Estimating Causal Effects with Interpretable Decision Trees

Abstract

In this work we explore three methods for estimating treatment effects from observational data using interpretable decision trees: the outcome variance tree, the propensity tree and the linear dependence tree. Each tree attempts to split the covariate space into balanced partitions from which treatment effects can be inferred. The outcome variance tree focuses on reducing the variance in the outcome variable, and makes use of a sensitivity analysis based on the residual standard deviation in the outcome. The propensity tree attempts to build a tree that approximates a separate estimate of the propensity score whilst remaining interpretable. The linear dependence tree measures the linear dependence in the partitions and attempts to minimize it directly. The three methods are compared, along with other benchmark methods, on two data sets: a synthetic data set generated from a simple model and the more realistic semi-synthetic IHDP data set. Performance is evaluated by comparing interval widths and coverage for confidence and sensitivity intervals. A functionally-grounded evaluation of interpretability is given with tree size as proxies. The results show that the outcome variance tree and the linear dependence tree perform better than the benchmarks in terms of sensitivity intervals but worse in terms of confidence intervals. The propensity tree however did not perform as well as expected and requires more work to better understand its behavior.