Causal inference for calibrated scaling interventions on time-to-event processes

This work develops a flexible inferential framework for nonparametric causal inference in time-to-event settings, based on stochastic interventions defined through multiplicative scaling of the intensity governing an intermediate event process. These interventions induce a family of estimands indexed by a scalar parameter α, representing effects of modifying event rates while preserving the temporal and covariate-dependent structure of the observed data generating mechanism. To enhance interpretability, we introduce calibrated interventions, where α is chosen to achieve a pre-specified goal, such as a desired level of cumulative risk of the intermediate event, and define corresponding composite target parameters capturing the downstream effects on the outcome process. This yields clinically meaningful contrasts while avoiding unrealistic deterministic intervention regimes. Under a nonparametric model, we derive efficient influence curves for α-indexed, calibrated, and composite target parameters and establish their double robustness properties. We further sketch a targeted maximum likelihood estimation (TMLE) strategy that accommodates flexible, machine learning based nuisance estimation. The proposed framework applies broadly to (causal) questions involving time-to-event treatments or mediators and is illustrated through different examples event-history settings. A simulation study demonstrates finite-sample inferential properties, and highlights the implications of practical positivity violations when interventions extend beyond observed data support.

💡 Research Summary

This paper introduces a novel causal inference framework for continuous‑time event‑history data that is built around stochastic interventions which scale the intensity of an intermediate event (e.g., treatment initiation, disease onset) by a positive scalar α. The authors define the α‑scaling intervention by replacing the original predictable intensity λz(t|F_{t‑}) with λz,α(t|F_{t‑}) = α·λz(t|F_{t‑}). The parameter α has a clear hazard‑ratio interpretation: α=1 corresponds to the observed practice, α→0 to complete prevention of the intermediate event, and α>1 to an accelerated event rate. Because the scaling is multiplicative, the dependence of λz on the subject’s past history is preserved, allowing heterogeneous risk profiles to remain intact under the intervention.

To make the intervention clinically interpretable, the authors propose a calibration step. A user‑specified target γ (for example, a desired cumulative incidence of the intermediate event by a fixed horizon) is linked to α through the mapping g(α)=Pα(Nz(τ)=1). The calibrated scaling factor α̂ is obtained as the inverse g^{-1}(γ). This calibrated α̂ defines a “composite causal parameter” Ψ(α̂)=E_{α̂}