Invited Commentary: Barker Meets Simpson

C. R. Weinberg 

From the Biostatistics Branch, National Institute of Environmental Health Sciences, Research Triangle Park, NC.

Received for publication July 8, 2004; accepted for publication August 31, 2004.


Abbreviations: DAG, directed acyclic graph.

In the current issue of the Journal, Tu et al. (1) show convincingly that if there is no correlation between birth weight and blood pressure but both are positively correlated with current weight (which they are), then adjustment for current weight can induce a negative correlation between birth weight and blood pressure. This demonstration may be important in stimulating epidemiologists to rethink recent evidence for the "fetal origins of adult disease" hypothesis. Articulated by Barker (2, 3), one fascinating example of such a phenomenon has been the negative relation between weight at birth and adult blood pressure, which is taken as evidence that prenatal events that impair fetal growth can set the course for susceptibility to chronic conditions in later life.

Tu et al. (1) remind us that models can lead us badly astray, even when trying to determine the direction of an effect. Many of us first encountered the "reversal paradox," also known as "Simpson’s paradox," in the context of categorical variables. An odds ratio that is 1.0 based on a two-by-two table can become greater (or less) than 1.0 if one disaggregates and instead calculates odds ratios separately within levels of a second factor. Tu et al. point out that qualitative reversals can also occur in the context of continuous variables where, instead of stratifying, we account for another variable by including it in a regression model. They admonish investigators to take such reversal effects into account when contemplating adjustment for a factor (such as current weight) that may be on a causal pathway.

In setting up and interpreting their simulations, Tu et al. (1) seem to presume that if there is no correlation between birth weight and blood pressure then there is "no genuine relation," that is, no causal relation between the two. They further argue from causal principles that because current weight (which is correlated with birth weight and also correlated with blood pressure) is on a causal pathway, it should not be adjusted for as a potential confounder. The appearance of a negative relation in the model that adjusts for current weight must accordingly be regarded as a statistical oddity with no valid causal interpretation. To further assess this argument, let us consider the meaning of confounding in this setting and reexamine what we can reasonably ask a linear regression model to tell us about the interrelatedness of birth weight, current (adult) weight, and blood pressure.

Some of the correlations among these factors are driven by genetics, as acknowledged by Tu et al. (1). In the language of causal graphs, birth weight and adult weight share one or more common "ancestors," and this connection produces an association. These relations are depicted as a directed acyclic graph (DAG) (4) in figure 1.



View larger version (16K):
[in this window]
[in a new window]
 
FIGURE 1. Directed acyclic graph describing one plausible causal basis for associations among birth weight, current weight, and blood pressure. The set A factors (e.g., abundance of nutrients) induce correlation because they are causally active both prenatally and postnatally. The set C factors could affect any subset of the three: birth weight, adult weight, adult blood pressure. The Barker hypothesis is focused on the possible existence of one or both of the black arrows, which represent effects of factors that act specifically during prenatal life.

 
Recent evidence for genetic influences on birth weight comes from analyses based on the large Norwegian birth registry showing that women who were themselves large as newborns tend to give birth to large babies; moreover, men who were large as newborns tend to father large babies (5). It is evidently also true that mothers and fathers who are large as adults have larger babies and that parents who produced larger babies have higher rates of all-cause mortality, and cardiovascular mortality specifically, suggesting an effect "transmissible across generations" (6).

The figure 1 causal diagram shows just one possible, oversimplified version of reality. Under this hypothetical scenario, set A includes environmental factors, such as abundance of nutrients or maternal cigarette smoking, that can act both pre- and postnatally to influence both birth weight and current weight. Set B factors cause blood pressure and current adult weight to be positively correlated for both genetic and environmental reasons (where "environment" includes diet). There are also direct effects of current weight, because overweight can elevate blood pressure. There might also, of course, be factors that affect both birth weight and adult blood pressure, and so on, and those are represented generically as set C.

