to break down the "total effect" of a treatment into four distinct pieces to understand exactly how the medicine works (or doesn't work) in this messy situation.

Here is the simple breakdown using an analogy of a Race with Obstacles.

The Race Analogy

Imagine a race where runners are trying to reach the finish line ("The Target"). However, there are obstacles on the track that can knock them out of the race early ("The Competitor").

The researchers ask: "How much did the medicine actually help the runners reach the finish line, and how much of that 'help' was just an illusion caused by the obstacles?"

They split the answer into four parts:

1. The Controlled Direct Effect (The "Pure" Medicine)

This measures how well the medicine works if we magically remove all obstacles from the track.

What it tells us: Does the medicine actually make the runners faster, regardless of the obstacles?
In the paper: This is the effect of the treatment on the target event if the competing event never happened.

2. The Reference Interception (The "Unchanged" Obstacles)

This measures how the obstacles naturally stop runners, even if the medicine doesn't change the obstacles at all.

What it tells us: Sometimes, the medicine helps the runner, but the obstacle (the competing event) still knocks them out before they finish. This part captures the "loss" caused by the obstacles existing in the real world, even if the medicine didn't make the obstacles worse or better.
In the paper: This happens when the competing event intercepts the target event based on its natural behavior under the "no treatment" scenario.

3. The Mediated Interception (The "Changed" Obstacles)

This measures how much the medicine changed the obstacles themselves, which then changed the race outcome.

What it tells us: Did the medicine make the obstacles appear sooner or later?
- Example A: If the medicine makes obstacles appear later, runners have more time to reach the finish line. This looks like a benefit, but it's actually because the obstacles were delayed.
- Example B: If the medicine makes obstacles appear sooner, runners get knocked out faster. This looks like a harm, but it's because the obstacles were accelerated.
In the paper: This is the change in interception that happens specifically because the treatment altered the competing event.

4. The Pure Indirect Effect (The "Side-Door" Exit)

This measures how the medicine changes the obstacles, which then prevents the target event from ever happening, even if the medicine had no direct effect on the target itself.

What it tells us: Sometimes the medicine doesn't help the runner at all, but it speeds up the obstacles so much that the runner is knocked out before they even have a chance to try. This "prevention" of the target event is actually a side effect of speeding up the competitor.
In the paper: This occurs when the treatment affects the competing event, which then intercepts the target event, even if the treatment has no direct effect on the target.

Why Do We Need This?

The paper argues that looking at the "Total Effect" (the final result) is often misleading.

Scenario 1: A medicine might look like it cures a disease because it delays a competing death. But if you look at the four parts, you see the medicine didn't actually cure the disease; it just delayed the other death, giving the disease more time to happen.
Scenario 2: A medicine might look like it causes a disease because it speeds up a competing death. But the four parts reveal the medicine was actually very good at curing the disease (Part 1), but it also sped up the competing death (Part 3 & 4), which hid the cure.

Real-World Examples from the Paper

The authors tested this "Four-Way Decomposition" on two real medical studies:

The FINGER Study (Lifestyle Intervention):
- Goal: Prevent cognitive decline.
- Competitor: Death from other causes.
- Result: The lifestyle intervention delayed both cognitive decline and other deaths. The analysis showed that the benefit was mostly the "Pure" effect (Part 1), but because it also delayed other deaths, it slightly increased the risk of cognitive decline later on (Part 4).
The Prostate Cancer Trial (Estrogen Treatment):
- Goal: Prevent death from prostate cancer.
- Competitor: Death from other causes.
- Result: The treatment actually increased the risk of dying from other causes. This made it look like the treatment prevented prostate cancer deaths. The decomposition showed that while the treatment did have a direct benefit (Part 1), a large part of the "benefit" was actually just because the treatment killed patients from other causes faster (Part 3 & 4), leaving less time for prostate cancer to kill them.

The Bottom Line

This paper provides a mathematical "lens" to separate the true power of a medicine from the confusing side effects caused by other things happening to patients at the same time. It helps researchers answer: "Did the medicine actually work, or did it just change the timing of other events?"

The authors note that this method relies on specific assumptions (like no hidden factors changing over time) and works best when we can measure the starting conditions of the patients accurately.

Technical Summary: Causal Treatment Effect Decompositions with Time-to-Event Outcomes under Competing Events

Problem Statement
Inference regarding treatment effects for time-to-event outcomes is frequently complicated by competing events, which prevent the event of interest (the target event) from occurring. This issue is particularly acute when the treatment itself influences the occurrence of the competing event. In such scenarios, standard risk-based measures can yield misleading interpretations: a treatment may appear protective against the target event simply by accelerating the competing event (thereby reducing the time available for the target to occur), or conversely, appear harmful by delaying the competing event. Existing frameworks, such as the separation of cause-specific and net risks or the separable effects framework, often rely on restrictive assumptions (e.g., the feasibility of decomposing a treatment into independent components) or fail to comprehensively distinguish the underlying mechanisms generating the apparent total effect.

