Article Text

## Statistics from Altmetric.com

In 1996 we published reference equations for the 5th percentiles of lung function parameters (FVC, FEV_{1}, PEF, FEF_{25}, FEF_{50}, FEF_{75}, FEF_{25–75}, FEV_{1}/FVC) as a function of age and height.1 These reference values were derived from the subsample of the Swiss SAPALDIA study population consisting of never smokers without respiratory symptoms (1267 men and 1890 women aged between 18 and 60 years). In the meantime our German colleagues have applied extrapolations of the 5th percentile curves to men aged between 60 and 70 years2 and have found that for some of the lung function parameters—for example, FEV_{1}—the 5th percentiles appeared to get too close to the mean at age 70 (fig 1).

A new method of estimating percentile curves provides slightly different estimates of the 5th percentile with more plausible extrapolations. This method uses weighted L_{1} regression. Thus, instead of minimising the sum of squared residuals,3a weighted sum of the absolute values of the residuals is minimised. For instance, in order to obtain an estimate of the 5th percentile curve, the weight assigned to terms stemming from negative residuals must be 19 times larger than the weight assigned to terms whose underlying residual is positive.4 (As in our original approach, we used the logarithms of individual ratios between observed and predicted lung function values (LF) as the basis for estimating the 5th percentile curves.) These residuals were regressed against age using weighted L_{1} regression as described above. If y = α + β age denotes the estimated regression line for the 5th percentile of *r* = ln (LFobserved/LFpredicted) as a function of age, then y = LFpredicted exp(α + β age) is an estimate of the 5th percentile of LF given age. To test whether a linear age term was sufficient to describe the age dependency of the 5th percentile of *r* we first defined an indicator variable U taking the value of 1 for residuals*r* ⩽ α + β age and the value 0 for residuals *r* >α + β age and then computed a logistic regression model for U in terms of the covariates age and age.2

The quadratic age term did not reach statistical significance for any of the lung function parameters considered, thus suggesting that the new model was sufficient throughout. In an analogous way we couldverify that the 5th percentile of*r* did not significantly depend on the height of the person. Our new estimates of the parameters α and β are shown in table 1. For the sake of completeness we reproduce in table2 the equations for the means of lung function parameters previously published.1

In contrast to our original estimates of the 5th percentile equations, those derived with the new method appear to provide plausibleextrapolations beyond the age of 60 years for all lung function parameters considered. However, this does not prove the validity of these extrapolations. Only empirical data on lung function from a sample of healthy never smoking subjects older than 60 years could provide truly reliable estimates of lung function parameters at this age. The original and revised estimates of the 5th percentiles of FEV_{1} for men and women are shown in figs 1 and 2.

## Request permissions

If you wish to reuse any or all of this article please use the link below which will take you to the Copyright Clearance Center’s RightsLink service. You will be able to get a quick price and instant permission to reuse the content in many different ways.