Tu et al. (1) regard current weight as lying on a causal pathway from birth weight to blood pressure and so would add another arrow to this figure. Current weight is a determinant of blood pressure, weight loss being an effective intervention for hypertension. However, note that low birth weight tends to be associated with low adult weight, which in turn is associated with lower blood pressure. It is therefore a paradox that low birth weight is associated with higher blood pressure. A negative correlation between birth weight and blood pressure clearly cannot be explained by a single causal pathway in which both of the component relations are positive: other causal pathways must be involved. Moreover, birth weight is just size, which can cause certain effects, for example, difficult delivery or greater weight gain during pregnancy (the fetus being a portion of that gain). However, it seems a stretch to think that birth weight per se can influence adult weight.

Nevertheless, part of the correlation between weight at birth and in adulthood could be due to a direct effect of a close correlate of birth weight on adult size, perhaps reflecting the size of stem cell populations laid down prenatally, and I suspect that is what people mean when they think of birth weight as "causing" some later effect. In fact, evidence suggests that adult weight is influenced by prenatal factors acting through effects on fetal growth (as measured by birth weight) (7). One can control for genetics by studying monozygotic twins. Although the difference in birth weights between pairs of monozygotic twins is reportedly correlated with the paired difference in their adult sizes (8, 9), the interpretation is not clear. This finding suggests the short black arrow in figure 1, namely, a role for certain aspects of the prenatal environment in setting the long-term growth trajectory, but these correlations may be primarily secondary to factors specific to monozygotic twinning, such as the transfusion syndrome (10). At the same time, there is a puzzling observation that although twins are often smaller at birth (even accounting for their shorter gestations), as adults they are evidently not smaller on average than singletons (11).

From the point of view of the fetal origins hypothesis, the interesting causal pathway would correspond to the hypothetical long black arrow in figure 1. Tu et al. refer to a scenario with "low birth weight affecting blood pressure directly (e.g., poor nutrition in utero having an irreversible impact on the subsequent development of cardiovascular systems)" (1, p. 30). Under such a scenario, poor prenatal nutrition acts as a common cause of both low birth weight and disoptimal development of the cardiovascular system.

How should an assessment of the causal associations inform our approach to regression modeling? Of the factors shown in figure 1, assume that only birth weight, current weight, and blood pressure are available, as in the paper by Tu et al. (1). Suppose (as in their simulations) that the distribution of the three measures is joint Gaussian. Tu et al. showed that inference regarding the existence and direction of an association between birth weight and adult blood pressure can depend on whether one adjusts or does not adjust for current weight in setting up the regression model. First, if the three are distributed as multivariate Gaussian, it is worth remembering that the adjusted and the unadjusted regression models are both mathematically correct.

Whether to base inference about causality on the adjusted or the unadjusted model should depend on the explicit or implicit causal diagram that governs the relations among the factors. What does a causal graph, if correct, tell us about choosing a model? From the public health viewpoint, what epidemiologists will want to know is not whether a given regression coefficient is positive or negative but whether interventions undertaken during pregnancy might be of benefit to the health of the offspring much later in life. The answers to that question will depend on the true relations among the causal factors at play.

Let us revisit the DAG (figure 1). The fetal origins hypothesis, as related to blood pressure, asserts the existence of a causal path (either black arrow) from prenatal factors to blood pressure (associations based on the white arrows in the figure would not reflect "fetal origins"). That is, in assessing this fetal origins hypothesis, we are trying to determine whether there is an arrow from modifiable (we hope) prenatal factors to adult blood pressure. Imagine first that only set A, but not set B, factors exist. With that modified DAG, adjustment for current weight would be needed to block the confounding path that goes from set A factors through current weight to blood pressure. (Note that, with this DAG, current weight would not be on a causal pathway from birth weight.) However, with the DAG as drawn, the existence of set B factors instead produces an M-shaped causal structure, implying that adjustment for current weight can induce an association between set A and set B factors and thereby create a new confounding path (4). Thus, with this causal diagram, confounding by unmeasured factors is seen to be uncontrollable, making it problematic or perhaps impossible to use an adjusted regression model to base inference about whether a causal path exists from prenatal factors to adult blood pressure. If we leave out adjustment for current weight, there is confounding. If Tu et al. (1) are right and there is also a causal path from birth weight to current weight (not shown), then adjustment for current weight is still inappropriate and could produce more bias than it cures. However, failure to adjust can still leave us with confounding. If we imagine yet another DAG where set C factors influence both birth weight and adult blood pressure but not adult weight, then, again, both the adjusted and the unadjusted models are subject to confounding. Therefore, we are led to the disheartening conclusion that under a variety of plausible DAGs, neither the adjusted nor the unadjusted model is helpful when the goal is to decide whether data that include only birth weight, current weight, and blood pressure support the fetal origins hypothesis.

