Adjustments and their Consequences-Collapsibility Analysis using Graphical Models

International Statistical Review

Volumn 79, Issue 3, 2011, Pages 401-426

  Greenland, Sander ^a   Pearl, Judea ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bias; Causal models; Causality; Collapsibility; Compliance; Confounding; Graphical models; Instrumental variables; Mediation analysis; Odds ratio

Indexed keywords

EID: 82055194473     PISSN: 03067734     EISSN: 17515823     Source Type: Journal    
DOI: 10.1111/j.1751-5823.2011.00158.x     Document Type: Article

References (102)

1. Austin, P.C., Grootendorst, P. & Anderson, G.M. (2007). A comparison of the ability of different propensity score models to balance measured variables between treated and untreated subjects: a monte carlo study. Stat. Med., 26, 734-753.
2. Bareinboim, E. & Pearl, J. (2011). Controlling Selection Bias in Causal Inference. UCLA Cognitive Systems Laboratory, Technical Report R-381, available at.
3. Bareinboim, E., Brito, C. & Pearl, J. (2011). Local characterizations of causal Bayesian networks. In Proceedings of the Second International IJCAI Workshop on Graph Structures for Knowledge Representation and Reasoning, vol. 1, Eds. M. Croitoru, O. Corby, J. Howse, S. Rudolph & N. Wilson, pp. 6-11. Barcelona: GKR.
4. Bhattacharya, J. & Vogt, W. (2007). Do Instrumental Variables Belong in Propensity Scores? Technical Working Paper 343, National Bureau of Economic Research, Cambridge, MA, available at.
5. Brenner, H. (1993). Bias due to non-differential misclassification of polytomous confounders. J. Clin. Epidemiol., 46, 57-63.
6. Brookhart, M., Schneeweiss, S., Rothman, K.J., Glynn, R., Avorn, J. & Stürmer, T. (2006). Variable selection for propensity score models. Amer. J. Epidemiol., 163, 1149-1156.
7. Chaudhuri, S., Richardson, T.S. (2003). Using the structure of d-connecting paths as a qualitative measure of the strength of dependence. In Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence, pp. 116-123. Corvallis, WA: AUAI.
8. Clogg, C.C., Petkova, E. & Haritou A. (1995). Statistical methods for comparing regression coefficients between models (with discussion). Amer. J. Sociol., 100, 1261-312.
9. Cole, S.R. & Frangakis, C.E. (2009). The consistency statement in causal inference: a definition or an assumption? Epidemiology, 20, 3-5.
10. Cole, S. & Hernán, M. (2002). Fallibility in estimating direct effects. Int. J. Epidemiol., 31, 163-165.
11. Cornfield, J. (1951). A method of estimating comparative rates from clinical data: application to cancer of the lung, breast and cervix. J. Nat. Cancer Inst., 11, 1269-1275.
12. Daniel, R.M., Kenward, M.G., Cousens, S.N. & De Stavola, B.L. (2011). Using causal diagrams to guide analysis in missing data problems. Statist. Meth. Med. Res., 20, in press.
13. Davis, L.J. (1986). Whittemore's notion of collapsibility in multidimensional contingency tables. Comm. Statist. Theory Methods, 15, 2541-2554.
14. Day, N.E., Byar, D.P. & Green, S.B. (1980). Overadjustment in case-control studies. Amer. J. Epidemiol., 112, 696-706.
15. de Luna, X., Thomas, S., Richardson, T.S. & Waernbaum, I. (2011). Covariate selection for the non-parametric estimation of an average treatment effect. Biometrika, in press.
16. De Stavola, B.L. & Cox, D.R. (2008). On the consequences of overstratification. Biometrika, 95, 992-996.
17. Didelez, V., Kreiner, S. & Keiding, N. (2010). On the use of graphical models for inference under outcome dependent sampling. Statist. Sci., 25, 368-387.
18. Ducharme, G.R. & Lepage, Y. (1986). Testing collapsibility in contingency tables. J. R. Stat. Soc. Ser. B, 48, 197-205.
19. Fung, K.Y. & Howe, G.R. (1984). The effect of joint misclassification of risk factors and confounding factors upon estimation and power. Int. J. Epidemiol., 13, 366-370.
20. Frydenberg, M. (1990). Marginalization and collapsibility in graphical statistical models. Ann. Statist., 18, 790-805.
21. Gail, M.H. (1986). Adjusting for covariates that have the same distribution in exposed and unexposed cohorts. In Modern Statistical Methods in Chronic Disease Epidemiology, Eds. S. H. Moolgavkar & R.L. Prentice, pp. 3-18. New York: Wiley.
