  Problem definition: Mining for heterogeneous responses to an intervention is
a crucial step for data-driven operations, for instance to personalize
treatment or pricing. We investigate how to estimate price sensitivity from
transaction-level data. In causal inference terms, we estimate heterogeneous
treatment effects when (a) the response to treatment (here, whether a customer
buys a product) is binary, and (b) treatment assignments are partially observed
(here, full information is only available for purchased items).
Methodology/Results: We propose a recursive partitioning procedure to estimate
heterogeneous odds ratio, a widely used measure of treatment effect in medicine
and social sciences. We integrate an adversarial imputation step to allow for
robust estimation even in presence of partially observed treatment assignments.
We validate our methodology on synthetic data and apply it to three case
studies from political science, medicine, and revenue management. Managerial
Implications: Our robust heterogeneous odds ratio estimation method is a simple
and intuitive tool to quantify heterogeneity in patients or customers and
personalize interventions, while lifting a central limitation in many revenue
management data.
