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Online Targeted Learning for Time Series

  • Mark J. van der Laan
  • Antoine Chambaz
  • Sam Lendle
Chapter
Part of the Springer Series in Statistics book series (SSS)

Abstract

We consider the case that we observe a time series where at each time we observe in chronological order a covariate vector, a treatment, and an outcome. We assume that the conditional probability distribution of this time specific data structure, given the past, depends on the past through a fixed (in time) dimensional summary measure, and that this conditional distribution is described by a fixed (in time) mechanism that is known to be an element of some model space (e.g., unspecified). We propose a causal model that is compatible with this statistical model and define a family of causal effects in terms of stochastic interventions on a subset of the treatment nodes on a future outcome, and establish identifiability of these causal effects from the observed data distribution.

References

  1. P.J. Bickel, C.A.J. Klaassen, Y. Ritov, J. Wellner, Efficient and Adaptive Estimation for Semiparametric Models (Springer, Berlin, Heidelberg, New York, 1997b)zbMATHGoogle Scholar
  2. L. Bottou, Stochastic gradient descent tricks, in Neural Networks: Tricks of the Trade (Springer, Berlin, 2012), pp. 421–436CrossRefGoogle Scholar
  3. A. Chambaz, M.J. van der Laan, Targeting the optimal design in randomized clinical trials with binary outcomes and no covariate: theoretical study. Int. J. Biostat. 7(1), Article 10 (2011a)Google Scholar
  4. A. Chambaz, M.J. van der Laan, Targeting the optimal design in randomized clinical trials with binary outcomes and no covariate: simulation study. Int. J. Biostat. 7(1), Article 11 (2011b)Google Scholar
  5. J.M. Robins, A new approach to causal inference in mortality studies with sustained exposure periods–application to control of the healthy worker survivor effect. Math. Modell. 7, 1393–1512 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  6. J.M. Robins, A. Rotnitzky, Recovery of information and adjustment for dependent censoring using surrogate markers, in AIDS Epidemiology (Birkhäuser, Basel, 1992)Google Scholar
  7. M.J. van der Laan, Estimation based on case-control designs with known prevalence probability. Int. J. Biostat. 4(1), Article 17 (2008a)Google Scholar
  8. M.J. van der Laan, S. Lendle, Online targeted learning. Technical Report, Division of Biostatistics, University of California, Berkeley (2014)Google Scholar
  9. M.J. van der Laan, S. Rose, Targeted Learning: Causal Inference for Observational and Experimental Data (Springer, Berlin, Heidelberg, New York, 2011)CrossRefGoogle Scholar
  10. M.J. van der Laan, D.B. Rubin, Targeted maximum likelihood learning. Int. J. Biostat. 2(1), Article 11 (2006)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Mark J. van der Laan
    • 1
  • Antoine Chambaz
    • 2
  • Sam Lendle
    • 3
  1. 1.Division of Biostatistics and Department of StatisticsUniversity of California, BerkeleyBerkeleyUSA
  2. 2.MAP5 (UMR CNRS 8145)Université Paris DescartesParis cedex 06France
  3. 3.Pandora Media Inc, 2100 Franklin St, Suite 600OaklandUSA

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