Polynomial estimation of the smoothing splines for the new Finnish reference values for spirometry

Abstract

Background Discontinuity of spirometry reference values from childhood into adulthood has been a problem with traditional reference values, thus modern modelling approaches using smoothing spline functions to better depict the transition during growth and ageing have been recently introduced. Following the publication of the new international Global Lung Initiative (GLI2012) reference values also new national Finnish reference values have been calculated using similar GAMLSS-modelling, with spline estimates for mean (Mspline) and standard deviation (Sspline) provided in tables. The aim of this study was to produce polynomial estimates for these spline functions to use in lieu of lookup tables and to assess their validity in the reference population of healthy non-smokers. Methods Linear regression modelling was used to approximate the estimated values for Mspline and Sspline using similar polynomial functions as in the international GLI2012 reference values. Estimated values were compared to original calculations in absolute values, the derived predicted mean and individually calculated z-scores using both values. Results Polynomial functions were estimated for all 10 spirometry variables. The agreement between original lookup table-produced values and polynomial estimates was very good, with no significant differences found. The variation slightly increased in larger predicted volumes, but a range of −0.018 to +0.022 litres of FEV1 representing ± 0.4% of maximum difference in predicted mean. Conclusions Polynomial approximations were very close to the original lookup tables and are recommended for use in clinical practice to facilitate the use of new reference values.

Key Words:

• Spirometry
• reference values
• lung function tests
• mathematical model
• pulmonary medicine

Acknowledgements

The HEVI project centers of Helsinki, Kemi, Kuopio, and Tampere are acknowledged for conducting the original reference values study producing spirometric measurements of the study subjects. The HEVI Project has been funded from Tampere Tuberculosis Foundation. The FinEsS-Helsinki study has received funding from the Special Governmental Subsidy for Health Sciences Research (project codes TYH1235, TYH 2303, TYH 4251 and TYH 2013354). Dr Annette Kainu has received a research grant from the Finnish Anti-tuberculosis Foundation, Jalmari and Rauha Ahokas Foundation and funding from the Special Governmental Subsidy for Health Sciences Research (HUCH Heart and Lung Center).

Disclosure statement

The authors report no other conflicts of interest. The authors alone are responsible for the content and writing of the paper.