AM  Vol.4 No.10 , October 2013
Confounding of Three Binary-Variable Counterfactual Model with DAG
ABSTRACT

Confounding of three binary-variable counterfactual model with directed acyclic graph (DAG) is discussed in this paper. According to the effect between the control variable and the covariate variable, we investigate three causal counterfactual models: the control variable is independent of the covariate variable, the control variable has the effect on the covariate variable and the covariate variable affects the control variable. Using the ancillary information based on conditional independence hypotheses and ignorability, the sufficient conditions to determine whether the covariate variable is an irrelevant factor or whether there is no confounding in each counterfactual model are obtained.


Cite this paper
Liu, J. and Hu, S. (2013) Confounding of Three Binary-Variable Counterfactual Model with DAG. Applied Mathematics, 4, 1397-1404. doi: 10.4236/am.2013.410189.
References
[1]   D. G. Kleinbaum, L. L. Kupper and H. Morgenstern, “Epidemiologic Research: Principle and Quantitative Me thods,” Van Nostrand Reinhold, New York, 1982.

[2]   K. J. Rothman, “Modern Epidemiology,” Little Brown, Boston, 1986.

[3]   S. Greenland, J. M. Robins and J. Pearl, “Confounding and Collapsibility in Causal Inference,” Statistical Sci ence, Vol. 14, No. 1, 1999, pp. 29-46. http://dx.doi.org/10.1214/ss/1009211805

[4]   J. Pearl, “Causality: Models, Reasoning and Inference,” Cambridge University Press, Cambridge, 2000.

[5]   Z. G. Zheng, Y. Y. Zhang and X. W. Tong, “Identifiability of Causal Effect for a Simple Causal Model,” Science in China, Vol. 45, No. 3, 2002, pp. 335-341.

[6]   Z. Geng, Y. B. He and X. L. Wang, “Relationship of Causal Effects in a Causal Chain and Related Inference,” Science in China Series A: Mathematics, Vol. 47, No. 5, 2004, pp. 730-740. http://
dx.doi.org/10.1360/02ys0374


[7]   X. H. Xie and Z. Geng, “A Recursive Method for Structural Learning of Directed Acyclic Graphs,” Journal of Machine Learning Research, Vol. 9, 2008, pp. 459-483.

[8]   D. B. Rubin, “Estimating Causal Effects of Treatments in Randomized and Non Randomized Studies,” Journal of Educational Psychology, Vol. 66, No. 5, 1974, pp. 688-701. http://dx.doi.org/10.1037/
h0037350


[9]   P. W. Holland, “Statistics and Causal Inference,” Journal of the American Statistical Association, Vol. 81, No. 396, 1986, pp. 945-970. http://dx.doi.org/10.1080/01621459.1986.10478354

[10]   S. Greenland and J. M. Robins, “Identifiability Exchange ability and Epidemiologic Confounding,” International Journal of Epidemiology, Vol. 15, No. 3, 1986, pp. 413-419. http://dx.doi.org/10.1093/
ije/15.3.413


[11]   Z. Geng, J. H. Guo and W. K. Fung, “Criteria for Con founders in Epidemiological Studies,” Journal of the Royal Statistical Society: Series B (Statistical Methodol ogy), Vol. 64, No. 1, 2002, pp. 3-15. http://dx.doi.org/10.1111/1467-9868.00321

[12]   C. Berzuini, P. Dawid and L. Bernardinelli, “Causality: Statistical Perspectives and Applications,” John Wiley & Sons, Hoboken, 2012. http://dx.doi.org/10.1002/9781119945710

[13]   Y. Liang and Z. G. Zheng, “The Identifiability Condition of Causal Effect for a Simple Causal Model,” Acta Ma thematica Scientia, Vol. 23A, No. 4, 2003, pp. 456-463.

[14]   G. Wunsch, “Confounding and Control,” Demographic Research, Vol. 16, No. 4, 2007, pp. 97-120. http://dx.doi.org/10.4054/DemRes.2007.16.4

[15]   J. E. Aten, “Causal Not Confounded Gene Networks: Inferring Acyclic and Non-acyclic Gene Bayesian Networks in mRNA Expression Studies using Recursive V Structures, Genetic Variation, and Orthogonal Causal Anchor Structural Equation Models,” Ph.D. Dissertation, University of California, Oakland, 2008.

[16]   P. J. Wickramaratne and T. R. Holford, “Confounding in Epidemiologic Studies: The Adequacy of the Control Groups as a Measure of Confounding,” Biometrics, Vol. 43, No. 4, 1987, pp. 751-765. http://dx.doi.org/10.2307/2531530

[17]   P. W. Holland, “Reader Reactions: Confounding in Epi demiologic Studies,” Biometrics, Vol. 45, No. 4, 1989, pp. 1310-1316.

[18]   O. S. Miettinen, “Standardization of Risk Ratios,” Ameri can Journal of Epidemiology, Vol. 96, No. 6, 1972, pp. 383-388.

[19]   Z. Geng, X. L. Wang and Y. B. He, “Conditions for Con founding of Causal Diagrams,” Chinese Journal of Epi demiology, Vol. 23, 2002, pp. 77-78.

[20]   Y. H. Hu and Z. Geng, “Discussion about the Concept of Confounding,” Chinese Journal of Epidemiology, Vol. 22, No. 6, 2001, pp. 459-461.

 
 
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