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Rejoinder: Choosing Effect Measures “If I Only Had a…”

VanderWeele, Tyler J.; Mumford, Sunni L.; Schisterman, Enrique F.

doi: 10.1097/EDE.0b013e31823b6990

From the Departments of aEpidemiology and bBiostatistics, Harvard School of Public Health, Boston, MA; and cEpidemiology Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD.

T.J.V. was supported by National Institutes of Health grant HD060696. S.L.M. and E.F.S. were supported by the Intramural Research Program of the Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health. The authors reported no other financial interests related to this research.

Editors' note: Related articles appear on pages 1 and 10.

Correspondence: Tyler J. VanderWeele, Harvard School of Public Health, Departments of Epidemiology and Biostatistics, 677 Huntington Avenue, Boston MA 02115. E-mail:

Although one might compare new methodology to wizardry, eventually, as MacLehose and Kaufman1 acknowledge at the conclusion of their commentary, new methodology often becomes more widespread and is incorporated into the standard epidemiologic toolkit. This process usually occurs gradually: methodology is proposed, gradually disseminated, applications emerge, its assumptions are subject to critical scrutiny, several competing methods may vie for attention, some degree of consensus may be reached, the methodology is incorporated into curricula, then textbooks, and it may eventually become standard practice. At this point, one may say of the challenges encountered by epidemiologists, following MacLehose and Kaufman, that “the magic needed to resolve their problem actually lies in … methodological knowledge in their own backyard.” In our view, however, with regard to methods for mediation and conditioning on intermediates, we are closer to the beginning of this “yellow-brick road” than to its end.

In our paper,2 we discussed 3 approaches related to “conditioning on intermediates in perinatal epidemiology.” Each of the 3 approaches at least partially circumvents problems and biases associated with including an intermediate (eg, birth weight or gestational age) in a regression model when there are unmeasured common causes of the intermediate and the outcome of interest. The 3 approaches correspond to (1) conditioning on the predicted risk of the intermediate, (2) conditioning on the intermediate itself (with sensitivity analysis), and (3) conditioning on the subgroup of individuals for whom the intermediate would occur irrespective of the exposure received. We discussed the interpretation of each of these 3 approaches and their respective causal estimands, as well as the methods and sensitivity analysis techniques relevant to each. We illustrated each approach by application to data with smoking as the exposure, birth weight as the intermediate, and infant mortality as the outcome.

Of particular emphasis in our paper2 was the fact that these approaches assess different causal effects. Which effect is of interest will vary across settings. Moreover, each of the 3 effects is distinct from the total effect of the exposure. The first or third of these approaches may be appropriate when what is of interest is the effect of the exposure among those considered at “high risk” for developing the intermediate. The second approach can be used when what is of interest is the “direct effect” of the exposure on the outcome, not through the intermediate. However, if what is of interest is the total effect of the exposure on the outcome, then, as noted in our paper and elsewhere,3,4 the investigator should not make use of the data on the intermediate at all. Of paramount importance then is carefully selecting the effect that is of interest. Choosing the effect—whether it is a conditional effect, a direct effect, or a total effect—will influence the methods used and the assumptions required for its estimation. Epidemiologists should—like the Scarecrow, the Tin Man, and the Cowardly Lion—have a clear sense as to what is being sought. Methodological wizardry can only have hope of success if we know what we are estimating and why.

Some of this becomes a bit blurred in the commentary by MacLehose and Kaufman.1 In the first approach described in our paper, we estimated the total effect of the exposure (smoking) in the subgroups with comparatively high versus low risk of low birth weight. We found that neither of the total-effect estimates for either subgroup suggested a protective effect of smoking, and we stated that this first approach “avoided the problems associated with conditioning on an intermediate and … circumvented the birth-weight paradox.” Contrary to what seems to have been implied by MacLehose and Kaufman, we did not state that this first approach demonstrated that there was no direct protective effect of smoking for low-birth-weight infants. The methodology of the first approach is not suited for making such assessments. The first approach provides a method to assess the total effect for what are the comparatively high- versus low-risk subpopulations, and the problems of the birth-weight paradox associated with conditioning on an intermediate itself simply do not arise here. Strangely, MacLehose and Kaufman insist on trying to convert estimates from this first approach back and forth from controlled direct effects. They seem to dismiss the possibility that the total effect within subgroups of risk for the intermediate may in fact be what is of interest. Incidentally, moreover, their calculation in equation (1) assumes that there is no unmeasured intermediate-outcome confounding, ie, it assumes away the very phenomenon that arguably gives rise to the birth-weight paradox. Contrary to MacLehose and Kaufman, our primary goal was not to be able to “detect a paradox were it to actually exist” (though we believe our second approach can be useful in this regard). Rather, we sought to provide a range of different causal effects, with different interpretations, using different methods, which can be assessed while at least partially circumventing the biases typically introduced by conditioning on an intermediate.

One can only hope for methodology, wizardry, to be of aid if the aspiration in “If I only had a …,” is clearly articulated and the sentence itself brought to completion. Reading MacLehose and Kaufman, one might think that the only desire was for a resolution of the birth weight paradox. We believe that this was provided some time ago5 (there is plenty of evidence of possible unmeasured common causes that affect birth weight and infant mortality—eg, birth defects and nutrition—and extensive simulation studies to elucidate the magnitude of the effects6,7). Our ambitions, rather, were somewhat broader—distinguishing between different effects and methods that may be of interest when the role of an intermediate is in view. Specifying what effect is of interest should precede analysis. Clarifying that there are multiple effects that might be estimated and then deciding on which of these is substantively most relevant for science or policy is a central part of epidemiologic analysis.

These issues have important consequences for the field of perinatal epidemiology. We have come across a number of reports of reviewers insisting on control for gestational age in models where the effect of interest is arguably the total effect of an exposure occurring before delivery. Lack of awareness of the distinction between total and direct effects and that the analytic methods and appropriate controls for these vary across effects will hinder progress in this field. It was our hope in the paper2 that in distinguishing between these various effects and in providing methods to help circumvent biases associated with conditioning on intermediates in perinatal epidemiology, we would prompt further reflection on what effects may be of interest and how best to go about estimating them.

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1. MacLehose RF, Kaufman JS. The wizard of odds. Epidemiology. 2012;23:10–12.
2. VanderWeele TJ, Mumford S, Schisterman EF. Conditioning on intermediates in perinatal epidemiology. Epidemiology. 2012;23:1–9.
3. Schisterman EF, Whitcomb BW, Mumford SL, Platt RW. Z-scores and the birthweight paradox. Paediatr Perinat Epidemiol. 2009;23:403–413.
4. Wilcox A, Weinberg CR, Basso O. On the pitfalls of adjusting for gestational age at birth. Am J Epidemiol. 2012;174:1062–1068.
5. Hernández-Díaz S, Schisterman EF, Hernán MA. The birth-weight “paradox” uncovered? Am J Epidemiol. 2006;164:1115–1120.
6. Basso O, Wilcox AJ, Weinberg CR. Birth weight and mortality: causality or confounding? Am J Epidemiol. 2006;164:303–311.
7. Whitcomb BW, Schisterman EF, Perkins NJ, Platt RW. Quantification of collider-stratifcation bias and the birthweight paradox. Paediatr Perinat Epidemiol. 2009;23:394–402.
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