# Global Lung Function Initiative for spirometry: what is new?

Capturing the non-linear relationship between spirometric indices and age and height, using standard linear regression techniques, is not possible. Occasionally this predicament was solved by splitting the age range up in two: adults, and children and adolescents, and deriving two sets of equations that joined well, see *e.g*. Hankinson *et al*. [1]. Prior to that pulmonary function in childhood was covered by a more complex model [2], or by a large number of regression equations, each spanning one year [3]. More sophisticated models were used similarly for the adult age range, paying special attention to accurately defining the lower limit of normal [4-5]. An elegant method for capturing non-linear curves is by adding a smoothing “spline” to a linear relationship:

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

Fig. 1 - The “spline”, which adds an age-specific term to the predicted value. Please note that the prediction equations use a logarithmic scale. |

This approach was adopted by Pistelli *et al*. [6-7]. However, the statistical package GAMLSS [8], first used to this end by Stanojevic *et al*. [9], offers more advanced methods for modelling pulmonary function. In practice the smoothing spline is modelled as a function of age. You can best envisage this as an age-specific adjustment of the predicted value: a correction that varies with age in the 3-95 year age range (figure 1). We operate on a logarithmic scale. This implies, *e.g*. in a 20 year old woman, that the predicted FEV1 calculated using the linear coefficients (a, b and c in the above equation) should be multiplied by exp(0.19) = 1.21, hence a 21% increase. In a 85 year old women we multiply by exp(-0.40) = 0.67, correcting the FEV1 by 33%.

Fig. 2 - The predicted FEV1 without use of a spline (yellow-green line) provides a bad fit, the one which includes a spline (black line) fits well. |

The difference between the predicted value with and without smoothing spline is illustrated in figure 2. The dashed line represents the predicted value without spline. In children and adolescents the fit looks passible, but in adults the fit is very poor. Conversely, the black line, which represents the predicted value when adding a spline function, fits the actual values over the entire age range.

### References

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*Am J Respir Crit Care Med*1995; 152: 179–187. Manuscript - Quanjer PH, Borsboom GJ, Brunekreef B, Zach M, Forche G, Cotes JE, Sanchis J, Paoletti P. Spirometric reference values for white European children and adolescents: Polgar revisited.
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*et al*. Reference ranges for spirometry across all ages. A new approach.*Am J Respir Crit Care Me*d 2008; 177: 253–260. Manuscript