Stochastic Treatment Regimes

  • Iván Díaz
  • Mark J. van der Laan
Part of the Springer Series in Statistics book series (SSS)


Standard statistical methods to study causality define a set of treatment-specific counterfactual outcomes as the outcomes observed in a hypothetical world in which a given treatment strategy is applied to all individuals. For example, if treatment has two possible values, one may define the causal effect as a comparison between the expectation of the counterfactual outcomes under regimes that assign each treatment level with probability one. Regimes of this type are often referred to as static. Another interesting type of regimes assign an individual’s treatment level as a function of the individual’s measured history. Regimes like this have been called dynamic, since they can vary according to observed pre-treatment characteristics of the individual. Static and dynamic regimes have often been called deterministic, because they are completely determined by variables measured before treatment.


  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)Google Scholar
  2. A.P. Dawid, V. Didelez, Identifying the consequences of dynamic treatment strategies: a decision-theoretic overview. Stat. Surv. 4, 184–231 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  3. L. Denby, C. Mallows, Variations on the histogram. J. Comput. Graph. Stat. 18(1), 21–31 (2009)MathSciNetCrossRefGoogle Scholar
  4. I. Díaz, M. van der Laan, Super learner-based conditional density estimation with application to marginal structural models. Int. J. Biostat. 7(1), 38 (2011)Google Scholar
  5. I. Díaz, M. van der Laan, Population intervention causal effects based on stochastic interventions. Biometrics 68(2), 541–549 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  6. I. Díaz, M.J. van der Laan, Assessing the causal effect of policies: an example using stochastic interventions. Int. J. Biostat. 9(2), 161–174 (2013a)Google Scholar
  7. F. Eberhardt, R. Scheines, Interventions and causal inference. Department of Philosophy. Paper 415 (2006)Google Scholar
  8. S. Haneuse, A. Rotnitzky, Estimation of the effect of interventions that modify the received treatment. Stat. Med. (2013)Google Scholar
  9. K. Korb, L. Hope, A. Nicholson, K. Axnick, Varieties of causal intervention. in PRICAI 2004: Trends in Artificial Intelligence, ed. by C. Zhang, H.W. Guesgen, W.-K. Yeap. Lecture Notes in Computer Science, vol. 3157 (Springer, Berlin, Heidelberg, 2004), pp. 322–331Google Scholar
  10. J.K. Mann, J.R. Balmes, T.A. Bruckner, K.M. Mortimer, H.G. Margolis, B. Pratt, S.K. Hammond, F.W. Lurmann, I.B. Tager, Short-term effects of air pollution on wheeze in asthmatic children in Fresno, California. Environ Health Perspect. 118(10), 06 (2010)Google Scholar
  11. A.I Naimi, E.E.M. Moodie, N. Auger, J.S. Kaufman, Stochastic mediation contrasts in epidemiologic research: interpregnancy interval and the educational disparity in preterm delivery. Am. J. Epidemiol. 180(4), 436–445 (2014)Google Scholar
  12. J. Pearl, Myth, confusion, and science in causal analysis. Technical Report R-348, Cognitive Systems Laboratory, Computer Science Department University of California, Los Angeles, Los Angeles, CA, May 2009bGoogle Scholar
  13. J.M. Robins, M.A. Hernán, U. Siebert, Effects of multiple interventions, in Comparative Quantification of Health Risks: Global and Regional Burden of Disease Attributable to Selected Major Risk Factors, vol. 1 (World Health Organization, Geneva, 2004), pp. 2191–2230Google Scholar
  14. S. Sapp, M.J. van der Laan, K. Page, Targeted estimation of binary variable importance measures with interval-censored outcomes. Int. J. Biostat. 10(1), 77–97 (2014)MathSciNetCrossRefGoogle Scholar
  15. I. Tager, M. Hollenberg, W. Satariano, Self-reported leisure-time physical activity and measures of cardiorespiratory fitness in an elderly population. Am. J. Epidemiol. 147, 921–931 (1998)CrossRefGoogle Scholar
  16. M.J. van der Laan, Causal inference for a population of causally connected units. J. Causal Inference 2(1), 13–74 (2014a)Google Scholar
  17. M.J. van der Laan, D.B. Rubin, Targeted maximum likelihood learning. Int. J. Biostat. 2(1), Article 11 (2006)Google Scholar
  18. M.J. van der Laan, A.R. Luedtke, I. Díaz, Discussion of identification, estimation and approximation of risk under interventions that depend on the natural value of treatment using observational data, by Jessica Young, Miguel Hernán, and James Robins. Epidemiol Methods 3(1), 21–31 (2014)zbMATHGoogle Scholar
  19. A.W. van der Vaart, Asymptotic Statistics (Cambridge, New York, 1998)CrossRefzbMATHGoogle Scholar
  20. J.G. Young, M.A. Hernán, J.M. Robins, Identification, estimation and approximation of risk under interventions that depend on the natural value of treatment using observational data. Epidemiol. Methods 3(1), 1–19 (2014)CrossRefzbMATHGoogle Scholar
  21. W. Zheng, M.J. van der Laan, Causal mediation in a survival setting with time-dependent mediators. Technical Report, Division of Biostatistics, University of California, Berkeley (2012a)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Division of Biostatistics and Epidemiology, Department of Healthcare Policy and ResearchWeill Cornell Medical College, Cornell UniversityNew YorkUSA
  2. 2.Division of Biostatistics and Department of StatisticsUniversity of California, BerkeleyBerkeleyUSA

Personalised recommendations