Calibration Error for Heterogeneous Treatment Effects

Recently, many researchers have advanced data-driven methods for modeling heterogeneous treatment effects (HTEs). Even still, estimation of HTEs is a difficult task -- these methods frequently over- or under-estimate the treatment effects, leading to poor calibration of the resulting models. However, while many methods exist for evaluating the calibration of prediction and classification models, formal approaches to assess the calibration of HTE models are limited to the calibration slope. In this paper, we define an analogue of the \smash{($\ell_2$)} expected calibration error for HTEs, and propose a robust estimator. Our approach is motivated by doubly robust treatment effect estimators, making it unbiased, and resilient to confounding, overfitting, and high-dimensionality issues. Furthermore, our method is straightforward to adapt to many structures under which treatment effects can be identified, including randomized trials, observational studies, and survival analysis. We illustrate how to use our proposed metric to evaluate the calibration of learned HTE models through the application to the CRITEO-UPLIFT Trial.