American Journal of Medical Sciences and Medicine
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American Journal of Medical Sciences and Medicine. 2013, 1(4), 55-61
DOI: 10.12691/ajmsm-1-4-2
Open AccessArticle

Identification of Causal Effect with the Non-Compliance and Its EM Algorithm

Li Xiaotong1, and Li Sichen2

1College of Science, China University of Petroleum in Beijing R.P. China

2School of Basic Medical Sciences, Capital Medical University, Beijing, China

Pub. Date: June 15, 2013

Cite this paper:
Li Xiaotong and Li Sichen. Identification of Causal Effect with the Non-Compliance and Its EM Algorithm. American Journal of Medical Sciences and Medicine. 2013; 1(4):55-61. doi: 10.12691/ajmsm-1-4-2

Abstract

Many practical studies in biology, medicine, behavior science and the social sciences seek to establish causal relationship between treatments and outcomes, rather than mere associations. In this paper, we use a graphical model to describe a causal graphical model and study its identification. For an unidentifiable model, we introduce covariates which are always observed into the model so that it becomes identifiable. We then give an identifiable condition of the causal graphical model and prove it mathematically. Finally, we give the algorithm for the identifiable average causal effect of outcomes to the accepted treatment and give an example to illustrate this method and algorithm.

Keywords:
the rubin causal model instrument variables graphical model identification non-compliance EM algorithm average causal effect

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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References:

[1]  Angrist, J. D., Imbens,G. W. &. Rubin, D.B, “Identification on Causal Effects using Instrumental Variables,” JASA vol.91, No.34, 444-472, 1996.
 
[2]  Imbens, G. W., & Rubins, D. B., “Bayesian Inference for Causal Effects in Randomized Experiments with Noncompliance,” Annals of Statistics, 25, 305-327,1997a.
 
[3]  Keisuke Hirano, G. W. Imbens, D. B. Rubin, & Xiao Hua Zhou, “ Estimating the Effect of an Influenza Vaccine in an Encouragement Design” Biometrics. 1997.
 
[4]  Balke, A. A. & Pearl, J., “Nonparametric bounds on Causal Effects from Partial Compliance Data,” Echnical Report No.199,Codnitive Systems Lab, UCLA Computer Science, Los Angles, CA,1993.
 
[5]  Whittaker, J., Graphical Models in Applied Multivariate statistics, John Wiley & Sons. 1990.
 
[6]  Lauritzen, S. L., Graphical models, Oxford, Oxford University Press, 1996.
 
[7]  Cox, D.R. & Wermuth, N., Multivariate Dependencies: Models, analysis and interpretation. London: Chapman & Hall, 1996.
 
[8]  Wen Qing Ma, Zhi Geng, & Xiao tong Li., “Identification of Graphical Chain Models for Nonignorable Nonresponse in Longitudinal Studies,” The seventh Japan-China Symposium on Statistics, 2000.
 
[9]  Wen Qing Ma, Zhi Geng, & Xiao tong Li. “Identification of nonresponse mechanisms for two way contingency tables,” Behaviormetrika , Vol.30, No.2, 1-20, 2003.
 
[10]  Fitzmaurice, G.M., Laird, N.M. & Zahner, G.E.P.. “Multivariate logistic models for incomplete binary responses,” Journal of the American Statistical Association, 91, 99-108, 1996.
 
[11]  Holland, P. W. & Rubin, D. B. “Causal inference in Retrospective studies, ”Evaluation Review Vol.12, 203-231, 1988.
 
[12]  Daniel F. Heitjan, “Causal Inference in a linical Trial: A Comparative Example,” Controlled clinical Trials, 20, 309-318, 1999.
 
[13]  Stuart,G. Baker, Willian F. Rosenberger, Rebecca Dersimonian, “Closed-Form Estimates For Missing Counts in Two-way Contingency Tables”, Ststistics in Medicine, Vol. 11, 643-657,1992.
 
[14]  G. F. V. Glonek, “On Identifiability in Models For Incomplete binary data”, Statistics and Probability, Letters 41, 191-197,1999.
 
[15]  R, l, Chambers and A. H. Welsh,, “Log-Linear Models for Survey Dada With Non-ignorable Non-response”, J.R.Statistics,Soc.B,55,No.1,157-170. 1993.
 
[16]  Balke,A. and Pearl,J., “Bounds on treatment effects from studies with imperfect compliance,”  Journal of the American Statistical Association, 92 1172-1176,1997.
 
[17]  Rosenbaum, P.R. & Rubin, D.B., “The central role of propensity score in observational studies for Causal effects,” Biometrika, vol.70, 41-45,1983.
 
[18]  Pearl,J., “Causal inference from indirect experiments,” Artifical Intelligence in Medicine,” Vol.7, 516-582. 1995.
 
[19]  Rubin D.B., “Bayesian inference for causal effect: the role of randomization,” Ann. Statist. Vol.6, 34-68, 1978.
 
[20]  Rubin D.B., “Estimating Causal effects of treatments in randomized and non-randomized studies,” J. Educ. Psychol. vol.66, 688-701, 1974.
 
[21]  Pearl,J.,“Causal Diagrams for Empirical research,” Biometrika, Vol. 82, No.4, 669-710,1995.