Longitudinal weighted and trimmed treatment effects with flip interventions

Weighting and trimming are popular methods for addressing positivity violations in causal inference. While well-studied with single-timepoint data, standard methods do not easily generalize to longitudinal data and remain vulnerable to time-varying positivity violations. We extend weighting and trimming to longitudinal settings via stochastic “flip” interventions, which maintain the treatment status of subjects who would have received the target treatment, and flip others’ treatment to the target with probability equal to their weight (e.g., overlap weight, trimming indicator). In single-timepoint data, we show that flip interventions yield a broad class of weighted average treatment effects, providing a novel policy interpretation to these estimands. For longitudinal data, flip interventions enable interpretable weighting or trimming on time-varying covariates and, crucially, can ensure identifiability under arbitrary positivity violations. We derive a flexible estimator based on efficient influence functions when weights are smooth functions of propensity scores. Namely, we construct a new sequentially second-order estimator achieving root-n consistency and asymptotic normality under nonparametric conditions. Finally, we illustrate our methods with simulations and an analysis of the effect of union membership on earnings.