Develop a doubly robust estimator for deterministic-exposure interrupted time series mediation

Develop a doubly robust, multiply robust, and semiparametric-efficient estimator of the natural direct and indirect effects for a single-series interrupted time series with a deterministic exposure onset.

Background

The proposed stabilized mediator-weighting estimator is singly robust: it relies on correct specification of the conditional mediator-density model. The discussion contrasts this limitation with existing multiply robust and semiparametric-efficient estimators for point exposures, as well as g-formula, weighting, and targeted-learning estimators for interventional analogues under time-varying exposures and mediators. According to the paper, none of these existing methods accommodates the combination of a single interrupted time series, deterministic exposure timing, and natural-effect mediation analysis. Constructing such an estimator is identified as the central open problem.

References

A doubly robust estimator for the single-series interrupted time series with a deterministic exposure onset is the central open problem: multiply robust and semiparametric-efficient estimators of the natural effects exist for point exposures, and g-formula, weighting, and targeted-learning estimators of interventional analogues exist for time-varying exposures and mediators, but none addresses the structure studied here.

— Causal Mediation Analysis for an Interrupted Time Series: Stabilized Mediator Weighting with an Application to a Vehicle Emissions Policy  (2608.18326 - Jayanetti et al., 18 Aug 2026) in Section 6, Discussion