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.

翻译：边际结构模型是估计时变暴露下因果效应的一种常用方法。尽管应用广泛，目前尚不存在适用于多值且时变处理的边际结构模型的可扩展非参数估计量。本文结合机器学习与纵向研究中半参数效率理论的最新进展，提出了此类估计量。该估计量建立在对非参数识别泛函的研究基础上，包括一阶冯·米塞斯展开、有效影响函数及效率界。我们证明了该估计量在满足特定条件时具有有效性、渐近正态性及序列双重稳健性——即只要在每个时间点上结果模型或处理机制之一被一致估计，该估计量即具有一致性。我们通过模拟研究展示了估计量的性质，并在COVID-19数据集上开展了关于流动性对累计确诊病例数影响的实证研究，呈现了相关结果。