# 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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2. 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. Pediatr Pulmonol 1995;19: 135-142. PubMed
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6. Pistelli F, Bottai M, Viegi G, et al. Smooth reference equations for slow vital capacity and flow-volume curve indexes. Am J Respir Crit Care Med 2000; 161: 899–905. Erratum in: Am J Respir Crit Care Med 2001; 164: 1740. Manuscript
7. Pistelli F, Bottai M, Carrozzi L, et al. Reference equations for spirometry from a general population sample in central Italy. Respir Med 2007; 101: 814-825. Manuscript
8. Rigby RA, Stasinopoulos DM. Generalized additive models for location, scale and shape (with discussion). Appl Statist 2005; 54: 507-554. Manuscript
9. 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. Manuscript
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