Optimal personalized treatment rules for marketing interventions: A review of methods, a new proposal, and an insurance case study

In many important settings, subjects can show significant heterogeneity in response to a stimulus or treatment. For instance, a treatment that works for the overall population might be highly ine ective, or even harmful, for a subgroup of subjects with specific characteristics. Similarly, a new treatment may not be better than an existing treatment in the overall population, but there is likely a subgroup of subjects who would bene t from it. The notion that one size may not fit all is becoming increasingly recognized in a wide variety of fields, ranging from economics to medicine. This has drawn signi cant attention to personalize the choice of treatment, so it is optimal for each individual. An optimal personalized treatment is the one that maximizes the probability of a desirable outcome. We call the task of learning the optimal personalized treatment "personalized treatment learning". From the statistical learning perspective, this problem imposes some challenges, primarily because the optimal treatment is unknown on a given training set. A number of statistical methods have been proposed recently to tackle this problem. However, to the best of our knowledge, there has been no attempt so far to provide a comprehensive view of these methods and to benchmark their performance. The purpose of this paper is twofold: i) to describe seven recently proposed methods for personalized treatment learning and compare their performance on an extensive numerical study, and ii) to propose a novel method labeled causal conditional inference trees and its natural extension to causal conditional inference forests. The results show that our new proposed method often outperforms the alternatives on the numerical settings described in this article. We also illustrate an application of the proposed method using data from a large Canadian insurer for the purpose of selecting the best targets for cross-selling an insurance product.