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Population Intervention Causal Effects Based on Stochastic Interventions

Authors

  • Iván Díaz Muñoz,

    Corresponding author
    1. Division of Biostatistics, School of Public Health, 101 Haviland Hall, University of California at Berkeley, Berkeley, California 94720-7358, U.S.A.
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  • Mark van der Laan

    Corresponding author
    1. Division of Biostatistics, School of Public Health, 101 Haviland Hall, University of California at Berkeley, Berkeley, California 94720-7358, U.S.A.
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email:ildiazm@berkeley.edu

email:laan@berkeley.edu

Abstract

Summary Estimating the causal effect of an intervention on a population typically involves defining parameters in a nonparametric structural equation model (Pearl, 2000, Causality: Models, Reasoning, and Inference) in which the treatment or exposure is deterministically assigned in a static or dynamic way. We define a new causal parameter that takes into account the fact that intervention policies can result in stochastically assigned exposures. The statistical parameter that identifies the causal parameter of interest is established. Inverse probability of treatment weighting (IPTW), augmented IPTW (A-IPTW), and targeted maximum likelihood estimators (TMLE) are developed. A simulation study is performed to demonstrate the properties of these estimators, which include the double robustness of the A-IPTW and the TMLE. An application example using physical activity data is presented.

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