Qini Curves for Multi-armed Treatment Rules

Qini curves have emerged as an attractive and popular approach for evaluating the benefit of data-driven targeting rules for treatment allocation. We propose a generalization of the Qini curve to multiple costly treatment arms that quantifies the value of optimally selecting among both units and treatment arms at different budget levels. We develop an efficient algorithm for computing these curves and propose bootstrap-based confidence intervals that are exact in large samples for any point on the curve. These confidence intervals can be used to conduct hypothesis tests comparing the value of treatment targeting using an optimal combination of arms with using just a subset of arms, or with a non-targeting assignment rule ignoring covariates, at different budget levels. We demonstrate the statistical performance in a simulation experiment and an application to treatment targeting for election turnout.