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Bounds on Direct and Indirect Effects of Treatment on a Continuous Endpoint

Published: 17 December 2015 Publication History

Abstract

Direct effect of a treatment variable on an endpoint variable and indirect effect through a mediate variable are important concepts for understanding a causal mechanism. However, the randomized assignment of treatment is not sufficient for identifying the direct and indirect effects, and extra assumptions and conditions are required, such as the sequential ignorability assumption without unobserved confounders or the sequential potential ignorability assumption. But these assumptions may not be credible in many applications. In this article, we consider the bounds on controlled direct effect, natural direct effect, and natural indirect effect without these extra assumptions. Cai et al. [2008] presented the bounds for the case of a binary endpoint, and we extend their results to the general case for an arbitrary endpoint.

References

[1]
Zhihong Cai, Manabu Kuroki, Judea Pearl, and Jin Tian. 2008. Bounds on direct effects in the presence of confounded intermediate variables. Biometrics 64, 3 (2008), 695--701.
[2]
Zhihong Cai, Manabu Kuroki, and Tosiya Sato. 2007. Non-parametric bounds on treatment effects with non-compliance by covariate adjustment. Statistics in Medicine 26, 16 (2007), 3188--3204.
[3]
Charles E. Clark. 1961. The greatest of a finite set of random variables. Operations Research 9, 2 (1961), 145--162.
[4]
Vanessa Didelez, Philip Dawid, and Sara Geneletti. 2012. Direct and indirect effects of sequential treatments. arXiv preprint arXiv:1206.6840 (2012).
[5]
Danella M. Hafeman and Tyler J. VanderWeele. 2011. Alternative assumptions for the identification of direct and indirect effects. Epidemiology 22, 6 (2011), 753--764.
[6]
Kosuke Imai, Luke Keele, and Teppei Yamamoto. 2010. Identification, inference and sensitivity analysis for causal mediation effects. Statistical Science (2010), 51--71.
[7]
Hui Jin and Donald B. Rubin. 2008. Principal stratification for causal inference with extended partial compliance. Journal of the American Statistical Association 103, 481 (2008), 101--111.
[8]
Judea Pearl. 2001. Direct and indirect effects. In Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence. Morgan Kaufmann, 411--420.
[9]
Maya L. Petersen, Sandra E. Sinisi, and Mark J. van der Laan. 2006. Estimation of direct causal effects. Epidemiology 17, 3 (2006), 276--284.
[10]
James Robins. 1986. A new approach to causal inference in mortality studies with a sustained exposure period: Application to control of the healthy worker survivor effect. Mathematical Modelling 7, 9 (1986), 1393--1512.
[11]
James M. Robins. 2003. Semantics of causal DAG models and the identification of direct and indirect effects. In P. Green, I. L. Jort, S. Richardson (Eds.), Highly Structured Stochastic Systems (2003), 70--78.
[12]
James M. Robins and Sander Greenland. 1992. Identifiability and exchangeability for direct and indirect effects. Epidemiology (1992), 143--155.
[13]
Sheldon M. Ross. 2014. Introduction to Probability Models. Academic Press.
[14]
Arvid Sjölander. 2009. Bounds on natural direct effects in the presence of confounded intermediate variables. Statistics in Medicine 28, 4 (2009), 558--571.
[15]
Ott Toomet and Arne Henningsen. 2008. Sample selection models in R: Package sampleSelection. Journal of Statistical Software 27, 7 (2008), 1--23.
[16]
Tyler J. VanderWeele. 2009. Marginal structural models for the estimation of direct and indirect effects. Epidemiology 20, 1 (2009), 18--26.
[17]
Tyler J. VanderWeele. 2011. Controlled direct and mediated effects: Definition, identification and bounds. Scandinavian Journal of Statistics 38, 3 (2011), 551--563.

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Published In

cover image ACM Transactions on Intelligent Systems and Technology
ACM Transactions on Intelligent Systems and Technology  Volume 7, Issue 2
Special Issue on Causal Discovery and Inference
January 2016
270 pages
ISSN:2157-6904
EISSN:2157-6912
DOI:10.1145/2850424
  • Editor:
  • Yu Zheng
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 17 December 2015
Accepted: 01 September 2014
Revised: 01 June 2014
Received: 01 March 2014
Published in TIST Volume 7, Issue 2

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Author Tags

  1. Causal inference
  2. bound
  3. direct and indirect effects
  4. mediation analysis

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