A counterfactual approach to bias and effect modification in terms of response types

BMC Medical Research Methodology

Eiji Yamamoto¹  Toshihide Tsuda³  Toshiharu Mitsuhashi²  Etsuji Suzuki² 

[1] Department of Information Science, Faculty of Informatics, Okayama University of Science, 1–1 Ridai-cho, Kita-ku, Okayama 700-0005, Japan;Department of Epidemiology, Graduate School of Medicine, Dentistry and Pharmaceutical Sciences, Okayama University, 2-5-1 Shikata-cho, Kita-ku, Okayama 700-8558, Japan;Department of Human Ecology, Graduate School of Environmental and Life Science, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530, Japan

关键词: Response types;    Randomization;    Exchangeability;    Effect modification;    Directed acyclic graphs;    Counterfactual;    Causal inference;    Bias;   

Others  :  1092062
DOI  :  10.1186/1471-2288-13-101

 received in 2012-10-17, accepted in 2013-07-15,  发布年份 2013

【 摘 要 】

Background

The counterfactual approach provides a clear and coherent framework to think about a variety of important concepts related to causation. Meanwhile, directed acyclic graphs have been used as causal diagrams in epidemiologic research to visually summarize hypothetical relations among variables of interest, providing a clear understanding of underlying causal structures of bias and effect modification. In this study, the authors aim to further clarify the concepts of bias (confounding bias and selection bias) and effect modification in the counterfactual framework.

Methods

The authors show how theoretical data frequencies can be described by using unobservable response types both in observational studies and in randomized controlled trials. By using the descriptions of data frequencies, the authors show epidemiologic measures in terms of response types, demonstrating significant distinctions between association measures and effect measures. These descriptions also demonstrate sufficient conditions to estimate effect measures in observational studies. To illustrate the ideas, the authors show how directed acyclic graphs can be extended by integrating response types and observed variables.

Results

This study shows a hitherto unrecognized sufficient condition to estimate effect measures in observational studies by adjusting for confounding bias. The present findings would provide a further understanding of the assumption of conditional exchangeability, clarifying the link between the assumptions for making causal inferences in observational studies and the counterfactual approach. The extension of directed acyclic graphs using response types maintains the integrity of the original directed acyclic graphs, which allows one to understand the underlying causal structure discussed in this study.

Conclusions

The present findings highlight that analytic adjustment for confounders in observational studies has consequences quite different from those of physical control in randomized controlled trials. In particular, the present findings would be of great use when demonstrating the inherent distinctions between observational studies and randomized controlled trials.

