📈 economics

Estimating Pathway Treatment Effects in the Presence of Intermediate Events with Multi-State Data

This paper proposes a semiparametrically efficient framework using hypothetical interventions on multi-state transitions to identify and estimate pathway-specific treatment effects in the presence of treatment-induced confounding from intermediate events, demonstrating its application to the LEADER Trial to reveal how liraglutide reduces mortality primarily through cardiovascular event mediation.

Original authors: Yuhao Deng, Haoyu Wei, Donglin Zeng, Rui Song, Xiao-Hua Zhou

Published 2026-08-25

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CC BY 4.0

Original authors: Yuhao Deng, Haoyu Wei, Donglin Zeng, Rui Song, Xiao-Hua Zhou

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

When doctors test a new medicine, they often watch to see if it helps patients live longer. But life is rarely a straight line from taking a pill to a final outcome. In between, patients might experience other health events, like a heart attack or kidney trouble, which can change their risk of dying. These intermediate events create a complex web of possibilities. A drug might work by preventing a heart attack, which then prevents death. Or it might work directly on the heart without causing any intermediate changes. Sometimes, a drug might even cause one problem while preventing another. To truly understand how a medicine works, researchers need to untangle these different routes. They need to know not just if the drug saves lives, but exactly which steps in the patient's journey the drug is influencing. This is difficult because the events that happen along the way can confuse the picture, making it hard to tell if the drug is acting directly or through a chain reaction.

A team of researchers has developed a new way to map these hidden pathways using data from clinical trials. Instead of trying to force the data to fit old, rigid rules that often fail when events are complicated, they created a method that imagines "what if" scenarios for every single step a patient could take. They treat the risk of moving from one health state to another—like moving from being healthy to having a heart attack—as something that can be adjusted independently. By mathematically simulating a world where they change the risk of just one specific step while leaving everything else alone, they can isolate the effect of the drug on that specific transition. This approach allows them to see the drug's impact on every possible route a patient might take, from the start of the trial to the final outcome, without needing to make impossible assumptions about unobserved factors.

The researchers applied this new method to data from the LEADER trial, a massive study involving over 9,000 people with type 2 diabetes who were at high risk for heart problems. The trial tested a drug called liraglutide against a placebo. The researchers were interested in how the drug affected the risk of death, but they knew that death could happen in different ways: directly from a cardiovascular event, from a non-cardiovascular cause, or after a patient first suffered a non-fatal heart or kidney event. Using their new framework, they broke down the journey from the start of the study to death into five distinct paths. These paths included going straight to death, going through a major heart event first, going through a kidney or eye problem first, or taking a longer route through both types of events before dying.

The analysis revealed that liraglutide significantly reduced the risk of major heart events and kidney or eye problems. When the researchers looked at how these reductions influenced the risk of death, they found a clear story. The drug did not have a direct effect on preventing death from causes unrelated to the heart or kidneys. However, it did have a strong direct effect on reducing the risk of major heart events and kidney damage. Crucially, the study showed that the reduction in overall death rates was primarily driven by the drug's ability to stop these intermediate events. By preventing heart attacks and kidney issues, the drug indirectly lowered the chance of dying. The researchers found that the most significant benefit came from preventing the initial heart events, which then stopped the chain of events that would have led to death.

The study also tested whether the drug had any hidden negative effects or if the results were skewed by unknown factors. They ran simulations to check if their findings held up even if there were unmeasured variables at play. The results remained consistent, suggesting that the influence of any hidden factors was weak. The researchers concluded that the drug's life-saving power comes almost entirely from its ability to stop the specific intermediate events of heart and kidney damage. This level of detail is something previous methods could not provide with the same clarity. By mapping out the exact transitions where the drug works, the study offers a precise view of the medicine's mechanism. It confirms that for patients at high risk, preventing the first major vascular event is the key to extending life, and it provides a new tool for doctors to understand how treatments work in complex, real-world scenarios.

Technical Summary: Estimating Pathway Treatment Effects in the Presence of Intermediate Events with Multi-State Data

Problem Statement
In clinical trials evaluating survival endpoints, patients often experience multiple intermediate events before reaching a primary terminal event (e.g., death). These events create complex multi-state data structures with competing and semi-competing risks. Traditional mediation frameworks, such as natural effects and separable effects, struggle in this context. Natural effects rely on sequential ignorability, which is violated when intermediate events act as treatment-induced confounders for subsequent transitions. Separable effects require the treatment to be decomposable into components that isolate specific pathways, a condition that is often biologically unidentifiable and fails to account for unobserved treatment-induced confounding inherent in disease progression. Consequently, existing methods cannot reliably identify treatment effects along specific transition pathways or decompose total effects into transition-, event-, and path-specific components without making untestable assumptions about unmeasured confounding.

