Long-range correlations of serial FEV1 measurements in emphysematous patients and normal subjects

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 alpha1-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 approximately 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 approximately 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.