652 – Miscellaneous Topics in Nonparametric Problems
TMLE for Marginal Structural Models Based on Instrument
Boriska Toth
Mark van der Laan
University of California at Berkeley School of Public Health
We consider estimation of a causal effect of a possibly continuous treatment when treatment assignment is potentially subject to unmeasured confounding, but an instrument is available. Our semiparametric structural equation for the outcome as a function of treatment and covariates assumes that the effect of treatment is linear, conditional on the observed baseline covariates. This weakens the commonly made linearity assumption. The structural equation also assumes that the conditional mean of its error, given the instrument and baseline covariates, equals zero, which is the typical instrumental variable assumption. We establish identi�ability of marginal causal effects of the treatment as de�ned by projections of the true causal dose-response curve onto a user supplied working marginal structural model. We derive the ef�cient influence curve of the resulting statistical parameter/estimand, and develop a targeted minimum loss-based estimator of this estimand. The TMLE can be viewed as a generalization of the two-stage regression method in the instrumental variable methodology to semiparametric models. The asymptotic ef�ciency and robustness of this substitution estimator is outlined. Finally, we implement this new estimator and evaluate its performance through a simulation study.
