Age- and size-related reference ranges: a case study of spirometry through childhood and adulthood

Abstract

Age-related reference ranges are useful for assessing growth in children. The LMS method is a popular technique for constructing growth charts that model the age-changing distribution of the measurement in terms of the median, coefficient of variation and skewness. Here the methodology is extended to references that depend on body size as well as age, by exploiting the flexibility of the generalised additive models for location, scale and shape (GAMLSS) technique. GAMLSS offers general linear predictors for each moment parameter and a choice of error distributions, which can handle kurtosis as well as skewness. A key question with such references is the nature of the age-size adjustment, additive or multiplicative, which is explored by comparing the identity link and log link for the median predictor.There are several measurements whose reference ranges depend on both body size and age. As an example, models are developed here for the first four moments of the lung function variables forced expiratory volume in 1 s (FEV(1)), forced vital capacity (FVC) and FEV(1)/FVC in terms of height and age, in a data set of 3598 children and adults aged 4 to 80 years. The results show a strong multiplicative association between spirometry, height and age, with a large and nonlinear age effect across the age range. Variability also depends nonlinearly on age and to a lesser extent on height. FEV(1) and FVC are close to normally distributed, while FEV(1)/FVC is appreciably skew to the left. GAMLSS is a powerful technique for the construction of such references, which should be useful in clinical medicine.

Figure 1

Age trend in the median (logμ) of FEV₁ in males adjusted for height, with cubic spline curves fitted versus age (dashed line) and log age (solid line). The 95 per cent confidence interval for the solid curve (dotted lines) and the partial residuals about the solid curve are also shown. The curve shows a large and complex effect of age, rising in children and falling in adults.

Figure 2

Log FEV₁ versus log height in males after adjustment for age, with the linear regression fit (solid line) and its 95 per cent confidence interval (dotted lines), along with the partial residuals. After adjustment for age, the height effect is linear across the range.

Figure 3

Age trend in the variability (logσ) of FEV₁ in males, with the fitted cubic spline curve (solid line) and its 95 per cent confidence interval (dotted lines), along with the partial residuals. Variability is greater in young children and the elderly.

Figure 4

The residual distribution of FEV₁ in males: quantile (standardised) residuals plotted against fitted values and against age, the density estimate with rug plot, and the quantile–quantile plot. The distribution is skew to the left.

Figure 5

Contour plots of FEV₁ versus age and height in males up to age 40. The dotted line is the median of the British 1990 height reference [26], and the plot is restricted to ±3 SDs about the median up to and beyond age 20. The two plots show the 5th and 50th centiles of predicted FEV₁ as functions of age and height.

Figure 6

Wireframe plot of FEV₁ in males up to age 40 predicted from age and height, the 5th and 50th centiles as in Figure 5.

Figure 7

The effects of (a) height; (b) age on the median μ; and (c) age on the variability σ, of FEV₁ (dashed lines) and FVC (solid lines) in males (left) and females (right).

Figure 8

Age trends in the median (log μ) of FEV₁/FVC by sex, adjusted for height, with fitted cubic spline curves (solid lines), 95 per cent confidence intervals (dotted lines) and partial residuals. The age trend is linear in males but non-linear in females.