Classifying Treatment Responders: Bounds and Algorithms

Treatment responders are individuals whose outcomes would change from negative to positive if treated, and learning a classifier to predict responders would help causal decision-making in real applications. Although many treatment effect estimation methods have been proposed to identify treatment responders, there are fundamental differences between treatment effect estimation and treatment responder classification, including: (1) accurate causal effect estimation is not necessary for optimal intervention decisions;

(2) methods for accurate causal effect estimation do not directly optimize classification loss; (3) treatment responder classification requires identifying joint potential outcomes, while treatment effect estimation focuses on marginal distributions. To fill this gap, we tackle the treatment responder classification problem without assuming monotonicity. We derive sharp bounds of the probability that an individual is a responder and determine a sharp upper bound on the weighted classification risk to measure the worst classification performance. Based on these findings, we further propose a Classifying Treatment Responder Learning (CTRL) algorithm to accurately identify the treatment responders, and theoretically demonstrate the superiority of jointly learning over two-stage learning. Extensive experiments on semi-synthetic and real-world datasets show that our method better predicts treatment responders and adaptively trades off false-positives and false-negatives with varying weight coefficients.