Experimental Evaluation of Individualized Treatment Rules

In recent years, the increasing availability of individual-level data has led to numerous applications of individualized (or personalized) treatment rules (ITRs). Policy makers often wish to empirically evaluate ITRs and compare their relative performance before implementing them in a target population. We propose a new evaluation metric, the population average prescriptive effect (PAPE). The PAPE compares the performance of ITR with that of non-individualized treatment rule, which randomly treats the same proportion of units. Averaging the PAPE over a range of budget constraints yields our second evaluation metric, the area under the prescriptive effect curve (AUPEC). The AUPEC represents an overall performance measure for evaluation, like the area under the receiver and operating characteristic curve (AUROC) does for classification. We use the Neyman's repeated sampling framework to estimate the PAPE and AUPEC and derive their exact finite-sample variances based on random sampling of units and random assignment of treatment. We also extend our analytical framework to a common evaluation setting, in which the same experimental data is used to both estimate and evaluate ITRs. In this case, our variance calculation incorporates the additional uncertainty due to random splits of data used for cross-validation. Unlike some of the existing methods, the proposed methodology does not require modeling assumptions, asymptotic approximation, or resampling method. As a result, it is applicable to any ITR including those based on complex machine learning algorithms. The open-source software package is available for implementing the proposed methodology.