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Inference and Non-regularity

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Book cover Statistical Methods for Dynamic Treatment Regimes

Part of the book series: Statistics for Biology and Health ((SBH))

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Abstract

In this chapter, we illustrated the problem of non-regularity that arises in the context of inference about the optimal current treatment rule, when the optimal treatments at subsequent stages are non-unique for at least some strictly positive proportion of subjects in the population. We discuss and illustrate the phenomenon using Q-learning and G-estimation, and propose a number of strategies to mitigate the non-regularity including thresholding and penalization of the estimators as well as non-standard implementations of the bootstrap.

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Notes

  1. 1.

    This is unpublished work, but the first author was pointed to this direction by Dr. Susan Murphy (personal communication).

  2. 2.

    If this unlikely event does occur, one should examine the observed values of \(\hat{p}\). If the values of \(\hat{p}\) are concentrated close to zero, ν may be increased; if not, the maximal value in the grid should be increased.

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Authors and Affiliations

  1. Department of Biostatistics, Columbia University, New York, USA

    Bibhas Chakraborty

  2. Department of Epidemiology, Biostatistics, and Occupational Health, McGill University, Montreal, Québec, Canada

    Erica E. M. Moodie

Authors
  1. Bibhas Chakraborty
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  2. Erica E. M. Moodie
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Chakraborty, B., Moodie, E.E.M. (2013). Inference and Non-regularity. In: Statistical Methods for Dynamic Treatment Regimes. Statistics for Biology and Health. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7428-9_8

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