An introduction to causal inference

International Journal of Biostatistics

Volumn 6, Issue 2, 2010, Pages

  Pearl, Judea ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Causal effects; Causes of effects; Confounding; Counterfactuals; Graphical methods; Mediation; Policy evaluation; Potential outcome; Structural equation models

Indexed keywords

COMPREHENSION; INTERVENTION STUDY; LANGUAGE; MATHEMATICAL ANALYSIS; METHODOLOGY; MULTIVARIATE ANALYSIS; OUTCOME ASSESSMENT; PROBABILITY; REVIEW; STATISTICAL ANALYSIS; STATISTICS; STRUCTURAL EQUATION MODELING; THEORY; ALGORITHM; EPIDEMIOLOGY; HUMAN; STATISTICAL MODEL;

ALGORITHMS; CAUSALITY; CONFOUNDING FACTORS (EPIDEMIOLOGY); HUMANS; MODELS, STATISTICAL; RESEARCH DESIGN;

EID: 77649295233     PISSN: 15574679     EISSN: None     Source Type: Journal    
DOI: 10.2202/1557-4679.1203     Document Type: Review

References (126)

1. Angrist, J., G. Imbens, and D. Rubin (1996): "Identification of causal effects using instrumental variables (with comments)," Journal of the American Statistical Association, 91, 444-472.
2. Arah, O. (2008): "The role of causal reasoning in understanding Simpson's paradox, Lord's paradox, and the suppression effect: Covariate selection in the analysis of observational studies," Emerging Themes in Epidemiology, 4, doi:10.1186/1742-7622-5-5, online at .
3. Arjas, E. and J. Parner (2004): "Causal reasoning from longitudinal data," Scandinavian Journal of Statistics, 31, 171-187.
4. Avin, C., I. Shpitser, and J. Pearl (2005): "Identifiability of path-specific effects," in Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence IJCAI-05, Edinburgh, UK: Morgan-Kaufmann Publishers, 357-363.
5. Balke, A. and J. Pearl (1995): "Counterfactuals and policy analysis in structural models," in P. Besnard and S. Hanks, eds., Uncertainty in Artificial Intelligence 11, San Francisco: Morgan Kaufmann, 11-18.
6. Balke, A. and J. Pearl (1997): "Bounds on treatment effects from studies with imperfect compliance," Journal of the American Statistical Association, 92, 1172-1176.
7. Baron, R. and D. Kenny (1986): "The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations," Journal of Personality and Social Psychology, 51, 1173-1182.
8. Berkson, J. (1946): "Limitations of the application of fourfold table analysis to hospital data," Biometrics Bulletin, 2, 47-53.
9. Bollen, K. (1989): Structural Equations with Latent Variables, New York: John Wiley.
10. Brent, R. and L. Lok (2005): "A fishing buddy for hypothesis generators," Science, 308, 523-529.
11. Cai, Z. and M. Kuroki (2006): "Variance estimators for three 'probabilities of causation'," Risk Analysis, 25, 1611-1620.
12. Cai, Z. and M. Kuroki (2008): "On identifying total effects in the presence of latent variables and selection bias," in D. A. McAllester and P. Myllymäki, eds., Uncertainty in Artificial Intelligence, Proceedings of the Twenty-Fourth Conference, Arlington, VA: AUAI, 62-69.
13. Cartwright, N. (2007): Hunting Causes and Using Them: Approaches in Philosophy and Economics, New York, NY: Cambridge University Press.
14. Chalak, K. and H. White (2006): "An extended class of instrumental variables for the estimation of causal effects," Technical Report Discussion Paper, UCSD, Department of Economics.
15. Chickering, D. and J. Pearl (1997): "A clinician's tool for analyzing non-compliance," Computing Science and Statistics, 29, 424-431.
16. Cole, P. (1997): "Causality in epidemiology, health policy, and law," Journal of Marketing Research, 27, 10279-10285.
17. Cole, S. and M. Hernán (2002): "Fallibility in estimating direct effects," International Journal of Epidemiology, 31, 163-165.
18. Cox, D. (1958): The Planning of Experiments, NY: John Wiley and Sons.
19. Cox, D. and N. Wermuth (2004): "Causality: A statistical view," International Statistical Review, 72, 285-305.
20. Dawid, A. (1979): "Conditional independence in statistical theory," Journal of the Royal Statistical Society, Series B, 41, 1-31.
21. Dawid, A. (2000): "Causal inference without counterfactuals (with comments and rejoinder)," Journal of the American Statistical Association, 95, 407-448.
