Statistical Inference in Dynamic Treatment Regimes

• Activity Number: 657
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Eric B Laber*+ and Daniel J Lizotte and Min Qian and William E Pelham and Susan Murphy
• Companies: North Carolina State University and University of Waterloo and Columbia University and SUNY at Stony Brook and University of Michigan
• Keywords: Dynamic treatment regimes ; Personalized medicine ; Nonregular asymptotics ; Adaptive inference

Abstract

Dynamic treatment regimes are increasingly being used to operationalize sequential clinical decision making associated with patient care. Common approaches to constructing a dynamic treatment regime from data, such as Q-learning, employ non-smooth functionals of the data. Therefore, simple inferential tasks such as constructing a confidence interval for the parameters in the Q-function are complicated by nonregular asymptotics under certain commonly-encountered generative models. Methods that ignore this nonregularity can suffer from poor performance in small samples. We construct confidence intervals for the parameters in the Q-function by first constructing smooth, data-dependent, upper and lower bounds on these parameters and then applying the bootstrap. The confidence interval is adaptive in that although it is conservative for nonregular generative models, it achieves asymptotically exact coverage elsewhere. The small sample performance of the method is evaluated on a series of examples and compares favorably to previously published competitors. Finally, we illustrate the method using data from the Adaptive Interventions for Children with with ADHD study.