  We propose Causal Interaction Trees for identifying subgroups of participants
that have enhanced treatment effects using observational data. We extend the
Classification and Regression Tree algorithm by using splitting criteria that
focus on maximizing between-group treatment effect heterogeneity based on
subgroup-specific treatment effect estimators to dictate decision-making in the
algorithm. We derive properties of three subgroup-specific treatment effect
estimators that account for the observational nature of the data -- inverse
probability weighting, g-formula and doubly robust estimators. We study the
performance of the proposed algorithms using simulations and implement the
algorithms in an observational study that evaluates the effectiveness of right
heart catheterization on critically ill patients.
