Relationship between lung volume and height
In children and adolescents, unlike in adults, lung
volumes and standing heights are not linearly related
(shown on the right for Dutch boys). Yet many linear relationships
have been published. Indeed, over a small age range, for
example school children, a linear relationship looks acceptable,
albeit not ideal. Another difference with adults is that
the scatter increases in proportion to the FVC (heteroscedasticity):
in adults the scatter was constant (homoscedastic).
It is very
convenient if the relationship between lung volume and
standing height can be linearized by some transformation,
as the relationship can then be described with most
standard statistical techniques. Similarly it is necessary
to stabilize the scatter about the regression line.
A logarithmic transformation of the FVC serves both
purposes. The figure shows the linear regression of
the (natural) logarithm (ln) of the FVC on standing
height, and the 90% confidence interval of individual
predictions based on height. The relationship is:
loge FVC = a + b·height
Back transformation to FVC is obtained by exponentiation:
FVC = exp(a + b·height)
Many people feel ill at ease with logarithms: not to worry, we are almost there.