Marginal Structural Models for Time-varying Endogenous Treatments: A Time-Varying Instrumental Variable Approach

TL;DR

This paper extends marginal structural models to settings with unmeasured confounding by using time-varying instrumental variables, providing new identification conditions and semiparametric estimators.

Contribution

It introduces identification conditions for MSMs with time-varying IVs when sequential randomization fails, and develops a class of robust estimators incorporating these IVs.

Findings

Derived a large class of semiparametric estimators for MSMs with IVs.

Extended inverse-probability weighting to include time-varying IVs.

Established influence functions for robust estimation.

Abstract

Robins (1998) 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. He established identification of MSM parameters under a sequential randomization assumption (SRA), which essentially rules out unmeasured confounding of treatment assignment over time. In this technical report, we consider sufficient conditions for identification of MSM parameters with the aid of a time-varying instrumental variable, when sequential randomization fails to hold due to unmeasured confounding. Our identification conditions essentially require that no unobserved confounder predicts compliance type for the time-varying treatment, the longitudinal generalization of the identifying condition of Wang and Tchetgen Tchetgen (2018). Under this assumption, We derive a large class of semiparametric estimators that extends standard inverse-probability weighting (IPW), the most popular approach for estimating MSMs under SRA, by incorporating the time-varying IV through a modified set of weights. The set of influence functions for MSM parameters is derived under a semiparametric model with sole restriction on observed data distribution given by the MSM, and is shown to provide a rich class of multiply robust estimators, including a local semiparametric efficient estimator.