Annals of Epidemiology xxx (2014) 1e2
Contents lists available at ScienceDirect
Annals of Epidemiology journal homepage: www.annalsofepidemiology.org
Letter to the Editor
A simple example as a pedagogical device?
To the Editor: At the Third North American Congress of Epidemiology held in Montreal from June 21 to 24, 2011, Maldonado [1] gave a poster presentation about a simple device for teaching causal concepts in epidemiology. He proposed a simple nonhealth example using four flashlights to represent the subjects of a study. Based on the presentation, an original article by Maldonado [2] was published online in October 2013. Maldonado should be commended for trying to explain complex causal concepts by using this simple example. We think, however, that there is some ambiguity in his example, which could lead to confusion and misunderstandings about the concept of confounding and the use of directed acyclic graphs. Thus, we submitted a commentary to the Annals of Epidemiology, in which we aimed to develop a clearer presentation of causal concepts in epidemiology by exploring another simple example, based on the one Maldonado used. The journal declined to publish our commentary. We therefore decided to submit this brief letter to succinctly describe how we feel Maldonado’s simple example can be improved as a pedagogical device. First, although Maldonado focused his discussion on causal effects in the exposed and the unexposed groups, we believe that it is preferable to use the total population as the target population to teach the concept of confounding more effectively. The notion of confounding can be defined both with respect to marginal distributions of potential outcomes (i.e., confounding in distribution) and with respect to a specific effect measure (i.e., confounding in measure) [3,4]. Although Maldonado implicitly used the latter notion, it is crucial to distinguish these because sufficient conditions for no confounding generally vary according to these notions [5]. When the target population is the exposed or the unexposed, however, sufficient conditions for no confounding are identical in the two definitions [5]. It would thus be helpful to use not only the exposed and the unexposed groups but also the total population as target populations to clarify the significance of differentiating the two notions of confounding. Second, Maldonado did not explain the mechanism that generates the exposure event (i.e., switch position of each flashlight). In other words, nonexchangeability of response types between the exposed and unexposed groups in his example could be due to the fact that one randomly observed this configuration but that the estimator is unconfounded in expectation or that there is a reason for the nonexchangeability that is not revealed in his example. This point is closely related to a deeper understanding of the concept of confounding because a further distinction can be drawn between confounding “in expectation” and “realized” confounding [4,6].
1047-2797/$ e see front matter Ó 2014 Elsevier Inc. All rights reserved.
Although Maldonado implicitly focused on “realized” confounding in the two subpopulations (i.e., the exposed and the unexposed groups), it would be also valuable to teach the notion of confounding “in expectation” since the concept of confounding bias has most often been defined by comparing the expected value of an estimator and the true value of the parameter [7,8]. This is usually explained using schematic illustrations of target shooting in introductory epidemiology textbooks [9,10]. In this regard, the total population is the population naturally chosen as the target of inference. Third, we are concerned that his Figure 1 does not properly portray the world Maldonado described, and thus his example does not necessarily demonstrate his implications (5) or (6) (see the abstract of Maldonado [2]). We should also note that there is only one sufficient cause of the outcome in his example, which is rare in practice [11]. In addition, we should not overlook the fact that flashlight color is, for unexplained reasons, correlated with a set of characteristics. Indeed, one must draw directed acyclic graphs for the total population to more readily identify the presence of bias. In conclusion, we are concerned that Maldonado’s example is useful as a pedagogical device only in the situation in which one teaches the notion of “realized” confounding in measure for just two specific subpopulations, when there is only one sufficient cause of the outcome of interest. Furthermore, although confounding in measure is scale dependent, neither incidenceproportion ratio nor incidence-proportion odds ratio can be defined in his example because no study subjects are classified as “doomed” or “preventive.” We recommend interested readers to refer to our full-length article on these points (“The power of simplicity: developing a clearer understanding of causal concepts in epidemiology”), which we have submitted to another journal. Letters have the potential to further dialog within our field, and we hope that this letter serves to draw attention to the strengths and limitations of Maldonado [2] and to greater attention to these subtle but important points. Etsuji Suzuki, MD, PhD Department of Epidemiology, Graduate School of Medicine Dentistry and Pharmaceutical Sciences, Okayama University Okayama, Japan Toshiharu Mitsuhashi, MD, PhD Center for Innovative Clinical Medicine Okayama University Hospital, Okayama University Okayama, Japan
2
Letter to the Editor / Annals of Epidemiology xxx (2014) 1e2
Toshihide Tsuda, MD, PhD Department of Human Ecology Graduate School of Environmental and Life Science Okayama University, Okayama, Japan Eiji Yamamoto, PhD Department of Information Science, Faculty of Informatics Okayama University of Science, Okayama, Japan http://dx.doi.org/10.1016/j.annepidem.2014.04.003 References [1] Maldonado G. A simple device for teaching causal concepts. Am J Epidemiol 2011;173(11 Suppl):S186. [2] Maldonado G. Toward a clearer understanding of causal concepts in epidemiology. Ann Epidemiol 2013;23(12):743e9. [3] Greenland S, Robins JM, Pearl J. Confounding and collapsibility in causal inference. Stat Sci 1999;14(1):29e46.
