title: Inference for non-regular parameters in optimal dynamic treatment regimes.
abstract: A dynamic treatment regime is a set of decision rules, one per stage, each taking a patient's treatment and covariate history as input, and outputting a recommended treatment. In the estimation of the optimal dynamic treatment regime from longitudinal data, the treatment effect parameters at any stage prior to the last can be non-regular under certain distributions of the data. This results in biased estimates and invalid confidence intervals for the treatment effect parameters. In this article, we discuss both the problem of non-regularity, and available estimation methods. We provide an extensive simulation study to compare the estimators in terms of their ability to lead to valid confidence intervals under a variety of non-regular scenarios. Analysis of a data set from a smoking cessation trial is provided as an illustration.
authors.affiliation: Department of Statistics, University of Michigan, Ann Arbor, MI 48109-1107, USA. bibhas@umich.edu
authors.forename: Bibhas
authors.initials: B
authors.lastname: Chakraborty
authors.forename: Susan
authors.initials: S
authors.lastname: Murphy
authors.forename: Victor
authors.initials: V
authors.lastname: Strecher
mesh_terms: D056808:Biostatistics; D002985:Clinical Protocols; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data; D016001:Confidence Intervals; D003657:Decision Making; D006801:Humans; D016014:Linear Models; D015233:Models, Statistical; D016540:Smoking Cessation / Q000706:statistics & numerical data; D016896:Treatment Outcome