22. Dawid, A. (2002): "Influence diagrams for causal modelling and inference," International Statistical Review, 70, 161-189.
23. Duncan, O. (1975): Introduction to Structural Equation Models, New York: Academic Press.
24. Eells, E. (1991): Probabilistic Causality, Cambridge, MA: Cambridge University Press.
25. Frangakis, C. and D. Rubin (2002): "Principal stratification in causal inference," Biometrics, 1, 21-29.
26. Glymour, M. and S. Greenland (2008): "Causal diagrams," in K. Rothman, S. Greenland, and T. Lash, eds., Modern Epidemiology, Philadelphia, PA: Lip-pincott Williams & Wilkins, 3rd edition, 183-209.
27. Goldberger, A. (1972): "Structural equation models in the social sciences," Econometrica: Journal of the Econometric Society, 40, 979-1001.
28. Goldberger, A. (1973): "Structural equation models: An overview," in A. Gold-berger and O. Duncan, eds., Structural Equation Models in the Social Sciences, New York, NY: Seminar Press, 1-18.
29. Greenland, S. (1999): "Relation of probability of causation, relative risk, and doubling dose: A methodologic error that has become a social problem," American Journal of Public Health, 89, 1166-1169.
30. Greenland, S., J. Pearl, and J. Robins (1999): "Causal diagrams for epidemiologic research," Epidemiology, 10, 37-48.
31. Greenland, S. and J. Robins (1986): "Identifiability, exchangeability, and epidemiological confounding," International Journal of Epidemiology, 15, 413-419.
32. Haavelmo, T. (1943): "The statistical implications of a system of simultaneous equations," Econometrica, 11, 1-12, reprinted in D.F. Hendry and M.S. Morgan (Eds.), The Foundations of Econometric Analysis, Cambridge University Press, 477-490, 1995.
33. Hafeman, D. and S. Schwartz (2009): "Opening the black box: A motivation for the assessment of mediation," International Journal of Epidemiology, 3, 838-845.
34. Halpern, J. (1998): "Axiomatizing causal reasoning," in G. Cooper and S. Moral, eds., Uncertainty in Artificial Intelligence, San Francisco, CA: Morgan Kaufmann, 202-210, also, Journal of Artificial Intelligence Research 12:3, 17-37, 2000.
35. Heckman, J. (1992): "Randomization and social policy evaluation," in C. Manski and I. Garfinkle, eds., Evaluations: Welfare and Training Programs, Cambridge, MA: Harvard University Press, 201-230.
36. Heckman, J. (2005): "The scientific model of causality," Sociological Methodology, 35, 1-97.
37. Heckman, J. (2008): "Econometric causality," International Statistical Review, 76, 1-27.
38. Heckman, J. and S. Navarro-Lozano (2004): "Using matching, instrumental variables, and control functions to estimate economic choice models," The Review of Economics and Statistics, 86, 30-57.
39. Heckman, J. and E. Vytlacil (2005): "Structural equations, treatment effects and econometric policy evaluation," Econometrica, 73, 669-738.
40. Hernán, M. and S. Cole (2009): "Invited commentary: Causal diagrams and measurement bias," American Journal of Epidemiology, 170, 959-962.
41. Holland, P. (1988): "Causal inference, path analysis, and recursive structural equations models," in C. Clogg, ed., Sociological Methodology, Washington, D.C.: American Sociological Association, 449-484.
42. Hurwicz, L. (1950): "Generalization of the concept of identification," in T. Koop-mans, ed., Statistical Inference in Dynamic Economic Models, Cowles Commission, Monograph 10, New York: Wiley, 245-257.
43. Imai, K., L. Keele, and T. Yamamoto (2008): "Identification, inference, and sensitivity analysis for causal mediation effects," Technical report, Department of Politics, Princton University.
44. Imbens, G. and J. Wooldridge (2009): "Recent developments in the econometrics of program evaluation," Journal of Economic Literature, 47, 5-86.
45. Judd, C. and D. Kenny (1981): "Process analysis: Estimating mediation in treatment evaluations," Evaluation Review, 5, 602-619.
46. Kaufman, S., J. Kaufman, and R. MacLenose (2009): "Analytic bounds on causal risk differences in directed acyclic graphs involving three observed binary variables," Journal of Statistical Planning and Inference, 139, 3473-3487.