[4] VanderWeele TJ. Confounding and effect modification: distribution and measure. Epidemiol Method 2012;1(1):55e82. http://dx.doi.org/10.1515/ 2161-962X.1004. [5] Suzuki E, Yamamoto E. Further refinements to the organizational schema for causal effects. Epidemiology; 2014. http://dx.doi.org/10.1097/ EDE.0000000000000114. [6] Greenland S, Robins JM. Identifiability, exchangeability and confounding revisited. Epidemiol Perspect Innov 2009;6:4. http://dx.doi.org/10.1186/17425573-6-4. [7] Porta MS, editor. A dictionary of epidemiology. 5th ed. New York, NY: Oxford University Press; 2008. [8] Everitt B, Skrondal A. The Cambridge dictionary of statistics. 4th ed. Cambridge, UK: Cambridge University Press; 2010. [9] Greenberg RS, Daniels SR, Flanders WD, Eley JW, Boring III JR. Medical epidemiology. 4th ed. New York, NY: Lange Medical Books/McGraw-Hill; 2005. [10] Jekel JF, Katz DF, Elmore JG, Wild DMG. Epidemiology, biostatistics, and preventive medicine. 3rd ed. Philadelphia, PA: Saunders/Elsevier; 2007. [11] Flanders WD, Johnson CY, Howards PP, Greenland S. Dependence of confounding on the target population: a modification of causal graphs to account for co-action. Ann Epidemiol 2011;21(9):698e705.
Contents lists available at ScienceDirect
Annals of Epidemiology journal homepage: www.annalsofepidemiology.org
Letter to the Editor
A simple example as a pedagogical device?
To the Editor: At the Third North American Congress of Epidemiology held in Montreal from June 21 to 24, 2011, Maldonado [1] gave a poster presentation about a simple device for teaching causal concepts in epidemiology. He proposed a simple nonhealth example using four flashlights to represent the subjects of a study. Based on the presentation, an original article by Maldonado [2] was published online in October 2013. Maldonado should be commended for trying to explain complex causal concepts by using this simple example. We think, however, that there is some ambiguity in his example, which could lead to confusion and misunderstandings about the concept of confounding and the use of directed acyclic graphs. Thus, we submitted a commentary to the Annals of Epidemiology, in which we aimed to develop a clearer presentation of causal concepts in epidemiology by exploring another simple example, based on the one Maldonado used. The journal declined to publish our commentary. We therefore decided to submit this brief letter to succinctly describe how we feel Maldonado’s simple example can be improved as a pedagogical device. First, although Maldonado focused his discussion on causal effects in the exposed and the unexposed groups, we believe that it is preferable to use the total population as the target population to teach the concept of confounding more effectively. The notion of confounding can be defined both with respect to marginal distributions of potential outcomes (i.e., confounding in distribution) and with respect to a specific effect measure (i.e., confounding in measure) [3,4]. Although Maldonado implicitly used the latter notion, it is crucial to distinguish these because sufficient conditions for no confounding generally vary according to these notions [5]. When the target population is the exposed or the unexposed, however, sufficient conditions for no confounding are identical in the two definitions [5]. It would thus be helpful to use not only the exposed and the unexposed groups but also the total population as target populations to clarify the significance of differentiating the two notions of confounding. Second, Maldonado did not explain the mechanism that generates the exposure event (i.e., switch position of each flashlight). In other words, nonexchangeability of response types between the exposed and unexposed groups in his example could be due to the fact that one randomly observed this configuration but that the estimator is unconfounded in expectation or that there is a reason for the nonexchangeability that is not revealed in his example. This point is closely related to a deeper understanding of the concept of confounding because a further distinction can be drawn between confounding “in expectation” and “realized” confounding [4,6].
