Robust and Heterogenous Odds Ratio: Estimating Price Sensitivity for Unbought Items

TL;DR

This paper introduces a robust recursive partitioning method to estimate heterogeneous odds ratios for binary responses, enabling personalized interventions in revenue management and other fields with partially observed treatment data.

Contribution

It develops a novel recursive partitioning approach with adversarial imputation to accurately estimate heterogeneous odds ratios under partial treatment observation.

Findings

Validated on synthetic data and real case studies

Demonstrated robustness to partial treatment data

Enabled personalized interventions in revenue management

Abstract

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.