【 授权许可】

   
2013 Suzuki et al.; licensee BioMed Central Ltd.

【 图 表 】

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【 参考文献 】

• [1]Little RJ, Rubin DB: Causal effects in clinical and epidemiological studies via potential outcomes: concepts and analytical approaches. Annu Rev Public Health 2000, 21:121-145.
• [2]Pearl J: Causality: Models, Reasoning, and Inference. 2nd edition. New York, NY: Cambridge University Press; 2009.
• [3]Greenland S, Robins JM: Identifiability, exchangeability, and epidemiological confounding. Int J Epidemiol 1986, 15:413-419.
• [4]Greenland S, Robins JM, Pearl J: Confounding and collapsibility in causal inference. Stat Sci 1999, 14:29-46.
• [5]Kaufman JS, Poole C: Looking back on "causal thinking in the health sciences". Annu Rev Public Health 2000, 21:101-119.
• [6]Greenland S, Morgenstern H: Confounding in health research. Annu Rev Public Health 2001, 22:189-212.
• [7]Maldonado G, Greenland S: Estimating causal effects. Int J Epidemiol 2002, 31:422-429.
• [8]Hernán MA: A definition of causal effect for epidemiological research. J Epidemiol Community Health 2004, 58:265-271.
• [9]Greenland S, Rothman KJ, Lash TL: Measures of effect and measures of association. In Modern Epidemiology. 3rd edition. Edited by Rothman KJ, Greenland S, Lash TL. Philadelphia, PA: Lippincott Williams & Wilkins; 2008:51-70.
• [10]Weisberg HI: Bias and Causation: Models and Judgment for Valid Comparisons. Hoboken, NJ: Wiley; 2010.
• [11]Morabia A: History of the modern epidemiological concept of confounding. J Epidemiol Community Health 2011, 65:297-300.
• [12]Höfler M: Causal inference based on counterfactuals. BMC Med Res Methodol 2005, 5:28. BioMed Central Full Text
• [13]Greenland S, Robins JM: Identifiability, exchangeability and confounding revisited. Epidemiol Perspect Innov 2009, 6:4. BioMed Central Full Text
• [14]Greenland S, Pearl J, Robins JM: Causal diagrams for epidemiologic research. Epidemiology 1999, 10:37-48.
• [15]Glymour MM, Greenland S: Causal diagram. In Modern Epidemiology. 3rd edition. Edited by Rothman KJ, Greenland S, Lash TL. Philadelphia, PA: Lippincott Williams & Wilkins; 2008:183-209.
• [16]Robins JM: Data, design, and background knowledge in etiologic inference. Epidemiology 2001, 12:313-320.
• [17]Hernán MA, Hernández-Díaz S, Werler MM, Mitchell AA: Causal knowledge as a prerequisite for confounding evaluation: an application to birth defects epidemiology. Am J Epidemiol 2002, 155:176-184.
• [18]VanderWeele TJ, Hernán MA, Robins JM: Causal directed acyclic graphs and the direction of unmeasured confounding bias. Epidemiology 2008, 19:720-728.
• [19]Shrier I, Platt RW: Reducing bias through directed acyclic graphs. BMC Med Res Methodol 2008, 8:70. BioMed Central Full Text
• [20]Evans D, Chaix B, Lobbedez T, Verger C, Flahault A: Combining directed acyclic graphs and the change-in-estimate procedure as a novel approach to adjustment-variable selection in epidemiology. BMC Med Res Methodol 2012, 12:156. BioMed Central Full Text
• [21]Hernán MA, Hernández-Díaz S, Robins JM: A structural approach to selection bias. Epidemiology 2004, 15:615-625.
• [22]VanderWeele TJ, Robins JM: Four types of effect modification: a classification based on directed acyclic graphs. Epidemiology 2007, 18:561-568.
• [23]Greenland S, Brumback B: An overview of relations among causal modelling methods. Int J Epidemiol 2002, 31:1030-1037.
• [24]Cole SR, Frangakis CE: The consistency statement in causal inference: a definition or an assumption? Epidemiology 2009, 20:3-5.
• [25]VanderWeele TJ: Concerning the consistency assumption in causal inference. Epidemiology 2009, 20:880-883.
• [26]Pearl J: On the consistency rule in causal inference: axiom, definition, assumption, or theorem? Epidemiology 2010, 21:872-875.
• [27]Petersen ML: Compound treatments, transportability, and the structural causal model: the power and simplicity of causal graphs. Epidemiology 2011, 22:378-381.
