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

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.

General targeted machine learning for modern causal mediation analysis

Causal mediation analyses investigate the mechanisms through which causes exert their effects, and are therefore central to scientific progress. The literature on the non-parametric definition and identification of mediational effects in rigourous causal models has grown significantly in recent years, and there has been important progress to address challenges in the interpretation and identification of such effects. Despite great progress in the causal inference front, statistical methodology for non-parametric estimation has lagged behind, with few or no methods available for tackling non-parametric estimation in the presence of multiple, continuous, or high-dimensional mediators. In this paper we show that the identification formulas for six popular non-parametric approaches to mediation analysis proposed in recent years can be recovered from just two statistical estimands. We leverage this finding to propose an all-purpose one-step estimation algorithm that can be coupled with machine learning in any mediation study that uses any of these six definitions of mediation. The estimators have desirable properties, such as $\sqrt{n}$-convergence and asymptotic normality. Estimating the first-order correction for the one-step estimator requires estimation of complex density ratios on the potentially high-dimensional mediators, a challenge that is solved using recent advancements in so-called Riesz learning. We illustrate the properties of our methods in a simulation study and illustrate its use on real data to estimate the extent to which pain management practices mediate the total effect of having a chronic pain disorder on opioid use disorder.