Non-parametric efficient estimation of marginal structural models with multi-valued time-varying treatments

TL;DR

This paper introduces a scalable non-parametric estimator for marginal structural models with multi-valued, time-varying treatments, leveraging machine learning and semiparametric efficiency theory to improve causal inference in longitudinal studies.

Contribution

It develops a novel estimator that is efficient, asymptotically normal, and sequentially doubly robust for complex treatment settings, filling a gap in existing methods.

Findings

Estimator is efficient and asymptotically normal.

Method is sequentially doubly robust under certain conditions.

Simulation and COVID-19 case study demonstrate practical effectiveness.

Abstract

Marginal structural models are a popular method for estimating causal effects in the presence of time-varying exposures. In spite of their popularity, no scalable non-parametric estimator exist for marginal structural models with multi-valued and time-varying treatments. In this paper, we use machine learning together with recent developments in semiparametric efficiency theory for longitudinal studies to propose such an estimator. The proposed estimator is based on a study of the non-parametric identifying functional, including first order von-Mises expansions as well as the efficient influence function and the efficiency bound. We show conditions under which the proposed estimator is efficient, asymptotically normal, and sequentially doubly robust in the sense that it is consistent if, for each time point, either the outcome or the treatment mechanism is consistently estimated. We perform a simulation study to illustrate the properties of the estimators, and present the results of our motivating study on a COVID-19 dataset studying the impact of mobility on the cumulative number of observed cases.