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Review
. 2010 Jun;19(3):317-43.
doi: 10.1177/0962280209105013. Epub 2009 Jul 16.

Inference for non-regular parameters in optimal dynamic treatment regimes

Bibhas Chakraborty  1 , Susan Murphy, Victor Strecher
Affiliations
Review

Inference for non-regular parameters in optimal dynamic treatment regimes

Bibhas Chakraborty et al. Stat Methods Med Res. 2010 Jun.

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.

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Figures

Figure 1
Figure 1
Hard-threshold and Soft-threshold pseudo-outcomes compared with the Hard-max pseudo-outcome.
Figure 2
Figure 2
Interaction plots: (a) source by self-efficacy (left panel), (b) story by education (right panel), along with confidence intervals for predicted stage 1 pseudo-outcome.
See this image and copyright information in PMC

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