We consider estimation of a causal effect of a possibly continuous treatment when treatment assignment is potentially subject to unmeasured confounding, but an instrumental variable is available. Our focus is on estimating heterogeneous treatment effects, so that the treatment effect can be a function of an arbitrary subset of the observed covariates. One setting where this framework is especially useful is with clinical outcomes. Allowing the causal dose-response curve to depend on a subset of the covariates, we define our parameter of interest to be the projection of the true dose-response curve onto a user-supplied working marginal structural model. We develop a targeted minimum loss-based estimator (TMLE) of this estimand. Our TMLE can be viewed as a generalization of the two-stage regression method in the instrumental variable methodology to a semiparametric model with minimal assumptions. The asymptotic efficiency and robustness of this substitution estimator is outlined. Through detailed simulations, we demonstrate that our estimator's finite-sample performance can beat other semiparametric estimators with similar asymptotic properties. In addition, our estimator can greatly outperform standard approaches. For instance, the use of data-adaptive learning to achieve a good fit can lead to both lower bias and lower variance than for an incorrectly specified parametric estimator. Finally, we apply our estimator to a real dataset to estimate the effect of parents' education on their infant's health.
Toth, Boriska and van der Laan, Mark J., "TMLE for Marginal Structural Models Based on an Instrument" (June 2016). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 350.