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Inference for non-regular parameters in optimal dynamic treatment regimes

¹ Department of Statistics, 439 West Hall, 1085 South University Avenue, Ann Arbor, MI 48109-1107, USA.
² Department of Statistics, University of Michigan, Ann Arbor, MI 48109-1107, USA
³ Center for Health Communications Research, University of Michigan, Ann Arbor, MI 48109-1107, USA

^* To whom correspondence should be addressed. E-mail: bibhas{at}umich.edu.

	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.

First published on July 16, 2009
Statistical Methods in Medical Research 2009, doi:10.1177/0962280209105013


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