Statistics – Methodology
Scientific paper
2010-06-30
Statistics
Methodology
Scientific paper
Dynamic treatment regimes, also known as treatment policies, 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 ADHD study (Pelham and Fabiano 2008).
Laber Eric
Lizotte Dan J.
Murphy Susan A.
Qian Min
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