Causal interaction trees: Finding subgroups with heterogeneous treatment effects in observational data.

We introduce causal interaction tree (CIT) algorithms for finding subgroups of individuals with heterogeneous treatment effects in observational data. The CIT algorithms are extensions of the classification and regression tree algorithm that use splitting criteria based on subgroup-specific treatment effect estimators appropriate for observational data. We describe inverse probability weighting, g-formula, and doubly robust estimators of subgroup-specific treatment effects, derive their asymptotic properties, and use them to construct splitting criteria for the CIT algorithms. We study the performance of the algorithms in simulations and implement them to analyze data from an observational study that evaluated the effectiveness of right heart catheterization for critically ill patients.