Estimating hypothetical estimands with time-to-event intercurrent events using controlled direct effect under semi-competing risk framework

Estimating the effect of clinical trials when there are time-to-event intercurrent events (ICEs) is an unresolved methodological issue. Hypothetical strategy is one of the five approaches proposed by the ICH E9 (R1) addendum for handling ICEs, and its estimands align with the controlled direct effect (CDE) in causal mediation. But no current study shows how to estimate the CDE given time-to-event ICEs. This study aims to propose an estimator unifying hypothetical strategy and causal mediation under a semi-competing framework and evaluate its accuracy targeting the hypothetical estimands. The effect of treatment under a hypothetical scenario in which the ICE does not occur was defined as the controlled direct effect (CDE) within a semi-competing risks framework. A generalized Nelson–Aalen estimator was developed, and its performance on the cumulative-hazard, survival, and restricted mean survival time (RMST) scales was evaluated in a structured simulation study based on a cardiovascular trial setting. The hypothetical, treatment-policy, and composite-variable estimators were evaluated, and differences between the treatment-policy or composite-variable estimates and the CDE estimand were summarized as estimand discrepancies. In 760 simulation replicates, the proposed estimator showed small bias across the prespecified follow-up times. Relative bias ranged from − 4.54% to 2.83% on the cumulative-hazard scale, from − 5.13% to 1.60% on the survival scale, and from − 8.84% to − 2.79% on the RMST scale. The three estimators closely tracked the true values of their corresponding estimands, with coverage probabilities ranging from 93.42% to 95.79% on the cumulative-hazard scale. The treatment-policy and composite-variable estimands showed different degrees of discrepancy from the CDE estimand over follow-up. In the case study, the three estimand strategies produced different estimates of the contrast in treatment-related death between the ALL and AML groups. The proposed estimator showed unbiased estimation for the hypothetical CDE under the simulation settings considered. The treatment-policy and composite-variable strategies produced different degrees of discrepancy for the CDE.