• [28]Hernán MA, VanderWeele TJ: Compound treatments and transportability of causal inference. Epidemiology 2011, 22:368-377.
• [29]VanderWeele TJ, Shpitser I: A new criterion for confounder selection. Biometrics 2011, 67:1406-1413.
• [30]VanderWeele TJ, Shpitser I: On the definition of a confounder. Ann Stat 2013, 41:196-220.
• [31]VanderWeele TJ: On the distinction between interaction and effect modification. Epidemiology 2009, 20:863-871.
• [32]Suzuki E, Yamamoto E, Tsuda T: On the link between sufficient-cause model and potential-outcome model. Epidemiology 2011, 22:131-132.
• [33]Suzuki E, Yamamoto E, Tsuda T: On the relations between excess fraction, attributable fraction, and etiologic fraction. Am J Epidemiol 2012, 175:567-575.
• [34]Greenland S, Poole C: Invariants and noninvariants in the concept of interdependent effects. Scand J Work Environ Health 1988, 14:125-129.
• [35]Hafeman DM: A sufficient cause based approach to the assessment of mediation. Eur J Epidemiol 2008, 23:711-721.
• [36]VanderWeele TJ: Mediation and mechanism. Eur J Epidemiol 2009, 24:217-224.
• [37]Suzuki E, Yamamoto E, Tsuda T: Identification of operating mediation and mechanism in the sufficient-component cause framework. Eur J Epidemiol 2011, 26:347-357.
• [38]Hafeman DM, VanderWeele TJ: Alternative assumptions for the identification of direct and indirect effects. Epidemiology 2011, 22:753-764.
• [39]Glynn RJ, Gagne JJ, Schneeweiss S: Role of disease risk scores in comparative effectiveness research with emerging therapies. Pharmacoepidemiol Drug Saf 2012, 21(Suppl 2):138-147.
• [40]Holland PW: Statistics and causal inference. J Am Stat Assoc 1986, 81:945-960.
• [41]Hernán MA, Robins JM: Estimating causal effects from epidemiological data. J Epidemiol Community Health 2006, 60:578-586.
• [42]Westreich D, Cole SR: Invited commentary: positivity in practice. Am J Epidemiol 2010, 171:674-677.
• [43]Petersen ML, Porter KE, Gruber S, Wang Y, van der Laan MJ: Diagnosing and responding to violations in the positivity assumption. Stat Methods Med Res 2012, 21:31-54.
• [44]Hernán MA: Beyond exchangeability: the other conditions for causal inference in medical research. Stat Methods Med Res 2012, 21:3-5.
• [45]Robins JM, Hernán MA: Estimation of the causal effects of time-varying exposures. In Longitudinal Data Analysis. Edited by Fitzmaurice GM, Davidian M, Verbeke G, Molenberghs G. Boca Raton, FL: CRC Press; 2009:553-599.
• [46]Sjölander A: The language of potential outcomes. In Causality: Statistical Perspectives and Applications. Edited by Berzuini C, Dawid P, Bernardinelli L. Hoboken, NJ: Wiley; 2012:6-14.
• [47]Rosenbaum PR, Rubin DB: The central role of the propensity score in observational studies for causal effects. Biometrika 1983, 70:41-55.
• [48]Stone R: The assumptions on which causal inferences rest. J Roy Stat Soc B Met 1993, 55:455-466.
• [49]Porta MS (Ed): A Dictionary of Epidemiology. 5th edition. New York, NY: Oxford University Press; 2008.
• [50]Greenland S, Lash TL, Rothman KJ: Concepts of interaction. In Modern Epidemiology. 3rd edition. Edited by Rothman KJ, Greenland S, Lash TL. Philadelphia, PA: Lippincott Williams & Wilkins; 2008:71-83.
• [51]Greenland S: Quantifying biases in causal models: classical confounding vs collider-stratification bias. Epidemiology 2003, 14:300-306.
• [52]Hernán MA, Cole SR: Invited commentary: causal diagrams and measurement bias. Am J Epidemiol 2009, 170:959-962.
• [53]Shahar E: Causal diagrams for encoding and evaluation of information bias. J Eval Clin Pract 2009, 15:436-440.
• [54]Shahar E, Shahar DJ: On the causal structure of information bias and confounding bias in randomized trials. J Eval Clin Pract 2009, 15:1214-1216.
• [55]VanderWeele TJ, Hernán MA: Results on differential and dependent measurement error of the exposure and the outcome using signed directed acyclic graphs. Am J Epidemiol 2012, 175:1303-1310.
• [56]Savitz DA: Interpreting Epidemiologic Evidence: Strategies for Study Design and Analysis. New York, NY: Oxford University Press; 2003.