47. Kiiveri, H., T. Speed, and J. Carlin (1984): "Recursive causal models," Journal of Australian Math Society, 36, 30-52.
48. Koopmans, T. (1953): "Identification problems in econometric model construction," in W. Hood and T. Koopmans, eds., Studies in Econometric Method, New York: Wiley, 27-48.
49. Kuroki, M. and M. Miyakawa (1999): "Identifiability criteria for causal effects of joint interventions," Journal of the Royal Statistical Society, 29, 105-117.
50. Lauritzen, S. (1996): Graphical Models, Oxford: Clarendon Press.
51. Lauritzen, S. (2001): "Causal inference from graphical models," in D. Cox and C. Kluppelberg, eds., Complex Stochastic Systems, Boca Raton, FL: Chapman and Hall/CRC Press, 63-107.
52. Lindley, D. (2002): "Seeing and doing: The concept of causation," International Statistical Review, 70, 191-214.
53. MacKinnon, D., A. Fairchild, and M. Fritz (2007a): "Mediation analysis," Annual Review of Psychology, 58, 593-614.
54. MacKinnon, D., C. Lockwood, C. Brown, W. Wang, and J. Hoffman (2007b): "The intermediate endpoint effect in logistic and probit regression," Clinical Trials, 4, 499-513.
55. Manski, C. (1990): "Nonparametric bounds on treatment effects," American Economic Review, Papers and Proceedings, 80, 319-323.
56. Marschak, J. (1950): "Statistical inference in economics," in T. Koopmans, ed., Statistical Inference in Dynamic Economic Models, New York: Wiley, 1-50, cowles Commission for Research in Economics, Monograph 10.
57. Meek, C. and C. Glymour (1994): "Conditioning and intervening," British Journal of Philosophy Science, 45, 1001-1021.
58. Miettinen, O. (1974): "Proportion of disease caused or prevented by a given exposure, trait, or intervention," Journal of Epidemiology, 99, 325-332.
59. Morgan, S. and C. Winship (2007): Counterfactuals and Causal Inference: Methods and Principles for Social Research (Analytical Methods for Social Research), New York, NY: Cambridge University Press.
60. Muller, D., C. Judd, and V. Yzerbyt (2005): "When moderation is mediated and mediation is moderated," Journal of Personality and Social Psychology, 89, 852-863.
61. Neyman, J. (1923): "On the application of probability theory to agricultural experiments. Essay on principles. Section 9," Statistical Science, 5, 465-480.
62. Pearl, J. (1988): Probabilistic Reasoning in Intelligent Systems, San Mateo, CA: Morgan Kaufmann.
63. Pearl, J. (1993a): "Comment: Graphical models, causality, and intervention," Statistical Science, 8, 266-269.
64. Pearl, J. (1993b): "Mediating instrumental variables," Technical Report R-210, , Department of Computer Science, University of California, Los Angeles.
65. Pearl, J. (1995): "Causal diagrams for empirical research," Biometrika, 82, 669-710.
66. Pearl, J. (1998): "Graphs, causality, and structural equation models," Sociological Methods and Research, 27, 226-284.
67. Pearl, J. (2000a): Causality: Models, Reasoning, and Inference, New York: Cambridge University Press, second ed., 2009.
68. Pearl, J. (2000b): "Comment on A.P Dawid's, Causal inference without counter-factuals," Journal of the American Statistical Association, 95, 428-431.
69. Pearl, J. (2001): "Direct and indirect effects," in Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, San Francisco, CA: Morgan Kaufmann, 411-420.
70. Pearl, J. (2004): "Robustness of causal claims," in M. Chickering and J. Halpern, eds., Proceedings of the Twentieth Conference Uncertainty in Artificial Intelligence, Arlington, VA: AUAI Press, 446-453.
71. Pearl, J. (2009a): "Causal inference in statistics: An overview," Statistics Surveys, 3,96-146, .
72. Pearl, J. (2009b): Causality: Models, Reasoning, and Inference, New York: Cambridge University Press, second edition.
73. Pearl, J. (2009c): "Letter to the editor: Remarks on the method of propensity scores," Statistics in Medicine, 28, 1415-1416, .
74. Pearl, J. (2009d): "Myth, confusion, and science in causal analysis," Technical Report R-348, Department of Computer Science, University of California, Los Angeles, CA, .