Methodology
The authors propose a four-way decomposition of the total treatment effect (TE) on a target event in the presence of competing risks. This approach is grounded in a causal model utilizing cross-world estimands.

Data Structure and Notation: The study employs a discrete-time model with binary treatment $A$ , a target event indicator process $Y$ , a competing event indicator process $D$ , and a censoring process $C$ .
Joint Process and Cross-World Estimators: The core methodological innovation is the definition of a joint process $Z^{a', a''}$ constructed by combining the indicators of the two events under hypothetical interventions where the competing event is eliminated. Specifically, $Y^{a', \emptyset}$ represents the target event under treatment $a'$ with the competing event process eliminated, and $D^{\emptyset, a''}$ represents the competing event under treatment $a''$ with the target event eliminated. The joint process $Z^{a', a''}$ tracks these until one event occurs.
Four-Way Decomposition: The total effect is partitioned into four distinct components based on these cross-world quantities:
- Controlled Direct Effect (CDE): The treatment effect in a hypothetical world where the competing event is eliminated.
- Reference Interception ( $INT_{ref}$ ): The contribution to the total effect arising from the interception of target events by the competing event under the reference (untreated) treatment level.
- Mediated Interception ( $INT_{med}$ ): The change in interception effects when the competing event is considered under the treated level versus the reference level. This component is non-zero only if the treatment affects the competing event.
- Pure Indirect Effect (PIE): The difference in intercepted portions when the target event follows its distribution under the reference treatment, reflecting how the treatment's effect on the competing event alters the risk of the target event.
Identification: The paper specifies a set of assumptions required to identify these population-level averages from observed data:
- Exchangeability: Conditional on baseline covariates, the controlled processes are independent of treatment assignment; sequential exchangeability holds for the processes.
- Consistency: Observed outcomes correspond to potential outcomes under the observed treatment.
- Positivity: It is possible to survive up to the end of follow-up for all covariate patterns.
  Under these assumptions, the components are identified using cause-specific hazards derived from observed data.

Key Results and Illustrations
The authors demonstrate the utility of this decomposition through simulation and two real-world randomized trials:

Simulation Scenarios: Three scenarios were simulated to illustrate how the components behave under different treatment-competing event dynamics:
1. Treatment delays the competing event: The total effect is driven by the CDE, but the Pure Indirect Effect (PIE) introduces a harmful contribution because delaying the competing event allows more time for the target event to occur.
2. Treatment accelerates the competing event: The total effect is beneficial. Here, the Pure Indirect Effect contributes positively because accelerating the competing event reduces the time available for the target event.
3. Treatment does not affect the competing event: The mediated interception and pure indirect effects are zero, highlighting that the competing event still influences the apparent total effect via the reference interception, even if the treatment does not alter the competing event's risk.
Empirical Applications:
- FINGER Trial (Cognitive Impairment/CVD): Analyzing a lifestyle intervention where the treatment likely delays both CVD and death. The decomposition showed the Controlled Direct Effect dominated, with minimal interference from competing events, suggesting the treatment effect on CVD is robust.
- Prostate Cancer Trial (DES vs. Placebo): Analyzing a treatment (DES) that increases the risk of death from other causes (competing event) while reducing prostate cancer mortality. The decomposition revealed that while the Controlled Direct Effect showed a protective effect, the Pure Indirect Effect also contributed to the apparent benefit by accelerating other-cause deaths, thereby reducing the time for prostate cancer death to occur.

Significance and Claims
The paper claims to provide a comprehensive framework for characterizing treatment effects in the presence of competing events without requiring the restrictive assumption that a treatment can be physically decomposed into independent components (as required by the separable effects framework).

Mechanistic Insight: The four-way decomposition reveals the specific role of the competing event in shaping the apparent treatment effect, distinguishing between mechanisms where the treatment acts directly on the target, acts via the competing event, or where the competing event intercepts the target.
Causal Interpretability: By relying on cross-world estimands, the authors define estimands that are causally interpretable even when the treatment influences the competing event.
Flexibility: The components can be recombined to form other standard estimands, such as the Natural Direct Effect (NDE) and Natural Indirect Effect (NIE), or the Total Direct Effect (TDE), allowing researchers to tailor the analysis to specific research questions (e.g., etiological mechanisms vs. holistic health improvements).
Limitations: The authors note that the approach currently relies on baseline covariates; the presence of time-varying confounders poses significant challenges for cross-world estimands, as it would require assumptions about unobservable longitudinal trajectories under conflicting treatment assignments.

In conclusion, the proposed decomposition serves as a basis for defining causally interpretable estimands that account for the complex interplay between treatment, target events, and competing events, offering a more nuanced understanding of treatment efficacy than total effect measures alone.