Estimating Heterogeneous Treatment Effect with Delayed Response

TL;DR — We propose CFR-DF, a principled learning approach that extends counterfactual regression (CFR) to estimate heterogeneous treatment effects with delayed response by incorporating delayed feedback outcomes.

Abstract

Estimation of heterogeneous treatment effects has gathered much attention in recent years and has been widely adopted in medicine, economics, and marketing. Previous studies assumed that one of the potential outcomes of interest could be observed timely and accurately. However, a more practical scenario is that treatment takes time to produce causal effects on the outcomes. For example, drugs take time to produce medical utility for patients and users take time to purchase items after being recommended, and ignoring such delays in feedback can lead to biased estimates of heterogeneous treatment effects. To address the above problem, we study the impact of observation time on estimating heterogeneous treatment effects by further considering the potential response time that potential outcomes have. We theoretically prove the identifiability results and further propose a principled learning approach, known as CFR-DF (Counterfactual Regression with Delayed Feedback), to simultaneously learn potential response times and potential outcomes of interest. Results on both simulated and real-world datasets demonstrate the effectiveness of our method.