Reference values for spirometry

Let us start by looking at FEV1 as a function of age in Caucasian females, aged 3-95 years. The FEV1 increases until about age 20, and then declines steadily. There is very considerable scatter about the mean, with a maximum at 20-40 year. Although the scatter diminishes with age in adults, it does not do so in proportion to the predicted value.

Obviously we cannot satisfactorily describe the relation between FEV1, age and height over the entire age range with a simple linear relationship of the form

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

However, let us do it anyway and see how the predicted values relate to the measured ones. To this end we have first derived the relationship of height with age. We then substituted age, and height for age, into the regression equation to obtain a continuous line.

As expected, the fit is very poor (right figure). It is obvious that we must make allowance for the rise and fall in FEV1 by making an age-specific adjustment. This can be done by adding an age-specific spline. Think of it as an age-specific correction to the above linear equation. The equation then has the following form:

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

For those who take a keen interest in how this is achieved in practice, consult 'GAMLSS in action'.

The figure on the left shows the spline for the predicted value of FEV1 in females as a function of age. It discloses that at about age 5 yr the predicted value based upon age and height to needs to be lowered by about 20%. At about ages 11 and 50 years no correction is required. At age 20 years the predicted value needs to be increased by about 20%, and at age 90 years diminished by about 40%.

Now let us see how this works out in practice. The regression line (black, figure on the right) now looks realistic.

Oviously, part of the scatter shown is due to between subject differences in standing height. In the data on Caucasian females, height in 3-20 year old subjects ranged between 85 and 188 cm, a twofold range. In adults the height range was 123-192 cm; obviously the shortest subjects are outliers compared to the rest. In the adult women average height is 164.6 cm at age 20, and 152.6 cm at age 90, a 12 cm difference. These age-related height differences have two causes:

• A tendency to become shorter in adulthood occurs among all races and both sexes. Height loss is related to aging changes in the bones.
• Secular trends: a person born, say 60 years ago, is likely to have been shorter at age 20 than someone born 20 years ago. This relates to changes in socio-economic conditions.

It is therefore worthwhile to explore how much of the scatter is due to differences in height (next).