High-dimensional confounding adjustment using continuous spike and slab priors

In observational studies, estimation of a causal effect of a treatment on an outcome relies on proper adjustment for confounding. If the number of the potential confounders ( p ) is larger than the number of observations ( n ), then direct control for all potential confounders is infeasible. Existing approaches for dimension reduction and penalization are generally aimed at predicting the outcome, and are less suited for estimation of causal effects. Under standard penalization approaches (e.g. Lasso), if a variable X j is strongly associated with the treatment T but weakly with the outcome Y , the coefficient β j will be shrunk towards zero thus leading to confounding bias.