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36 Am J Epidemiol 2005;161:3637

American Journal of Epidemiology

Copyright 2005 by the Johns Hopkins Bloomberg School of Public Health

All rights reserved

Vol. 161, No. 1

Printed in U.S.A.

DOI: 10.1093/aje/kwi004

Tu et al. Respond to Barker Meets Simpson

Yu-Kang Tu1,2, George T. H. Ellison3, Robert West1, and Mark S. Gilthorpe1

1 Biostatistics Unit, Centre for Epidemiology and Biostatistics, University of Leeds, Leeds, United Kingdom.2 Leeds Dental Institute, University of Leeds, Leeds, United Kingdom.3 St. Georges Hospital Medical School, London, United Kingdom.

Received for publication September 22, 2004; accepted for publication September 28, 2004.

Weinberg (1) highlights the challenges and pitfalls facedwhen statistically analyzing data from observational(nonrandomized) studies to explore causal hypotheses. Shereminds us that statistically significant associations betweenvariables in such studies can be ambiguous. Extreme cautionis required when statistical modeling of data from observa-tional studies is used to infer causality from statistical asso-ciations between exposure and outcome variables. Whenknowledge regarding the relation between exposure(s) andpotential confounder(s) is incomplete, no causal inferenceshould be made based on such data alone. Indeed, underthese circumstances, it is questionable whether one caninvoke a statistical artifact (as we have done) without refer-ence to an accepted causal model. This is why, when demon-strating a serious potential flaw in the statistical analyses ofobservational data believed to support the fetal origins ofadult disease hypothesis, our article (2) invoked a widelyaccepted causal model linking adult blood pressure, birthweight, and current weight.

Using our simple model, we demonstrated one reason whythe statistical relation between birth weight and adult bloodpressure should not be adjusted for current weight if this isnot a true confounder (2). In Weinbergs more complexcausal model (1), which she describes in the form of adirected acyclic graph and which includes prenatal environ-mental and genetic factors (set A factors) that influence bothbirth weight and current weight, adjustment for currentweight can be justified provided there is no direct causalpathway from birth weight to current weight. However, if setB factors (which affect current weight and blood pressure)and/or set C factors (which affect current weight, blood pres-sure, and birth weight) are also present or there is a causalpathway from birth weight to current weight, adjustment forcurrent weight remains inappropriate. These last twoscenarios seem more likely than the first simply because, likeany analytical variable, birth weight is both a correlate of anda proxy for a range of other variables. Like any biologicentity, birth weight is both a consequence and a cause of

other biologic phenomena; like any phenotype, birth weightis the product of the interaction between genetic and envi-ronmental factors. Thus, while many studies exploring the

fetal origins of adult disease hypothesis use birth weight as amarker for prenatal factors responsible for size at birth, birthweight is also a variable that captures those other genetic andenvironmental phenomena with which it is associated,directly and indirectly, causally and by chance. The problemis therefore this: What is the correct causal graph to representreality?

Weinbergs directed acyclic graph (1) is one of manypossible causal models linking prenatal factors, birth weight,current weight, and blood pressure. Although some causalmodels seem more plausible than others, it is crucial toacknowledge that several feasible models exist. For propo-nents of the fetal origins of adult disease hypothesis, current

weight is a confounder because there is at least a possi-bility (in one or more potential causal models) that adjust-ment for current weight is justified. Until we have clearerevidence from experimental studies (3) and a greater under-standing of the complex anatomic, physiologic, andbiochemical processes linking birth weight, current weight,and blood pressure (4), all causal models will be subject todebate. Epidemiologic studies need to be more transparentand rigorous in their reports of the formulation of researchquestions, the underlining biologic mechanism(s), and thestatistical testing of specific research hypotheses (5, 6).

Whatever the preferred causal model, researchers into thefetal origins of adult disease need to be aware that adjust-

ment for variables, such as current weight, is subject to thereversal (Simpson) paradox. Otherwise, old paradoxes neverdie.

REFERENCES

1. Weinberg C. Invited commentary: Barker meets Simpson. AmJ Epidemiol 2005;161:3335.

Correspondence to Dr. Yu-Kang Tu, Biostatistics Unit, Centre for Epidemiology and Biostatistics, University of Leeds, 30/32 Hyde Terrace,

Leeds, LS2 9LN, United Kingdom (e-mail: y.k.tu@leeds.ac.uk).

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2. Tu YK, West R, Ellison ETH, et al. Why evidence for the fetalorigins of adult disease might be a statistical artifact: the rever-sal paradox for the relation between birth weight and bloodpressure in later life. Am J Epidemiol 2005;161:2732.

3. Ceesay SM, Prentice AM, Cole TJ, et al. Effects on birth weightand perinatal mortality of maternal dietary supplements in ruralGambia: 5 year randomised controlled trial. BMJ 1997;315:78690.

4. Gluckman PD, Hanson MA. The developmental origins of themetabolic syndrome. Trends Endocrinol Metab 2004;15:1837.

5. Huxley RR, Neil A, Collins R. Unravelling the fetal originshypothesis: is there really an inverse association between birth-weight and subsequent blood pressure? Lancet 2002;360:65965.

6. Lucas A, Fewtrell M, Cole TJ. Fetal origins of adult diseasethe hypothesis revisited. BMJ 1999;319:2459.

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