22. Geneletti, S., Ricequalityson, S. & Best, N. (2009). Adjusting for selection bias in retrospective case-control studies. Biostatistics, 10, 17-31.
23. Geng, Z. (1992). Collapsibility of relative risk in contingency tables with a response variable. J. R. Stat. Soc.Ser. B, 54, 585-593.
24. Geng, Z. & Li, G. (2002). Conditions for non-confounding and collapsibility without knowledge of completely constructed causal diagrams. Scand. J. Stat., 29, 169-181.
25. Geng, Z., Guo, J.H., Lau, T.S. & Fung, W.K. (2001). Confounding, homogeneity and collapsibility for causal effects in epidemiologic studies. Statist. Sinica, 11, 63-75.
26. Geng, Z., Guo, J.H & Fung, W.K. (2002). Criteria for confounders in epidemiological studies. J. R. Stat. Soc.Ser. B, 64, 3-15.
27. Glymour, M.M. & S. Greenland (2008). Causal Diagrams. Ch. 12. In Modern Epidemiology, Eds. K.J. Rothman, S. Greenland & T.L. Lash, 3rd ed. Philadelphia: Lippincott.
28. Greenland, S. (1980). The effect of misclassification in the presence of covariates. Amer. J. Epidemiol., 112, 564-569.
29. Greenland, S. (1991). Reducing mean squared error in the analysis of stratified epidemiologic studies. Biometrics, 47, 773-775.
30. Greenland, S. (1996). Absence of confounding does not correspond to collapsibility of the rate ratio or rate difference. Epidemiology, 7, 498-501.
31. Greenland, S. (2003). Quantifying biases in causal models: classical confounding versus collider-stratification bias. Epidemiology, 14, 300-306.
32. Greenland, S. (2005a). Epidemiologic measures and policy formulation: lessons from potential outcomes (with discussion). Emerging Themes in Epidemiology (online journal) 2:1-4. (Originally published as "Causality theory for policy uses of epidemiologic measures, "Chapter 6.2. In Summary Measures of Population Health, Eds. C.J.L. Murray, J.A. Salomon, C.D. Mathers & A.D. Lopez (2002), pp. 291-302. Cambridge, MA: Harvard University Press/WHO.).
33. Greenland, S. & Mickey, R.M. (1988). Closed-form and dually consistent methods for inference on collapsibility in 2xJxK tables. Appl. Stat., 37, 335-343.
34. Greenland, S. & Pearl, J. (2010). Causal diagrams. In International Encyclopedia of Statistical Sciences, Ed. M. Lovric New York: Springer.
35. Greenland, S., Pearl, J. & Robins, J.M. (1999a). Causal diagrams for epidemiologic research. Epidemiology, 10, 37-48.
36. Greenland, S., Robins, J.M. & Pearl, J. (1999b). Confounding and collapsibility in causal inference. Statist. Sci., 14, 29-46.
37. Greenland, S. (2010). Overthrowing the tyranny of null hypotheses hidden in causal diagrams. Ch. 22. In Heuristics, Probabilities, and Causality: A Tribute to Judea Pearl, Eds. R. Dechter, H. Geffner & J.Y. Halpern, pp.365-382. London: College Press.
38. Guo, J.H. & Geng, Z. (1995). Collapsibility of logistic regression coefficients. J. R. Stat. Soc. Ser. B, 57, 263-267.
39. Guo, J., Geng, Z. & Fung, W.-K. (2001). Consecutive collapsibility of odds ratios over an ordinal background variable. J. Multivariate Anal., 79, 89-98.
40. Halloran, M.A. & Struchiner, C.J. (1995). Causal inference for infectious diseases. Epidemiology, 6, 142-151.
41. Hastie, T., Tibshirani, R. & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed. New York: Springer.
42. Hausman, J.A. (1978). Specification tests in econometrics. Econometrica, 43, 1251-1271.
43. Hernán, M.A. (2005). Hypothetical interventions to define causal effects-afterthought or prerequisite? Amer. J. Epidemiol., 162, 618-620.
44. Hernán, M.A. & Robins, J.M. (2006). Instruments for causal inference. Epidemiology, 17, 360-372.
45. Hernán M.A., Hernandez-Diaz, S. & Robins, J.M. (2004). A structural approach to selection bias. Epidemiology, 15, 615-625.
46. Hirano, K. & Imbens, G.W. (2001). Estimation of causal effects using propensity score weighting: an application to data on right heart catheterization. Health Serv. Outcomes Res. Methodol., 2, 259-278.
47. Horvitz, D.G. & Thompson, D.J. (1952). A generalization of sampling without replacement from a finite universe. J. Amer. Stat. Assoc., 47, 663-685.
48. Janes, H., Dominici, F. & Zeger, S. (2010). On quantifying the magnitude of confounding. Biostatistics, 11, 572-582.