75. Pearl, J. (2009e): "On a class of bias-amplifying covariates that endanger effect estimates," Technical Report R-346, Department of Computer Science, University of California, Los Angeles, CA, .
76. Pearl, J. (2009f): "On measurement bias in causal inference," Technical Report R-357, , Department of Computer Science, University of California, Los Angeles.
77. Pearl, J. and A. Paz (2009): "Confounding equivalence in observational studies," Technical Report R-343, Department of Computer Science, University of California, Los Angeles, CA, .
78. Pearl, J. and J. Robins (1995): "Probabilistic evaluation of sequential plans from causal models with hidden variables," in P. Besnard and S. Hanks, eds., Uncertainty in Artificial Intelligence 11, San Francisco: Morgan Kaufmann, 444-453.
79. Pearl, J. and T. Verma (1991): "A theory of inferred causation," in J. Allen, R. Fikes, and E. Sandewall, eds., Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference, San Mateo, CA: Morgan Kaufmann, 441-452.
80. Petersen, M., S. Sinisi, and M. van der Laan (2006): "Estimation of direct causal effects," Epidemiology, 17, 276-284.
81. Richard, J. (1980): "Models with several regimes and changes in exogeneity," Review of Economic Studies, 47, 1-20.
82. Robertson, D. (1997): "The common sense of cause in fact," Texas Law Review, 75, 1765-1800.
83. Robins, J. (1986): "A new approach to causal inference in mortality studies with a sustained exposure period - applications to control of the healthy workers survivor effect," Mathematical Modeling, 7, 1393-1512.
84. Robins, J. (1987): "A graphical approach to the identification and estimation of causal parameters in mortality studies with sustained exposure periods," Journal of Chronic Diseases, 40, 139S-161S.
85. Robins, J. (1989): "The analysis of randomized and non-randomized aids treatment trials using a new approach to causal inference in longitudinal studies," in L. Sechrest, H. Freeman, and A. Mulley, eds., Health Service Research Methodology: A Focus on AIDS, Washington, D.C.: NCHSR, U.S. Public Health Service, 113-159.
86. Robins, J. (1999): "Testing and estimation of directed effects by reparameterizing directed acyclic with structural nested models," in C. Glymour and G. Cooper, eds., Computation, Causation, and Discovery, Cambridge, MA: AAAI/MIT Press, 349-405.
87. Robins, J. (2001): "Data, design, and background knowledge in etiologic inference," Epidemiology, 12, 313-320.
88. Robins, J. and S. Greenland (1989a): "Estimability and estimation of excess and etiologic fractions," Statistics in Medicine, 8, 845-859.
89. Robins, J. and S. Greenland (1989b): "The probability of causation under a stochastic model for individual risk," Biometrics, 45, 1125-1138.
90. Robins, J. and S. Greenland (1992): "Identifiability and exchangeability for direct and indirect effects," Epidemiology, 3, 143-155.
91. Rosenbaum, P. (2002): Observational Studies, New York: Springer-Verlag, second edition.
92. Rosenbaum, P. and D. Rubin (1983): "The central role of propensity score in observational studies for causal effects," Biometrika, 70, 41-55.
93. Rothman, K. (1976): "Causes," American Journal of Epidemiology, 104, 587-592.
94. Rubin, D. (1974): "Estimating causal effects of treatments in randomized and non-randomized studies," Journal of Educational Psychology, 66, 688-701.
95. Rubin, D. (2004): "Direct and indirect causal effects via potential outcomes," Scandinavian Journal of Statistics, 31, 161-170.
96. Rubin, D. (2005): "Causal inference using potential outcomes: Design, modeling, decisions," Journal of the American Statistical Association, 100, 322-331.
97. Rubin, D. (2007): "The design versus the analysis of observational studies for causal effects: Parallels with the design of randomized trials," Statistics in Medicine, 26, 20-36.
98. Rubin, D. (2009): "Author's reply: Should observational studies be designed to allow lack of balance in covariate distributions across treatment group?" Statistics in Medicine, 28, 1420-1423.
99. Shpitser, I. and J. Pearl (2006): "Identification of conditional interventional distributions," in R. Dechter and T. Richardson, eds., Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence, Corvallis, OR: AUAI Press, 437-444.
