An important problem in epidemiology and medical research is the estimation of a causal effect of a treatment action at a single point in time on the mean of an outcome within a population defined by strata of some of the observed covariates. Marginal structural models (MSM) are models for marginal distributions of treatment-specific counterfactual outcomes, possibly conditional on a subset of the baseline covariates, and are therefore precisely modelling such causal effects. These models were introduced by Robins (e.g., Robins (2000a), Robins (2000b), van der Laan and Robins (2002)). Inverse probability of treatment weighted estimators, double robust inverse probability of treatment weighted estimators, and G-computation (likelihood)-based estimators, have been developed and studied in detail (Robins (2000b), Neugebauer and van der Laan (2004), Yu and van der Laan (2003), van der Laan and Robins (2002)). These methods require from the user specification of a parametric model (i.e., a marginal structural model) for the treatment specific mean as function of the treatment and adjustment covariates, and a model for the nuisance parameter representing either the treatment mechanism (IPTW) and/or regression of the outcome on treatment and all baseline covariates (DR-IPTW, G-comp). In this article we develop and implement a general data adaptive loss-based estimation (as in machine learning) methodology, involving cross-validation to data adaptively select model complexities for the marginal structural model, as well as the nuisance parameter model. We implemented our data adaptive methodology in a publicly available R-package, and illustrate its practical performance with an extensive simulation study. In addition, we provide an application involving the estimation of the effect of lung function on survival in an elderly population.
