As shown in Fig. 1, 2931 healthy subjects were included in the modelling group, 478 healthy subjects were included in the validation group. The demographic characteristics and spirometric variables of the healthy subjects are presented in Table 1 and Supplementary Fig. 1. After propensity score matching (PSM), 280 patients with COPD (70 patients in each stage) and 70 COPD-matched healthy subjects were included in the analysis. As the number of stage IV asthmatic patients was limited, PSM was performed between stage I-III asthmatic patients and healthy subjects, and 285 asthmatic patients (78 patients in stage I–III, 51 patients in stage IV) and 78 asthma-matched healthy subjects were included in the analysis. The distributions of age, height and sex ratio were similar between the matched healthy subjects and patients with COPD or asthma (Tables 2 and 3).

The left panel displays the data inclusion and exclusion of healthy subjects in the modelling group, the right panel displays the data inclusion and exclusion of healthy subjects in the validation group and patients with COPD and asthma.

A series of models composed of different variables were built by multiple linear regression, piecewise linear regression, and the natural cubic spline method, respectively. Models with the highest adjusted R2 values of each method are presented in Fig. 2 and Supplementary Table 1. Among these models, the one with the highest adjusted R2 was built by the spline method and composed of FEV1, FEF50%, FEF75%, and height as explanatory variables (Table 4). This model was defined as the estimation equation of lung age and was used to derive lung age for patient groups.

Panel A, fitting curves of lung age estimation equatitons in males; Panel B, fitting curves of lung age estimation equatitons in females.

Internal validation showed that the coefficients of independent variables, adjusted R2 and mean square error (MSE) of the models of bootstrap validation were similar to those of the primary model (see Supplementary Table 2), suggesting that the equations developed in this study performed well in internal prediction. External validation showed that the MSE of ∆ lung age in the validation group (69.9) was smaller than that of the modelling group (73.0–75.6), indicating that the validation group did not present larger differences between the estimated lung age and the chronological age compared to the modelling group (Supplementary Tables 2 and 3). The MSE of ∆ lung age estimated by nonlinear regression (piecewise linear regression: 69.3, spline method: 69.9) was smaller than that by the multiple linear regression (78.8), suggesting nonlinear regression had smaller errors than the multiple linear regression in estimating lung age in validation group (Supplementary Table 3).

Lung age and ∆ lung age of healthy subjects in the modelling group were calculated using the new lung age equations. As ∆ lung age is of greater practical use in the interpretation of lung age, the normal limit of ∆ lung age was explored. Analysis of the ∆ lung age of the modelling group showed that ∆ lung age was negatively correlated with chronological age but not with height or FEV1 (shown in Supplementary Fig. 2), and there was no significant difference in ∆ lung age between healthy males and females (male median: 0.92 years, female median: 0.89 years, P = 0.966). Thus, age-dependent normal limits of ∆ lung age were derived from a regression model between ∆ lung age and chronological age (Supplementary Fig. 2a). Since those with higher ∆ lung age (older lung age) are of greater clinical interest, we only derived the upper limit of normal (ULN) of ∆ lung age, which was calculated according to the results of the regression model as follows: ULN of ∆ lung age (years) = 12.243–0.323 × Age (years) + 1.645 × 7.037 (residual standard error). In addition, we derived a constant ULN of ∆ lung age by calculating the 95th percentile of the healthy subjects, which was 12.5 years. To compare the practical use of lung age estimated by different regression methods, we also derived the ULN of ∆ lung age estimated by the multiple linear regression (MLR) method in the same way, that is, the ULN of ∆ lung age (MLR) (years) = 14.690–0.392 × Age (years) + 1.645 × 7.387.

As shown in Table 5, the proportions of patients with ∆ lung age above different ULNs (age-dependent ULN derived by spline method, constant ULN derived by spline method, age-dependent ULN derived by multiple linear regression, ULN proposed by the previous study [Yamaguchi et al., 2012]11) were compared. The age-dependent ULN derived by the spline method identified more patients with COPD or asthma than other ULNs, with 52.9% of stage I and 100% of stage II-IV COPD patients exceeding the age-dependent ULN (Table 5). For healthy subjects in the validation group, 94.1% (450/478) of ∆ lung age was within the age-dependent ULN derived by spline method (Fig. 3), indicating the equations and the derived normal limit are acceptable in healthy subjects.

The grey area represents the upper limit of normal of the ∆ lung age.

As shown in Fig. 4, the ∆ lung age of stage I COPD patients (Mean ± SD: 4.88 ± 6.81 years) was higher than that of the matched healthy subjects (−4.59 ± 9.42 years, P < 0.05), and a progressive increase in ∆ lung age was shown in stage I–IV COPD patients (stage II: 25.85 ± 9.30 years, stage III: 50.56 ± 9.00 years, stage IV: 65.43 ± 10.08 years, between-group P < 0.05). Similarly, the ∆ lung age of stage I asthmatic patients (2.45 ± 9.16 years) was higher than that of the matched healthy subjects (−1.95 ± 7.99 years, P < 0.05), and a progressive increase in ∆ lung age was shown in stage I–IV COPD patients (stage II: 28.44 ± 11.63 years, stage III: 54.27 ± 12.90 years, stage IV: 68.85 ± 12.77 years, between-group P < 0.05).

Stage I, 80% ≤FEV1 %pred; Stage II, 50% ≤FEV1 %pred <80%; Stage III, 30% ≤FEV1 %pred <50%; Stage IV, 30% >FEV1 %pred. The centre line in the box indicates the median, the lower and upper bound of the box and whiskers indicate the first and the third quartile, and the minimum and maximum value, the point indicates the outlier.