Risk factor adjustment in marginal structural model estimation of optimal treatment regimes

Marginal structural models (MSMs) are an increasingly popular tool, particularly in epidemiological applications, to handle the problem of time-varying confounding by intermediate variables when studying the effect of sequences of exposures. Considerable attention has been devoted to the optimal choice of treatment model for propensity score-based methods and, more recently, to variable selection in the treatment model for inverse weighting in MSMs. However, little attention has been paid to the modeling of the outcome of interest, particularly with respect to the best use of purely predictive, non-confounding variables in MSMs. Four modeling approaches are investigated in the context of both static treatment sequences and optimal dynamic treatment rules with the goal of estimating a marginal effect with the least error, both in terms of bias and variability.