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Health econometric evaluation of the effects of a continuous treatment: a machine learning approach


  • Kreif, N.
  • Grieve, R.
  • Díaz, I.
  • Harrison, D.


When the treatment under evaluation is continuous rather than binary, the marginal causal effect can be reported from the estimated dose-response function. Here, regression methods can be employed that specify a model for the endpoint, given the treatment and covariates. An alternative is to estimate the generalised propensity score (GPS), which can adjust by the conditional density of the treatment, given the covariates. Witheither regression or GPS approaches, model misspecification can lead to biased estimates. This paper introduces a machine learning approach, the “Super Learner†, to estimate both the GPS and the dose-response function. The Super Learner selects the convex combination of candidate estimation algorithms, to create new estimators. We take a two stage estimation approach whereby the Super Learner selects a GPS, and then a dose-response function conditional on the GPS. We compare this approach to parametric implementations of the GPS and regression methods. We contrast the methods in the Risk Adjustment In Neurocritical care (RAIN) cohort study, in which we estimate the marginal causal effects of increasing transfer time from emergency departments to specialised neuroscience centres, for patients with traumatic brain injury. With parametric models for the outcome we find that dose-response curves differ according to choice of parametric specification. With the Super Learner approach to both regression and the GPS, we find that transfer time does not have a statistically significant marginal effect on the outcome.

Suggested Citation

  • Kreif, N. & Grieve, R. & Díaz, I. & Harrison, D., 2014. "Health econometric evaluation of the effects of a continuous treatment: a machine learning approach," Health, Econometrics and Data Group (HEDG) Working Papers 14/19, HEDG, c/o Department of Economics, University of York.
  • Handle: RePEc:yor:hectdg:14/19

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    1. repec:ags:stataj:122599 is not listed on IDEAS
    2. Kosuke Imai & David A. van Dyk, 2004. "Causal Inference With General Treatment Regimes: Generalizing the Propensity Score," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 854-866, January.
    3. BIA Michela & FLORES Carlos A. & MATTEI Alessandra, 2011. "Nonparametric Estimators of Dose-Response Functions," LISER Working Paper Series 2011-40, LISER.
    4. Carlos A. Flores & Alfonso Flores-Lagunes & Arturo Gonzalez & Todd C. Neumann, 2012. "Estimating the Effects of Length of Exposure to Instruction in a Training Program: The Case of Job Corps," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 153-171, February.
    5. Jochen Kluve & Hilmar Schneider & Arne Uhlendorff & Zhong Zhao, 2012. "Evaluating continuous training programmes by using the generalized propensity score," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 175(2), pages 587-617, April.
    6. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
    7. Donald B. Rubin, 2005. "Causal Inference Using Potential Outcomes: Design, Modeling, Decisions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 322-331, March.
    8. Michela Bia & Alessandra Mattei, 2008. "A Stata package for the estimation of the dose–response function through adjustment for the generalized propensity score," Stata Journal, StataCorp LP, vol. 8(3), pages 354-373, September.
    9. Gruber Susan & van der Laan Mark J., 2010. "An Application of Collaborative Targeted Maximum Likelihood Estimation in Causal Inference and Genomics," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-31, May.
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    program evaluation; generalised propensity score; machine learning;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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