To the Editor:
The article by Howards et al1 provides a lucid and educational description about directed acyclic graphs (DAGs) and instructive examples of how to decide what variables are appropriate to adjust for to remove confounding bias with real data. We agree that it is important to draw careful DAGs underlying the research hypotheses, especially in complex scenarios.
With regard to the effect of E1 on O1, Howards et al state that there are 2 backdoor paths from E1 to O1 (E1←O0←Cb→O1 and E1←Ca → E0 → O1) in the DAG 5.1(p547) They also indicate that Ca and Cb are one of the sufficient combinations to remove confounding bias in this DAG. However, there seems to be another backdoor path E1 to O1 (E1←O0←E0→O1) opened even after Ca and Cb are adjusted for. By adjusting for Ca, for instance, E0 and E1 would be d-separated if there were no other associations between them, thus the spurious association between them caused by Ca would be removed. Nonetheless, since there is a directed path from E0 to E1 through O0 in this DAG, this “true” association would remain. Therefore, we think that the additional adjustments would be required to remove confounding bias completely if only Ca and Cb are adjusted for.
The third hypothesis in their paper refers to the joint effect of the 2 exposure variables, that is E0 and E1 on O1. The 5 DAGs in Figure 1 are then used to choose the relevant confounders. In the DAGs 1 through 4, however, there is no direct arrow from E0 to O1. We think that this research hypothesis would be more clearly depicted if a direct arrow from E0 to O1 is added. In particular, in the DAG 4, the only indirect path from E0 to O1 goes through E1 (E0→O0 → E1 → O1), and the necessity to estimate the effect of E0 on O1 is seemingly unwarranted. Thus, we think that the coefficient of E0 of equation 10 would have no causal interpretation in this case.
We agree that “clearly defining the research question with respect to the outcome, the exposure, and the specific effect of interest is a prerequisite to identifying variables that confound the effect estimate”.1(p545) In this regard, DAGs are of great help in resolving complex scenarios if they are depicted based on the research hypotheses.
Etsuji Suzuki
Hirokazu Komatsu
Takashi Yorifuji
Department of Hygiene and Preventive Medicine
Okayama University Graduate School of Medicine, Dentistry and Pharmaceutical Sciences
Okayama, Japan
[email protected]
Toshihide Tsuda
Department of Environmental Epidemiology
Okayama University Graduate School of Environmental Health
Okayama, Japan
REFERENCE
1. Howards PP, Schisterman EF, Heagerty PJ. Potential confounding by exposure history and prior outcomes: an example from perinatal epidemiology.
Epidemiology. 2007;18:544–51.