1047-2797/$ e see front matter Ó 2014 Elsevier Inc. All rights reserved.
Although Maldonado implicitly focused on “realized” confounding in the two subpopulations (i.e., the exposed and the unexposed groups), it would be also valuable to teach the notion of confounding “in expectation” since the concept of confounding bias has most often been defined by comparing the expected value of an estimator and the true value of the parameter [7,8]. This is usually explained using schematic illustrations of target shooting in introductory epidemiology textbooks [9,10]. In this regard, the total population is the population naturally chosen as the target of inference. Third, we are concerned that his Figure 1 does not properly portray the world Maldonado described, and thus his example does not necessarily demonstrate his implications (5) or (6) (see the abstract of Maldonado [2]). We should also note that there is only one sufficient cause of the outcome in his example, which is rare in practice [11]. In addition, we should not overlook the fact that flashlight color is, for unexplained reasons, correlated with a set of characteristics. Indeed, one must draw directed acyclic graphs for the total population to more readily identify the presence of bias. In conclusion, we are concerned that Maldonado’s example is useful as a pedagogical device only in the situation in which one teaches the notion of “realized” confounding in measure for just two specific subpopulations, when there is only one sufficient cause of the outcome of interest. Furthermore, although confounding in measure is scale dependent, neither incidenceproportion ratio nor incidence-proportion odds ratio can be defined in his example because no study subjects are classified as “doomed” or “preventive.” We recommend interested readers to refer to our full-length article on these points (“The power of simplicity: developing a clearer understanding of causal concepts in epidemiology”), which we have submitted to another journal. Letters have the potential to further dialog within our field, and we hope that this letter serves to draw attention to the strengths and limitations of Maldonado [2] and to greater attention to these subtle but important points. Etsuji Suzuki, MD, PhD Department of Epidemiology, Graduate School of Medicine Dentistry and Pharmaceutical Sciences, Okayama University Okayama, Japan Toshiharu Mitsuhashi, MD, PhD Center for Innovative Clinical Medicine Okayama University Hospital, Okayama University Okayama, Japan
2
Letter to the Editor / Annals of Epidemiology xxx (2014) 1e2
Toshihide Tsuda, MD, PhD Department of Human Ecology Graduate School of Environmental and Life Science Okayama University, Okayama, Japan Eiji Yamamoto, PhD Department of Information Science, Faculty of Informatics Okayama University of Science, Okayama, Japan http://dx.doi.org/10.1016/j.annepidem.2014.04.003 References [1] Maldonado G. A simple device for teaching causal concepts. Am J Epidemiol 2011;173(11 Suppl):S186. [2] Maldonado G. Toward a clearer understanding of causal concepts in epidemiology. Ann Epidemiol 2013;23(12):743e9. [3] Greenland S, Robins JM, Pearl J. Confounding and collapsibility in causal inference. Stat Sci 1999;14(1):29e46.
[4] VanderWeele TJ. Confounding and effect modification: distribution and measure. Epidemiol Method 2012;1(1):55e82. http://dx.doi.org/10.1515/ 2161-962X.1004. [5] Suzuki E, Yamamoto E. Further refinements to the organizational schema for causal effects. Epidemiology; 2014. http://dx.doi.org/10.1097/ EDE.0000000000000114. [6] Greenland S, Robins JM. Identifiability, exchangeability and confounding revisited. Epidemiol Perspect Innov 2009;6:4. http://dx.doi.org/10.1186/17425573-6-4. [7] Porta MS, editor. A dictionary of epidemiology. 5th ed. New York, NY: Oxford University Press; 2008. [8] Everitt B, Skrondal A. The Cambridge dictionary of statistics. 4th ed. Cambridge, UK: Cambridge University Press; 2010. [9] Greenberg RS, Daniels SR, Flanders WD, Eley JW, Boring III JR. Medical epidemiology. 4th ed. New York, NY: Lange Medical Books/McGraw-Hill; 2005. [10] Jekel JF, Katz DF, Elmore JG, Wild DMG. Epidemiology, biostatistics, and preventive medicine. 3rd ed. Philadelphia, PA: Saunders/Elsevier; 2007. [11] Flanders WD, Johnson CY, Howards PP, Greenland S. Dependence of confounding on the target population: a modification of causal graphs to account for co-action. Ann Epidemiol 2011;21(9):698e705.
