Primary Submission Category: Marginal Structural Models
Efficient Counterfactual Mean Estimation Implies Efficient Marginal Structural Model Estimation
Authors: Jacob M Chen, Ilya Shpitser,
Presenting Author: Jacob M Chen*
Marginal structural models (MSMs) are a class of causal models that allow for the estimation of causal effects from observational data that are widely used due to their interpretability as well as generalizability to continuous treatments and multiple treatments in longitudinal settings. An MSM posits that the expectation of the counterfactual outcome had treatments been intervened on – sometimes also conditional on a subset of observed pretreatment covariates – is a function indexed by a finite set of parameters. We aim to estimate the parameters of this function, which allows us to infer causal quantities of interest, such as the average causal effect (ACE) or conditional ACE. Estimation strategies for parameters of an MSM are well studied under the coarsening at random (CAR) assumption, which states that all variables affecting treatment assignment are observed. Here, we show how to estimate the parameters of any MSM as long as the counterfactual mean is identified even when CAR does not hold, such as in the frontdoor and proximal causal learning settings, using a loss minimization technique. Our estimator for the MSM parameters inherits desirable properties from the mean estimator, if the mean estimator possesses such qualities, such as robustness to misspecification of a subset of nuisance models and asymptotic normality. Our results will allow practitioners to employ MSMs in a wider range of settings, especially when unmeasured confounding is unavoidable.