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Modelling pulmonary function

For the same standing height and age males have larger lungs than females. Therefore regression equations for predicting indices of lung function must be derived separately for males and females.

Lung volumes increase with height, they increase with age in children and adolescents, and subsequently decline with age. Until recently it was therefore very difficult to derive prediction equations encompassing the age range from pre-school child to old age. This resulted in the derivation of separate regression equations for children, adults, and people of old age. Inevitably they join poorly at the transition from one to another age group. Also, when looking at limited age ranges, it is difficult to discern a non-linear pattern between pulmonary function and age. When reviewing 53 published reference equations for healthy adults, 40 used a simple linear model:

Y = a + b•height + c•age

where Y = lung function index, and b and c are regression coefficients.
Occasionally age2 (3x) or weight (5x) were included in the regression equation.

In childhood and adolescence indices are most often log transformed:

log(Y) = a + b•height + c•age, or

log(Y) = a + b•log(height) + c•log(age)

It is difficult to accept that in adulthood, but not in childhood and adolescence, lung function relates linearly to standing height. After all, through millions of years of evolution, nature has provided mammals with a successful design that makes it possible to scale the lung and airways so that both small and large creatures are equipped with a system that serves their metabolic needs at rest and during exercise. It has been shown that such a design implies that lung volumes are a power function of height in man (Cole), in keeping with allometric laws that apply to small and large mammals (West).

Until recently, modelling pulmonary function properly from early childhood to old age was not possible. However, a new statistical technique (GAMLSS) changed all this. Cole and Stanojevic were the first to fully exploit the new possibilities and derive ‘all age’ equations.

• Cole TJ. Linear and proportional regression models in the prediction of ventilatory function (with Discussion). J Roy Statist Soc, Series A. 1975;138:297–337. Link
• West GB, Brown JH. Enquist BJ. A general model for the origin of allometric scaling laws in biology. Science 1997; 276: 122-126. Pubmed
• West GB, Brown JH. Review. The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization. J Exp Biol 2005; 208: 1575-1592. Pubmed
• Cole TJ, Stanojevic S, Stocks J, Coates AL, Hankinson JL, Wade AM. Age- and size related reference ranges: A case study of spirometry through childhood and adulthood. Statist Med 2009; 28: 880-898. Pubmed
• Stanojevic S, Wade A, Stocks J, et al. Reference ranges for spirometry across all ages. A new approach. Am J Respir Crit Care Med 2008; 177: 253–260. Pubmed
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