Uplift model evaluation with ordinal dominance graphs

Uplift modeling is the subfield of causal inference that focuses on the ranking of individuals by their treatment effects. Uplift models are typically evaluated using Qini curves or Qini scores. While intuitive, the theoretical grounding for Qini in the literature is limited, and the mathematical connection to the well-understood Receiver Operating Characteristic ROC is unclear. In this paper, we first introduce the ROCini, an uplift evaluation metric similar in intuition to Qini but derived from the well understood ROC. Using Ordinal Dominance Graph theory, the ROCini is extended to the pROCini, a mathematically better behaved metric that facilitates theoretical analysis. Exploiting the theoretical properties of pROCini, confidence bounds are derived. Finally, the empirical performance of ROCini and pROCini is validated in a simulation study.