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1 Department of Respiratory
Medicine, The Rigshospital, DK-2200 Copenhagen N; Departments of
2 Medical Physiology and
3 Biostatistics,
In obstructive
lung disease the annual change in lung function is usually estimated
from serial measurements of forced expiratory volume in 1 s
(FEV1). Frequent measurements in
each patient may not improve this estimate because data are not
statistically independent; i.e., the measurements are autocorrelated.
The purpose of this study was to describe the correlation structure in
time series of FEV1 measurements.
Nineteen patients with severe
1-antitrypsin deficiency
(phenotype PiZ) and moderate to severe emphysema and two subjects with
normal lungs were followed for several years with daily
self-administered spirometry. FEV1
measurements fulfilling standard criteria were detrended, and the
autocorrelation profile and the power spectrum were calculated. On
average the subjects were followed for >3 yr and performed >1,000
acceptable spirometries. The autocorrelation of
FEV1 measurements in the
emphysematous patients was ~0.35 for short intervals and decreased
almost exponentially with a half time of 38 days. Between 3 and 4 mo,
the autocorrelation function became negative. It reached a minimum of
0.1 at ~8 mo and then increased toward zero over the following
12 mo. The autocorrelation function in the two normal subjects showed a
similar pattern, but with a faster decay toward zero. In the patients,
the power spectrum had a peak at 1 cycle/wk and showed a
1/f pattern, where f is frequency, with a slope of
0.88 at lower frequencies. We conclude that serial spirometric
measurements show long-range correlations. The practical implication is
that FEV1 need not be measured
more often than once every 3 mo in studies of the long-term trends in
lung function.
spirometry; periodicity; Fourier analysis; power spectrum
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