49. Joffe, M.M., Yang, W.P. & Feldman, H.I. (2010). Selective ignorability assumptions in causal inference. Int. J. Biostat., 6(2), article 11, available at.
50. Kang, J.D., Shafer, J.L. (2007). Demystifying double robustness: a comparison of alternative strategies for estimating a population mean from incomplete data (with discussion). Statist. Sci., 22, 523-580.
51. Kiiveri, H., Speed, T.P., Carlin, J.B. (1984) Recursive causal models. J. Austral. Math. Soc. Ser. A, 36, pp. 30-52.
52. Lauritzen, S. (1996). Graphical Models. Oxford: Clarendon Press.
53. Lauritzen, S.L. & D.J. Spiegelhalter, D.J. (1988). Local computations with probabilities on graphical structures and their application to expert systems (with discussion). J. R. Stat. Soc. Ser. B, 50, 157-224.
54. Lee, B.K., Lessler, J. & Stuart E.A. (2011) Weight trimming and propensity score weighting. PLoS One, 6(3), 1-6: e18174. doi:.
55. McCaffrey, D.F., Ridgeway, G. & Morral, A.R. (2004) Propensity score estimation with boosted regression for evaluating causal effects in observational studies. Psychol. Meth., 9, 403-425.
56. Miettinen, O.S. & Cook E.F. (1981). Confounding: essence and detection. Amer. J. Epidemiol., 114, 593-603.
57. Ogburn, E.L. & VanderWeele, T.J. (2012). On the nondifferential misclassification of a binary confounder. Epidemiology, in press.
58. Pearl, J. (1986). Fusion, propagation and structuring in belief networks. Artif. Intell., 9, 241-288.
59. Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems. San Mateo, CA: Morgan Kaufmann.
60. Pearl, J. (1995). Causal diagrams for empirical research (with discussion). Biometrika, 82, 669-710.
61. Pearl, J. (2009). Causality, 2nd ed. New York: Cambridge University Press.
62. Pearl, J. (2010a). An introduction to causal inference. Int. J. Biostat. (online journal), 6(2), Article 7, available at.
63. Pearl, J. (2010b). On the consistency rule in causal inference. Epidemiology, 21, 872-875.
64. Pearl, J. (2010c). On measurement bias in causal inference. InProceedings of the 26th Conference on Uncertainty and Artificial Intelligence, Eds. P. Grunwald & P. Spirtes, pp. 425-432. Corvallis, WA: AUAI Press. Available at.
65. Pearl, J. (2010d). On a class of bias-amplifying variables that endanger effect estimates. In Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, pp. 417-427. Corvallis, WA: AUAI Press. Available at.
66. Pearl, J. (2011). Understanding bias amplification. Amer. J. Epidemiol., available at.
67. Pearl, J. & Paz, A. (2010). Confounding equivalence in observational studies. In Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, pp. 433-441. Corvallis, WA: AUAI Press. Available at.
68. Robins, J.M. (1997). Causal inference from complex longitudinal data. InLatent Variable Modeling with Applications to Causality, Ed. M. Berkane, pp. 69-117. New York: Springer-Verlag.
69. Robins J.M. (1999). Testing and estimation of direct effects by reparameterizing directed acyclic graphs with structural nested models. In Computation, Causation, and Discovery, Eds. C. Glymour & G. Cooper, pp. 349-405. Menlo Park, CA / Cambridge, MA: AAAI Press/The MIT Press.
70. Robins, J.M. (2001). Data, design, and background knowledge in etiologic inference. Epidemiology, 12, 313-320.
71. Robins, J.M. & Greenland, S. (1992). Identifiability and exchangeability for direct and indirect effects. Epidemiology, 3, 143-155.
72. Robins, J.M. & Richardson, T.S. (2010). Alternative graphical causal models and the identification of direct effects. In Causality and Psychopathology: Finding the Determinants of Disorders and Their Cures, Ed. P. Shrout New York: Oxford University Press.
73. Robins J.M., Hernán M.A. & Brumback B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology, 11, 550-560.
74. Robinson, L.D. & Jewell, N.P. (1991). Some surprising results about covariate adjustment in logistic regression models. Int. Statist. Rev., 2, 227-240.
75. Rothman, K.J., Greenland S. & Lash T.L., eds. (2008). Modern Epidemiology, 3rd ed. Philadelphia: Lippincott.
76. Rubin, D.B. (2002). Using propensity scores to help design observational studies: application to the tobacco litigation. Health Serv. Outcomes Res. Methodol., 2, 169-188.
