Experimental Evaluation of Individualized Treatment Rules

Abstract

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, and is a generalization of the QINI coefficient used in uplift modeling. We use 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 extend our methodology to a common setting, in which the same experimental data are 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. The proposed evaluation metrics can be estimated without requiring modeling assumptions, asymptotic approximation, or resampling methods. 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. Supplementary materials for this article are available online.

KEYWORDS:

• Causal inference
• Heterogeneous treatment effects
• Machine learning
• Precision medicine
• Uplift modeling

Acknowledgments

We thank to Naoki Egami, Colin Fogarty, Zhichao Jiang, Susan Murphy, Nicole Pashley, Stefan Wager, three anonymous reviewers, and especially the Associate Editor for many helpful comments. We thank Dr Hsin-Hsiao Wang who inspired us to write this article. The proposed methodology is implemented through an open-source R package, evalITR, which is freely available for download at the Comprehensive R Archive Network (CRAN; https://CRAN.R-project.org/package=evalITR).

Funding

Imai thanks to the Alfred P. Sloan Foundation (# 2020-13946) for partial support of this research.

Supplementary Materials

The proofs for the theoretical results are included in the supplementary material.