Model-Free Confidence Intervals for Optimal Treatment Regimes

• Activity Number: 499 - Section on Nonparametric Statistics - Student Paper Competition Presentations
• Type: Topic Contributed
• Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yunan Wu* and Lan Wang
• Companies: University of Minnesota and University of Minnesota
• Keywords: Confidence interval; Individualized treatment rule; Inference; Optimal treatment regime; Weighted bootstrap

Abstract

An optimal treatment regime is a decision rule which aims to maximize the average outcome if being applied to assign the treatment for each individual in the population. The problem of constructing confidence intervals for the parameters indexing the optimal treatment regime or the optimal value function is challenging and has been relatively little studied in the literature. Estimation of the optimal treatment regime is known to be sensitive to the specification of the outcome regression model. Robust methods that do not rely on an outcome regression model also lead to nonstandard asymptotics. To overcome the difficulty for inference, we propose a smoothed robust estimator that has an asymptotic normal distribution and does not require to specify an outcome regression model. We rigorously prove that the bootstrapped confidence intervals provide asymptotically accurate inference for both the parameters indexing the optimal treatment regime and the optimal value function. Furthermore, we present a new algorithm to calculate the proposed estimator with substantially improved speed and stability. Numerical results demonstrate the satisfactory performance of the new methods.