77. Rubin, D.B. (2009). Should observational studies be designed to allow lack of balance in covariate distributions across treatment group Stat. Med., 28, 1420-1423.
78. Samuels, M.L. (1981). Matching and design efficiency in epidemiological studies. Biometrika, 68, 577-588.
79. Sato, T. & Matsuyama, Y. (2003). Marginal structural models as a tool for standardization. Epidemiology, 14, 680-686.
80. Savitz, D.A. & Baron, A.E. (1989). Estimating and correcting for confounder misclassification. Amer. J. Epidemiol., 129, 1062-1071.
81. Schisterman, E., Cole, S. & Platt, R. (2009). Overadjustment bias and unnecessary adjustment in epidemiologic studies. Epidemiology, 20, 488-495.
82. Sommer, A.S. & Zeger, S. (1991). On estimating efficacy from clinical trials. Stat. Med., 10, 45-52.
83. Shpitser, I. & Pearl, J. (2008). Dormant independence. In Proceedings of the 23rd Conference on Uncertainty and Artificial Intelligence, pp. 1081-1087. Corvallis, WA: AUAI Press. Available at.
84. Shpitser, I. & Pearl, J. (2009). Effects of treatment on the treated: identification and generalization. In Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, Eds. J. Bilmes & A. Ng, pp. 514-521. Corvallis, WA: AUAI Press.
85. Shpitser, I., VanderWeele, T.J. & Robins, J. M. (2010). On the validity of covariate adjustment for estimating causal effects. In Proceedings of the 26th Conference on Uncertainty and Artificial Intelligence, Eds. P. Grunwald & P. Spirtes, pp. 527-536. Corvallis, WA: AUAI Press. Available at.
86. Shpitser, I., Richardson, T.S. & Robins, J.M. (2011). An efficient algorithm for computing interventional distributions in latent variable causal models. In Proceedings of the 27th Conference on Uncertainty and Artificial Intelligence. Corvallis, WA: AUAI Press, in press.
87. Spiegelhalter, D. (1987). Coherent evidence propagation in expert systems. J. R. Stat. Soc. Ser. D (The Statistician), 36, 201-210.
88. Spirtes, P., Glymour, C. & Scheines, R. (2001). Causation, Prediction, and Search, 2nd ed. Cambridge, MA: MIT Press.
89. Thomas, D.C. & Greenland, S. (1983). The relative efficiencies of matched and independent sample designs for case-control studies. J. Chronic Dis., 36, 685-697.
90. Tian, J. & Pearl, J. (2002). On the testable implications of causal models with hidden variables. In Proceedings of the Eighteenth National Conference on Artificial Intelligence, pp. 61-68. Menlo Park, CA: AAAI Press/The MIT Press. Available at.
91. Tian, J., Paz, A. & Pearl, J. (1998). Finding a minimal d-separator. UCLA Cognitive Systems Laboratory, Technical Report (R-254), Feb. 1998. Available at.
92. van der Laan, M.J. & Rose, S. (2011). Targeted Learning: Causal Inference for Observational and Experimental Data. New York: Springer.
93. VanderWeele, T.J. (2009a). On the relative nature of over-adjustment and unnecessary adjustment. Epidemiology, 20, 496-499.
94. VanderWeele, T.J. (2009b). Concerning the consistency assumption in causal inference. Epidemiology, 20, 880-883.
95. VanderWeele, T.J. & Robins, J.M. (2010). Signed directed acyclic graphs for causal inference. J. R. Stat. Soc. Ser. B, 72, 111-127.
96. VanderWeele, T.J., Hernán, M.A. & Robins, J.M. (2008). Causal directed acyclic graphs and the direction of unmeasured confounding bias. Epidemiology, 19, 720-728.
97. Wermuth, N. (1987). Parametric collapsibility and the lack of moderating effects in contingency tables with a dichotomous response variable. J. R. Stat. Soc. Ser. B, 49, 353-364.
98. Westreich, D. (2011). Berkson's bias, selection bias, and missing data. Epidemiology, in press.
99. White, H. & Lu, X. (2011), Causal diagrams for treatment effect estimation with application to efficient covariate selection. Rev. Econ. Stat., in press.
100. Whittemore, A.S. (1978). Collapsibility of multidimensional contingency tables. J. R. Stat. Soc. Ser. B, 40, 328-340.
101. Yanagawa, T. (1984). Case-control studies: assessing the effect of a confounding factor. Biometrika, 71, 191-194.
102. Yule, G.U. (1934). On some points related to vital statistics, more especially statistics of occupational mortality. J. R. Stat. Soc., 97, 1-84.