American Journal of Epidemiology Advance Access originally published online on July 13, 2005
American Journal of Epidemiology 2005 162(4):395; doi:10.1093/aje/kwi232
American Journal of Epidemiology Copyright © 2005 by the Johns Hopkins Bloomberg School of Public Health All rights reserved
THE AUTHORS REPLY
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 LS2 9LN, United Kingdom
2 Leeds Dental Institute, University of Leeds, Leeds LS2 9LU, United Kingdom
3 St. George's Hospital Medical School, University of London, London SW17 0RE, United Kingdom
Professor Cole's letter (1
) confirms our findings (2) and offers an elegant algebraic proof. Together with our simulations, and the slightly different approach we adopted in a similar proof published in the Appendix of our original article (2, p. 32), we hope that the issues we sought to raise are now accessible and persuasive to a range of readers, including those without formal statistical training or mathematical expertise.
Meanwhile, Professor Cole's proof (1) raises another important issue that tends to be overlooked: that the relation between blood pressure and current body weight will also be increased by adjusting for birth weight. Following the notation in Professor Cole's letter, the regression coefficient of current weight is 
Because r1 (the correlation between blood pressure and birth weight) is weak and close to zero whereas r12 is generally larger, ß2 is very likely to be larger than r2. Regarding the overall fitness of the model in terms of R2, the proportion of variance in blood pressure explained by birth weight and current weight is
because
r1 is close to zero,
R2 is very likely to be greater than the
sum of
and
Therefore, even if birth weight explains almost none of the variance in
blood pressure, the overall variance in blood pressure explained
by birth weight and current weight in the multiple regression
will be greater than the sum of the variance in blood pressure
explained by current weight alone plus the variance in blood
pressure explained by birth weight alone. In the statistical
literature, this is known as "suppression," in that birth weight
"suppresses" that part of the variance in current weight that
is not correlated with blood pressure. An excellent discussion
of conditions causing such suppression effects can be found
in a recent review by Friedman and Wall (3
).
Finally, space does not permit a detailed response to Professor Cole's suggestion that a "change in sign of the weight-versus-outcome correlation over time indicates the importance of weight change as opposed to birth weight" (1, p. 394). Because body weight increases with age, it becomes more and more difficult to distinguish current weight from "weight change since birth"; indeed, if weight change is defined as "current weight minus birth weight," weight change will eventually operate as if it were statistically equivalent to current weight. We are therefore cautious about alternative versions of the fetal origins of adult disease hypothesis suggesting that "catch-up growth" (i.e., weight change from birth) is a greater risk factor for disease in later life than birth weight alone (4), because the evidence to support these alternative hypotheses is based on statistical models similar to those underpinning the original hypothesis. We have prepared a manuscript using n-dimensional vector geometry to demonstrate the problematic interpretation of what might be called the "catch-up growth hypothesis," and we trust that it will explain in greater detail our substantive reservations.
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ACKNOWLEDGMENTS
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Conflict of interest: none declared.
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References
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- Cole TJ. Re: "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." (Letter). Am J Epidemiol 2005;162:394–5.[Free Full Text]
- 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]
- Friedman L, Wall M. Graphical views of suppression and multicollinearity in multiple linear regression. Am Stat 2005;59:127–36.[CrossRef]
- Williams S, Poulton R. Birth size, growth, and blood pressure between the ages of 7 and 26 years: failure to support the fetal origins hypothesis. Am J Epidemiol 2002;155:849–52.[Abstract/Free Full Text]
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