# "Lower Limit of Normal" for spirometric test results

In clinical medicine, the ‘normal range’ is generally defined as the range of values which encompasses 95% of a healthy population. The lower limit of normal (LLN) is the cut-off below which results from only 2.5% of healthy individuals will fall, while the upper limit of normal (ULN) represents the threshold above which results from only 2.5% of healthy individuals will be found. Accordingly 95% of the healthy population is considered to have “normal” test results, whereas in 2½% they are “too low” and in 2½% ”too high”, resulting in 5% false-positive test results. Results of spirometric tests characteristically lead to values for FEV1 and VC which are too low rather than too high in disease. This probably explains why in respiratory medicine the lower limit of normal is defined as that value which identifies the lower 5th centile of a healthy population of non-smokers.

 Fig. 1 - Relationship between standard deviation and percentage of data under the curve in the case of a normal distribution.

There are various methods for technically deriving the lower limit of normal. The most elegant one is based on a “normal distribution” of test results. In that case (figure 2) 68% of observations are between +1 and -1 standard deviation (SD) of the distribution, 90% between +1.64 and -1.64 SD, 95% between +1.96 and -1.96 SD, and 99.7% between +3 and -3 SD.
In a healthy subject spirometric data vary with age, height, sex and ethnic group. After taking these into account we are left with the residual (measured – predicted value). If the residual is normally distributed the average of residuals is 0. Dividing the residuals by the SD of the distribution [(measured - predicted)/SD] yields a dimensionless number, the z-score. In the case of a normal distribution the average of all z-scores is 0, and the SD is 1 (fig. left).

 Fig. 2 - The coefficient of variation (CoV) for FEV1 in healthy white females varies with age.

The SD (or coefficient of variation: CoV = 100•SD/predicted) varies with age [1,2]. Hence the coefficient of variation must be modelled so that we obtain a normal distribution, i.e. independent of age. Again a spline can be used for optimal modelling:

log(CoV) = a + b•log(age) + spline + error

The coefficient of variation for FEV1 in white females varies between 12½% and 25% (fig. 2). How does this affect the lower limit of normal? At ages 3, 20 and 80 year the coefficient of variation is approximately 16%, 12½% and 21%, respectively. The lower limit of normal in respiratory medicine is the 5th percentile, when the z-score is -1.64, i.e. at the predicted value minus 1.64 times the coefficient of variation. It follows that the lower limit of normal for FEV1 in a 3, 20 and 80 year old white healthy female is at 74%, 80% and 66% of the predicted value. Once again confirmation that we should not regard 80% of predicted as the lower limit of normal.

 Fig. 3 - Predicted FEV1 and LLN in healthy white females, and 80% predicted, as a function of age. Fig. 4 - Distribution of z-scores for FEV1 in healthy white females.

To put this in further perspective we can depict the predicted value and the lower limit of normal for FEV1 (according to GLI-2012) in white females as a function of age. Adding the line representing 80% of predicted illustrates that, particularly in adults, this line creeps progressively higher up in the normal range, leading to a progressively larger proportion of false-positive test results (figure 3).

As explained above the procedure adopted should lead to a normal distribution of residuals, so that the z-scores have an average of 0 and SD 1. Figure 4 demonstrates that this is achieved with the statistical package GAMLSS. This is associated with tremendous benefits: the z-score is completely independent of age, height and sex. For example, if the z-score for any index is -1.64, this signifies in males, females, children and adults that the measured value is at the 5th percentile; in lung function testing this is regarded as the lower limit of normal.

1. 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
2. Quanjer PH, Stanojevic S, Cole TJ et al. and the ERS Global Lung Function Initiative. Multi-ethnic reference values for spirometry for the 3-95 years age range: the Global Lung Function 2012 equations. Eur Respir J 2012; 40: 1324-1343. PubMed
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