Inferring Causal Effects in Subpopulations Using a Matched-Tree Approach

Music City Center 

Inferring causal effects from observational studies is a key focus in various scientific fields, including social science, healthcare, and medicine. While statistical methodologies for estimating the population average causal effect are well-established, techniques for identifying and estimating subpopulation causal effects are comparatively less developed. A significant challenge is that subgroup structures are often unknown, requiring adaptations to methods designed for population-level inference.
We propose a tree-based method, built on a matched design, to identify subgroups with differential treatment effects. To address observed confounding, we first create propensity-score-matched pairs. Next, we apply classification and regression trees (CART) to the differences in outcomes within matched pairs, uncovering subgroup structures with distinct causal effects. This nonparametric approach is robust against model misspecification—an essential feature given the difficulty of specifying parametric outcome models in the presence of complex subgroup effects.
We outline the assumptions under which the proposed matching estimator remains unbiased and provide algorithms for identifying subgroup structures. Simulations demonstrate that our method outperforms competing tree-based approaches—including causal trees, causal inference trees, and the virtual twins approach—in accurately identifying the true subgroup structure. Finally, we apply our method to evaluate the potential subgroup effect of Tobramycin timing on chronic infection outcomes among pediatric Cystic Fibrosis patients.

Potential outcomes

Propensity score

Matched design

Classification and regression tree