Tree-structured analysis of treatment effects with large observational data

Treatment effect in an observational study of relatively large scale can be described as a mixture of effects among subgroups. In particular, analysis for estimating the treatment effect at the level of an entire sample potentially involves not only differential effects across subgroups of the entire study cohort, but also differential propensities - probabilities of receiving treatment given study subjects' pretreatment history. Such complex heterogeneity is of great research interest because the analysis of treatment effects can substantially depend on the hidden data structure for effect sizes and propensities. To uncover the unseen data structure, we propose a likelihood-based regression tree method which we call marginal tree (MT). The MT method is aimed at a simultaneous assessment of differential effects and propensity scores so that both become homogeneous within each terminal node of the resultant tree structure. We assess simulation performances of the MT method by comparing it with other existing tree methods and illustrate its use with a simulated data set, where the objective is to assess the effects of dieting behavior on its subsequent emotional distress among adolescent girls.