Optimal Allocation of Treatments to Individuals

Keywords: classification, decision tree, nearest neighbor, simulated annealing

Abstract: The problem we consider is a generalization of the classification problem in which one wishes to assign an individual with predictor vector x to one of k treatments in such a way as to optimize the expected outcome. The outcome may be discrete or continuous, and in general will be dependent on x and the chosen treatment. We assume given a training data set in which treatments are randomized and outcomes recorded.

This problem arises frequently in database marketing (and perhaps elsewhere) but seems not to have received much attention.

We consider approaches to optimal allocation based on ANOVA-type models with treatment interaction and suggest reasons why these may perform poorly in applications. In order to provide a more flexible approach, we adapt nonparametric classification techniques such as decision trees and nearest-neighbor-type classifiers.