Instrumental Variable Estimation of Marginal Structural Mean Models for Time-Varying Treatment

Robins introduced Marginal Structural Models (MSMs), a general class of counterfactual models for the joint effects of time-varying treatment regimes in complex longitudinal studies subject to time-varying confounding. In his work, identification of MSM parameters is established under a Sequential Randomization Assumption (SRA), which rules out unmeasured confounding of treatment assignment over time. We consider sufficient conditions for identification of the parameters of a subclass, Marginal Structural Mean Models (MSMMs), when sequential randomization fails to hold due to unmeasured confounding, using instead a time-varying instrumental variable. Our identification conditions require that no unobserved confounder predicts compliance type for the time-varying treatment. We describe a simple weighted estimator and examine its finite-sample properties in a simulation study. We apply the proposed estimator to examine the effect of delivery hospital type on neonatal survival probability. for this article are available online.

Automated summary

This article introduces Marginal Structural Models (MSMs), a type of counterfactual models for studying the joint effects of time-varying treatment regimes in complex longitudinal studies subject to time-varying confounding. The author establishes identification of MSM parameters under a Sequential Randomization Assumption (SRA), which assumes no unmeasured confounding of treatment assignment over time. When the Sequential Randomization Assumption fails, we propose using a time-varying instrumental variable to identify the parameters of a subset called Marginal Structural Mean Models (MSMMs). The article presents a weighted estimator and evaluates its performance through simulation studies, applying it to investigate the effect of delivery hospital type on neonatal survival probability.