  Effect modification occurs when the effect of the treatment on an outcome
differs according to the level of a third variable (the effect modifier, EM). A
natural way to assess effect modification is by subgroup analysis or include
the interaction terms between the treatment and the covariates in an outcome
regression. The latter, however, does not target a parameter of a marginal
structural model (MSM) unless a correctly specified outcome model is specified.
Our aim is to develop a data-adaptive method to select effect modifying
variables in an MSM with a single time point exposure. A two-stage procedure is
proposed. First, we estimate the conditional outcome expectation and propensity
score and plug these into a doubly robust loss function. Second, we use the
adaptive LASSO to select the EMs and estimate MSM coefficients. Post-selection
inference is then used to obtain coverage on the selected EMs. Simulations
studies are performed in order to verify the performance of the proposed
methods.
