Causal Rule Ensemble: Interpretable Inference of Heterogeneous Treatment Effects

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Abstract
In social and health sciences, it is critically important to identify subgroups of the study population where a treatment has a notably larger or smaller causal effect compared to the population average. In recent years, there have been many methodological developments for addressing heterogeneity of causal effects. A common approach is to estimate the conditional average treatment effect (CATE) given a pre-specified set of covariates. However, this approach does not allow to discover new subgroups. Recent causal machine learning (ML) approaches estimate the CATE at an individual level in presence of large number of observations and covariates with great accuracy. Nevertheless, the bulk of these ML approaches do not provide an interpretable characterization of the heterogeneous subgroups. In this paper, we propose a new Causal Rule Ensemble (CRE) method that: 1) discovers de novo subgroups with significantly heterogeneous treatment effects (causal rules); 2) ensures interpretability of these subgroups because they are defined in terms of decision rules; and 3) estimates the CATE for each of these newly discovered subgroups with small bias and high statistical precision. We provide theoretical results that guarantee consistency of the estimated causal effects for the newly discovered causal rules. A nice feature of CRE is that it is agnostic to the choices of the ML algorithms that can be used to discover the causal rules, and the estimation methods for the causal effects within the discovered causal rules. Via simulations, we show that the CRE method has competitive performance as compared to existing approaches while providing enhanced interpretability. We also introduce a new sensitivity analysis to unmeasured confounding bias. We apply the CRE method to discover subgroups that are more vulnerable to the causal effects of long-term exposure to air pollution on mortality.

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