Causal Rule Sets for Identifying Subgroups with Enhanced Treatment Effects

Abstract

A key question in causal inference analyses is how to find subgroups with elevated treatment effects. This paper takes a machine learning approach and introduces a generative model, causal rule sets (CRS), for interpretable subgroup discovery. A CRS model uses a small set of short decision rules to capture a subgroup in which the average treatment effect is elevated. We present a Bayesian framework for learning a causal rule set. The Bayesian model consists of a prior that favors simple models for better interpretability as well as avoiding overfitting and a Bayesian logistic regression that captures the likelihood of data, characterizing the relation between outcomes, attributes, and subgroup membership. The Bayesian model has tunable parameters that can characterize subgroups with various sizes, providing users with more flexible choices of models from the treatment-efficient frontier. We find maximum a posteriori models using iterative discrete Monte Carlo steps in the joint solution space of rules sets and parameters. To improve search efficiency, we provide theoretically grounded heuristics and bounding strategies to prune and confine the search space. Experiments show that the search algorithm can efficiently recover true underlying subgroups. We apply CRS on public and real-world data sets from domains in which interpretability is indispensable. We compare CRS with state-of-the-art rule-based subgroup discovery models. Results show that CRS achieves consistently competitive performance on data sets from various domains, represented by high treatment-efficient frontiers. Summary of Contribution: This paper is motivated by the large heterogeneity of treatment effect in many applications and the need to accurately locate subgroups for enhanced treatment effect. Existing methods either rely on prior hypotheses to discover subgroups or greedy methods, such as tree-based recursive partitioning. Our method adopts a machine learning approach to find an optimal subgroup learned with a carefully global objective. Our model is more flexible in capturing subgroups by using a set of short decision rules compared with tree-based baselines. We evaluate our model using a novel metric, treatment-efficient frontier, that characterizes the trade-off between the subgroup size and achievable treatment effect, and our model demonstrates better performance than baseline models.