Consistent Causal Inference of Group Effects in Non-Targeted Trials with Finitely Many Effect Levels

A treatment may be appropriate for some group (the sick" group) on whom it has a positive effect, but it can also have a detrimental effect on 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 effects on the different groups get tangled. We propose an efficient nonparametric approach to estimating the group effects, called {\bf 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. Our approach applies more generally to consistent estimation of functions with a finite range.