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Growth, current size and the role of the 'reversal paradox' in the foetal origins of adult disease: an illustration using vector geometry

Tu, Y-K., Ellison, G.T.H. and Gilthorpe, M.S. (2006) Growth, current size and the role of the 'reversal paradox' in the foetal origins of adult disease: an illustration using vector geometry. Epidemiologic Perspectives & Innovations, 3 (9). ISSN 1742-5573

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Abstract

BACKGROUND

Numerous studies have reported inverse associations between birth weight and a range of diseases in later life. These have led to the development of the 'foetal origins of adult disease hypothesis'. However, many such studies have only been able to demonstrate a statistically significant association between birth weight and disease in later life by adjusting for current size. This has been interpreted as evidence that the impact of low birth weight on subsequent disease is somehow dependent on subsequent weight gain, and has led to a broadening of the hypothesis into the 'developmental origins of health and disease'. Unfortunately, much of the epidemiological evidence used for both of these interpretations is prone to a statistical artefact known as the 'reversal paradox'. The aim of this paper is to illustrate why, using vector geometry.

MATERIALS AND METHODS

This paper introduces the key concepts of vector geometry as applied to multiple regression analysis. This approach is then used to illustrate the similar statistical problems encountered when adjusting for current size or growth when exploring the association between birth weight and disease in later life.

RESULTS

Geometrically, the three covariates – birth size, growth, and current size – span only 2-dimensional space. Regressing disease in later life (i.e. the outcome variable) on any two of these covariates equates to projecting the disease variable onto the plane spanned by the three covariate vectors. The three possible regression models – where any two covariates are considered – are therefore equivalent and yield exactly the same model fit (R2).

CONCLUSION

Vector geometry illustrates why it is impossible to differentiate between the effects of growth from the effects of current size in studies exploring the relationship between size at birth and subsequent disease. For similar reasons, it is impossible to differentiate between the effects of growth and the effects of birth weight. Assessing the 'independent' impact of growth on later disease by adjusting for either birth weight or current size is therefore illusory.

Item Type: Article
Copyright, Publisher and Additional Information: © 2006 Tu et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Academic Units: The University of Leeds > Faculty of Medicine and Health (Leeds) > Leeds Dental Institute
The University of Leeds > Faculty of Medicine and Health (Leeds) > Leeds Institute of Genetics, Health and Therapeutics (LIGHT) > Biostatistics (Leeds)
The University of Leeds > Faculty of Medicine and Health (Leeds) > School of Medicine (Leeds) > Leeds Institute of Genetics, Health and Therapeutics (LIGHT) > Biostatistics (Leeds)
Depositing User: Sherpa Assistant
Date Deposited: 17 Oct 2008 13:01
Last Modified: 08 Feb 2013 17:05
Published Version: http://dx.doi.org/10.1186/1742-5573-3-9
Status: Published
Publisher: Biomed Central Ltd.
Refereed: Yes
Identification Number: 10.1186/1742-5573-3-9
URI: http://eprints.whiterose.ac.uk/id/eprint/4760

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