It is common practice in perinatal epidemiology to calculate gestational-age-specific or birth-weight-specific associations between an exposure and a perinatal outcome. Gestational age or birth weight, for example, might lie on a pathway from the exposure to the outcome. This practice of conditioning on a potential intermediate has come under critique for various reasons. First, if one is interested in assessing the overall effect of an exposure on an outcome, it is not necessary to stratify, and indeed, it is important not to stratify, on an intermediate. Second, if one does condition on an intermediate, to try to obtain what might conceived of as a “direct effect” of the exposure on the outcome, then various biases and paradoxical results can arise. It is now well documented theoretically and empirically that, when there is an unmeasured common cause of the intermediate and the outcome, associations adjusted for the intermediate are subject to bias. In this paper, we propose 3 approaches to facilitate valid inference when effects conditional on an intermediate are in view. These 3 approaches correspond to (i) conditioning on the predicted risk of the intermediate, (ii) conditioning on the intermediate itself in conjunction with sensitivity analysis, and (iii) conditioning on the subgroup of individuals for whom the intermediate would occur irrespective of the exposure received. The second and third approaches both require sensitivity analysis, and they result in a range of estimates. Each of the 3 approaches can be used to resolve the “birth-weight paradox” that exposures such as maternal smoking seem to have a protective effect among low-birth-weight infants. The various methodologic approaches described in this paper are applicable to a number of similar settings in perinatal epidemiology.
From the aDepartments of Epidemiology and Biostatistics, Harvard School of Public Health, Boston, MA; and bEpidemiology Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD.
Submitted 29 September 2011; accepted 30 September 2011.
Supported by National Institutes of Health grant HD060696 (to T.J.V.) and Intramural Research Program of the Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health (to S.L.M. and E.F.S.). The authors reported no other financial interests related to this research.
Editors' note: Related articles appear on pages 10 and 13.
Correspondence: Tyler J. VanderWeele, Departments of Epidemiology and Biostatistics, Harvard School of Public Health, 677 Huntington Ave, Boston, MA 02115. E-mail: email@example.com.