Invited commentary: Barker meets Simpson.

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. 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 preand 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