Calibration of Heterogeneous Treatment Effects in Randomized Experiments

Abstract

Machine learning is commonly used to estimate the heterogeneous treatment effects (HTEs) in randomized experiments. Using large-scale randomized experiments on Facebook and Criteo platforms, we observe substantial discrepancies between machine learning-based treatment effect estimates and difference-in-means estimates directly from the randomized experiment. This paper provides a two-step framework for practitioners and researchers to diagnose and rectify this discrepancy. We first introduce a diagnostic tool to assess whether bias exists in the model-based estimates from machine learning. If bias exists, we then offer a model-agnostic method to calibrate any HTE estimates to known, unbiased, subgroup difference-in-means estimates, ensuring that the sign and magnitude of the subgroup estimates approximate the model-free benchmarks. This calibration method requires no additional data and can be scaled for large data sets. To highlight potential sources of bias, we theoretically show that this bias can result from regularization, and further use synthetic simulation to show biases result from misspecification and high-dimensional features. We demonstrate the efficacy of our calibration method using extensive synthetic simulations and two real-world randomized experiments. We further demonstrate the practical value of this calibration in three typical policy-making settings: a prescriptive, budget-constrained optimization framework; a setting seeking to maximize multiple performance indicators; and a multitreatment uplift modeling setting.