Untangling Effect and Side Effect: Consistent Causal Inference in Non-Targeted Trials

A treatment is usually appropriate for some group (the ``sick" group) on whom it has an effect, but it can also have a side-effect when given to subjects from another group (the ``healthy" group). In a non-targeted trial both sick and healthy subjects may be treated, producing heterogeneous effects within the treated group. Inferring the correct treatment effect on the sick population is then difficult, because the effect and side-effect are tangled. We propose an efficient nonparametric approach to untangling the effect and side-effect, called PCM (pre-cluster and merge). We prove its asymptotic consistency in a general setting and show, on synthetic data, more than a 10x improvement in accuracy over existing state-of-the-art.