To answer the question about whether prenatal factors affect adult blood pressure, it may be more useful to exploit certain natural experiments. For example, dizygotic twins are not genetically different from singleton babies but are born weighing less because of their prenatal environment. It would thus be interesting to see whether dizygotic twins tend to have higher blood pressure as adults than nontwins do. In fact, such a study was recently reported (11), and the reduced birth weights seen in twins did not correspond to elevation of adult blood pressure.

The paper by Tu et al. (1) can serve to remind us that etiologic inferences cannot be trusted to a regression package and that decisions about confounding and when to adjust can have a qualitative impact on our conclusions. While we often cannot construct a complete causal graph, we can gain important guidance from the attempt, clarify the assumptions we are making, and then focus on those epidemiologic questions that are answerable.


    NOTES
 
Correspondence to Dr. C. R. Weinberg, Biostatistics Branch, MD A3-03, National Institute of Environmental Health Sciences, P.O. Box 12233, Research Triangle Park, NC 27709 (e-mail: weinberg{at}niehs.nih.gov). Back


    REFERENCES
 TOP
 REFERENCES
 

  1. Tu YK, West R, Ellison GTH, et al. Why evidence for the fetal origins of adult disease might be a statistical artifact: the "reversal paradox" for the relation between birth weight and blood pressure in later life. Am J Epidemiol 2005;161:27–32.[Abstract/Free Full Text]
  2. Barker DJ. Fetal origins of coronary heart disease. BMJ 1995;311:171–4.[Free Full Text]
  3. Barker DJ, Eriksson JG, Forsen T, et al. Fetal origins of adult disease: strength of effects and biological basis. Int J Epidemiol 2002;31:1235–9.[Abstract/Free Full Text]
  4. Greenland S, Pearl J, Robins JM. Causal diagrams for epidemiologic research. Epidemiology 1999;10:37–48.[CrossRef][ISI][Medline]
  5. Magnus P, Gjessing HK, Skrondal A, et al. Paternal contribution to birth weight. J Epidemiol Community Health 2001;55:873–7.[Abstract/Free Full Text]
  6. Davey Smith G, Hart C, Ferrell C, et al. Birth weight of offspring and mortality in the Renfrow and Paisley study: prospective observational study. BMJ 1997;315:1189–93.[Abstract/Free Full Text]
  7. Li L, Manor O, Power C. Early environment and child-to-adult growth trajectories in the 1958 British birth cohort. Am J Clin Nutr 2004;80:185–92.[Abstract/Free Full Text]
  8. Allison D, Paultre F, Heymsfield SB, et al. Is the intra-uterine period really a critical period for the development of adiposity? Int J Obes Relat Metab Disord 1995;19:397–402.[Medline]
  9. Loos R, Beunen G, Fagard R, et al. Birth weight and body composition in young women: a prospective twin study. Am J Clin Nutr 2002;75:676–82.[Abstract/Free Full Text]
  10. Fisk NM, Galea P. Twin-twin transfusion—as good as it gets? N Engl J Med 2004;351:182–4.[Free Full Text]
  11. McNeill G, Tuya C, Campbell DM, et al. Blood pressure in relation to birth weight in twins and singleton controls matched for gestational age. Am J Epidemiol 2003;158:150–5.[Abstract/Free Full Text]