Causal inference in multi-state models with multiple intermediate events
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Multi-state models are widely used in biomedical sciences to illustrate the mechanisms of disease progression. However, causal inference in these models is challenging due to the complex interaction between treatment and history in transition rates. To overcome these challenges, we adopt the counterfactual cumulative incidence of an event as the estimand. Treatment effects are then defined by contrasting counterfactual cumulative incidences under different combinations of transition-specific treatment components. Under a dismissible treatment components condition, we derive semiparametric efficient estimators for the counterfactual cumulative incidences and treatment effects. Additionally, we provide hypothesis testing methods to evaluate these treatment effects. The proposed framework has three key applications: (1) estimating path-specific treatment effects, (2) detecting which events are affected by treatment, and (3) inferring optimal dynamic treatment regimes. We demonstrate the utility of this framework through a real-world application in the LEADER trial.