The authors respond:
We thank Jørn Olsen1 for his interest in our paper2 and wholeheartedly agree that the role of reproductive history in the study of pregnancy outcomes is complex. Olsen raises concerns about women modifying their behavior because of their reproductive history. We illustrated this in directed acyclic graphs (DAGs) 3–5.2 In Olsen’s example, the woman modifies a behavior (working nights) that was not the cause of her first pregnancy outcome (preterm birth). If working nights causes preterm birth at the population level, then it would still be appropriate to have an arrow between E0 and O0 because DAGs represent the underlying causal structure at the population level. They are not deterministic at the individual level. If working nights affects only second pregnancies, then there would be no arrow between E0 and O0. If working nights does not affect pregnancies at all, then there would be no arrow between Ei and Oi where i refers to the ith pregnancy (of course, if that were the proposed DAG, then working nights would probably not be studied).
We also agree that unknown confounders are problematic. Olsen suggests a situation where a variable is a confounder during both pregnancies, but the distribution of the confounder is different during the second pregnancy because the woman modifies her behavior in reaction to her prior pregnancy outcome (Fig.). If we are interested in the effect of Ei on Oi and Ci was measured at both times, an unbiased effect could be estimated by controlling for Ci (assuming the figure is correct). If C1 and C2 were unmeasured, restriction to first pregnancies would not solve the problem (although the effect estimate based on first pregnancies might be less biased than that based on second pregnancies, depending on how the distribution of the confounder changed). If we were interested in the effect of E0 and E1 on O1, then C1 is both a confounder and an intermediate variable, and marginal structural models would be needed.
We agree with Olsen that one should carefully consider the research question of interest (using DAGs), develop the best study design for that question, and then use the most appropriate statistical methods for the analyses rather than relying on statistical methods to be omnipotent. We further agree that the best study design is not always obvious, and an in-depth analytic exploration of the data may shed light on complex issues and improve future studies.
Penelope P. Howards
Department of Epidemiology
Enrique F. Schisterman
Division of Epidemiology, Statistics, and Prevention Research
National Institute of Child Health and Human Development
1. Olsen J. Confounding by exposure history and prior outcome [letter]. Epidemiology
2. Howards PP, Schisterman EF, Heagerty PJ. Potential confounding by exposure history and prior outcomes: an example from perinatal epidemiology. Epidemiology