Bias and variance inflation in hierarchical multi-treatment DML: Diagnosis and correction

Many business and clinical decisions depend on the conditional average treatment effect (CATE) of each of several continuous treatments that move together: advertising spend and discount levels driven by the same campaign, or drug doses adjusted in a common protocol. Several estimator families produce CATE at every query point with a confidence interval, including meta-learners, doubly robust learners, Causal Forests and Double Machine Learning (DML); DML in particular gives both in closed form and is widely deployed. We show that, when treatments remain correlated after conditioning on covariates, the bias of the standard DML estimator is amplified along the directions in which two treatments are nearly indistinguishable. The plug-in confidence interval is asymptotically valid as long as the residual correlation does not reach one, but the convergence is so slow under strong correlation that coverage is far from nominal at practical sample sizes. We propose a hierarchy-aware bias correction that combines two CATE estimators of different complexity through a projector built from a user-supplied grouping of treatments by shared cause: the more flexible estimator on the directions where the data is informative and the less expressive estimator on the contrast directions among sibling treatments, where it has lower bias. Across four synthetic data-generating processes, the IHDP public benchmark and a treatment graph with two disjoint sibling triples, the correction lifts coverage on the correlated treatments from 30% for vanilla DML to 94%, reduces mean squared error by a factor of 51 and produces 30% narrower intervals. A second contribution adds a bias-augmented variance term that lifts coverage further to 99% at the cost of wider intervals, for use in extreme-correlation regimes where residual bias persists.