100. Shpitser, I. and J. Pearl (2008): "Dormant independence," in Proceedings of the Twenty-Third Conference on Artificial Intelligence, Menlo Park, CA: AAAI Press, 1081-1087.
101. Shpitser, I. and J. Pearl (2009): "Effects of treatment on the treated: Identification and generalization," in Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence, Montreal, Quebec: AUAI Press.
102. Shrier, I. (2009): "Letter to the editor: Propensity scores," Statistics in Medicine, 28, 1317-1318, see also Pearl 2009 .
103. Shrout, P. and N. Bolger (2002): "Mediation in experimental and nonexperimental studies: New procedures and recommendations," Psychological Methods, 7, 422-445.
104. Simon, H. (1953): "Causal ordering and identifiability," in W. C. Hood and T. Koop-mans, eds., Studies in Econometric Method, New York, NY: Wiley and Sons, Inc., 49-74.
105. Simon, H. and N. Rescher (1966): "Cause and counterfactual," Philosophy and Science, 33, 323-340.
106. Sobel, M. (1998): "Causal inference in statistical models of the process of socioeconomic achievement," Sociological Methods & Research, 27, 318-348.
107. Sobel, M. (2008): "Identification of causal parameters in randomized studies with mediating variables," Journal of Educational and Behavioral Statistics, 33, 230-231.
108. Spirtes, P., C. Glymour, and R. Scheines (1993): Causation, Prediction, and Search, New York: Springer-Verlag.
109. Spirtes, P., C. Glymour, and R. Scheines (2000): Causation, Prediction, and Search, Cambridge, MA: MIT Press, 2nd edition.
110. Stock, J. and M. Watson (2003): Introduction to Econometrics, New York: Addison Wesley.
111. Strotz, R. and H. Wold (1960): "Recursive versus nonrecursive systems: An attempt at synthesis," Econometrica, 28, 417-427.
112. Suppes, P. (1970): A Probabilistic Theory of Causality, Amsterdam: North-Holland Publishing Co.
113. Tian, J., A. Paz, and J. Pearl (1998): "Finding minimal separating sets," Technical Report R-254, University of California, Los Angeles, CA.
114. Tian, J. and J. Pearl (2000): "Probabilities of causation: Bounds and identification," Annals of Mathematics and Artificial Intelligence, 28, 287-313.
115. Tian, J. and J. Pearl (2002): "A general identification condition for causal effects," in Proceedings of the Eighteenth National Conference on Artificial Intelligence, Menlo Park, CA: AAAI Press/The MIT Press, 567-573.
116. VanderWeele, T (2009): "Marginal structural models for the estimation of direct and indirect effects," Epidemiology, 20, 18-26.
117. VanderWeele, T. and J. Robins (2007): "Four types of effect modification: A classification based on directed acyclic graphs," Epidemiology, 18, 561-568.
118. Verma, T. and J. Pearl (1990): "Equivalence and synthesis of causal models," in Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence, Cambridge, MA, 220-227, also in P. Bonissone, M. Henrion, L.N. Kanal and J.F. Lemmer (Eds.), Uncertainty in Artificial Intelligence 6, Elsevier Science Publishers, B.V., 255-268, 1991.
119. Wermuth, N. (1992): "On block-recursive regression equations," Brazilian Journal of Probability and Statistics (with discussion), 6, 1-56.
120. Wermuth, N. and D. Cox (1993): "Linear dependencies represented by chain graphs," Statistical Science, 8, 204-218.
121. Whittaker, J. (1990): Graphical Models in Applied Multivariate Statistics, Chichester, England: John Wiley.
122. Wilkinson, L., the Task Force on Statistical Inference, and APA Board of Scientific Affairs (1999): "Statistical methods in psychology journals: Guidelines and explanations," American Psychologist, 54, 594-604.
123. Woodward, J. (2003): Making Things Happen, New York, NY: Oxford University Press.
124. Wooldridge, J. (2002): Econometric Analysis of Cross Section and Panel Data, Cambridge and London: MIT Press.
125. Wooldridge, J. (2009): "Should instrumental variables be used as matching variables?" Technical Report , Michigan State University, MI.
126. Wright, S. (1921): "Correlation and causation," Journal of Agricultural Research, 20, 557-585.