Methodology
The authors propose a framework based on randomized interventional effects adapted for multi-state data. Instead of attempting to isolate natural direct/indirect effects, the method envisions hypothetical interventions on the instantaneous risk (hazard) of transitions between states.

Hypothetical Interventions: The framework defines a vector of interventions $a = (a_{kg})$ for each transition $(k, g)$ in the state graph. An intervention $a_{kg}=1$ sets the transition hazard to the level observed under treatment, while $a_{kg}=0$ sets it to the control level. This allows for the construction of counterfactual transition trajectories where specific pathways are manipulated while others remain under control.
Identifiability: The counterfactual cumulative incidence function (CIF) for reaching a state $j$ is identified by integrating transition hazards derived from observed data. Crucially, the method marginalizes over potential treatment-induced confounders within the definition of the hazard, rendering the estimand identifiable without requiring cross-world independence assumptions (sequential ignorability).
Estimation:
- Efficient Influence Function (EIF): The authors derive the EIF for the counterfactual CIF under an extended Markovness assumption (where transition hazards depend on the set of visited states rather than the specific timing of past transitions).
- Multiply Robust Estimator: A one-step estimator is constructed using the EIF. This estimator is multiply robust, meaning it remains consistent if either:
  - All transition hazards along a path are correctly specified; OR
  - The propensity score and censoring hazard are correctly specified, and all but one transition hazard along the path are correctly specified.
- Efficiency: The estimator is semiparametrically efficient, achieving the lowest possible asymptotic variance under the model assumptions.
Inference: The framework provides methods for hypothesis testing using the restricted mean survival time lost (RMSTL) and constructs confidence intervals based on the asymptotic normality of the EIF-based estimator.

Key Contributions

Novel Estimands: The paper defines transition-specific, event-specific, and path-specific treatment effects for multi-state data, allowing researchers to pinpoint exactly where and how a treatment exerts its influence (e.g., via a specific transition or a specific sequence of events).
Robustness to Confounding: By utilizing randomized interventional effects, the method avoids the untestable sequential ignorability assumption required by natural effects and the biologically implausible component isolation required by separable effects. It remains valid even in the presence of unmeasured treatment-induced confounding.
Statistical Efficiency: The derivation of the EIF and the construction of a multiply robust, semiparametrically efficient estimator address the inefficiency and model-dependence of standard plug-in estimators in multi-state settings.
Decomposition of Total Effects: The framework demonstrates that the total treatment effect on a terminal event can be decomposed into a sum of interventional effects arising from sequentially intervening at each transition.

Results (Application to LEADER Trial)
The authors applied their framework to the LEADER trial data, which investigated the effect of liraglutide on cardiovascular outcomes in patients with type 2 diabetes. The multi-state model included baseline (O), expanded major adverse cardiovascular events (EMACE, E), microvascular events (MVE, M), and death (D).

Direct Effects: Liraglutide showed significant direct effects in reducing the risk of EMACE ( $P=0.0013$ ) and MVE ( $P=0.0040$ ). However, the direct effect on other-cause death was not significant ( $P=0.8638$ ).
Path-Specific Effects: The analysis revealed that the reduction in all-cause mortality is primarily mediated through the pathway involving EMACE. Specifically, the path-specific effect along $O \to E \to D$ was significant, contributing to a gain in restricted mean survival time. The effect along the direct path $O \to D$ was negligible.
Mechanism: The study concluded that liraglutide reduces all-cause mortality largely by preventing non-fatal EMACE and MVE, which subsequently lowers the risk of death. It does not appear to directly affect non-cardiovascular causes of death.

Significance and Claims
The paper claims that its framework provides a rigorous, assumption-light approach to dissecting complex treatment mechanisms in survival analysis. By moving away from untestable causal assumptions toward hypothetical interventions on transition hazards, the method enables the examination of treatment effects through each transition, on each event, and along each path. The authors assert that this approach can inform the development of optimal dynamic treatment policies and enhance the understanding of drug efficacy and safety by identifying specific biological pathways (e.g., targeting high-risk transitions for EMACE) rather than just overall survival outcomes. The paper notes that while the method recovers useful knowledge even in the presence of unmeasured confounding, it does not claim to recover "sharp" causal effects if time-varying confounding offsets genuine effects, but rather provides a robust basis for motivating further biological investigation.

Technical Summary: Estimating Pathway Treatment Effects in the Presence of Intermediate Events with Multi-State Data

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