Subgroup causal effect identification and estimation via matching tree

Inferring causal effect from observational studies is a central topic in many scientific fields, including social science, health and medicine. The statistical methodology for estimating population average causal effect has been well established. However, the methods for identifying and estimating subpopulation causal effects are relatively less developed. Part of the challenge is that the subgroup structure is usually unknown, therefore, methods working well for population level effect need to be modified to address this. A tree method based on a matched design is proposed to identify subgroups with differential treatment effects. To remove observed confounding, propensity-score-matched pairs are first created. Then the classification and regression tree is applied to the within-pair outcome differences to identify the subgroup structure. This nonparametric approach is robust to model misspecification, which is important because it becomes much harder to specify a parametric outcome model in the presence of subgroup effects. In addition to describing assumptions under which our matching estimator is unbiased, algorithms for identifying subgroup structures are provided. Simulation results indicate that the proposed approach compares favorably, in terms of the percentage of correctly identifying true tree structure, with other competing tree-based methods, including causal trees, causal inference trees and the virtual twins approach. Finally the proposed method is implemented to examine the potential subgroup effect of the timing of Tobramycin use on chronic infection among pediatric Cystic Fibrosis patients.