Doubly Robust Adaptive LASSO for Effect Modifier Discovery

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.