INTRODUCTION

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Longitudinal change in FEV₁ over time (FEV₁ or slope ) is a valuable health outcome measure when assessing the adverse effects of exposures or diseases in individuals and groups. However, spirometry results are subject to many sources of measurement noise, making it difficult to detect the effects of interest (the signal) (1). Three sources of variation that affect the accuracy of estimation in FEV₁ slope have been studied by previous investigators: variations arising in the measurement process, variations within an individual between occasions, and variability between individuals. With the relatively high variability associated with short-term measurements of FEV₁, the detection of important declines in FEV₁ is difficult with short periods of observation (2). Up to 8 yr of follow-up has been recommended to appreciate with precision the rates of decline in FEV₁, an intimidating prospect for most investigators (3). The absolute difference between estimated mean FEV₁ slope (^µ ) and the "true" mean slope (µ), expressed by the "error" term (e = | ^µ   µ|), can be minimized by increasing the number of subjects (N), the years of follow-up (D), and/or the frequency of measurements (P) (4, 5).

From a longitudinal field spirometry survey, using equipment and procedures recommended by the American Thoracic Society (ATS) (6), we calculated the intra- and intersubject variability, under various available combinations of study duration and measurement frequency. We defined the term maximum error (e_max) by setting the probability equal to 95% that the error (e) is less than or equal to e_max. That is, P[|^µ   µ|  e_max] = 0.95, and accordingly, e_max is one-half the width of the 95% confidence interval for µ. Using the field test results, we present tables of the maximum error values (e_max) for FEV₁, the anticipated accuracy in estimation of FEV₁, the magnitude of differences in FEV₁ between two groups that can be reliably detected, and finally the number of subjects needed in each of the two groups for detecting anticipated differences in FEV₁. These results should provide guidance for investigators in designing more efficient longitudinal spirometry studies.

	METHODS

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Subjects and Spirometry

The subject selection and the spirometry measurements have been detailed elsewhere (7). A cohort of 411 underground coal miners and working nonminers was established in our previous study. Spirometry testing was conducted with an 8-L survey spirometer with an attached microprocessor (Eagle II; Warren E. Collins, Braintree, MA). All testing was performed at the worksite, using the 1979 spirometry standards of the American Thoracic Society (6). Forced exhalation maneuvers were done in the standing position with a nose clip in place. Three to five maneuvers were obtained from each subject. Spirometry was repeated at 6-mo intervals and individual 5-yr FEV₁ slopes were calculated by linear regression. In the present study, we used data obtained from 160 subjects who had completed 11 measurements in approximately 5 yr.

Estimating the Maximum Error Values

The absolute difference between the estimated FEV₁ mean slope (^µ ) and the unknown "true" mean slope (µ) gives the amount of error in the estimation. To evaluate the precision of different study design strategies for repeated measurements of spirometry, we computed the maximum error values by setting the probability equal to 95% that the error is less than or equal to e_max (P[|^µ   µ|  e_max] = 0.95), and thus e_max is one-half the width of the 95% confidence interval (CI). Values for e_max were determined for the various combinations of study duration and number of equally spaced spirometry tests that were available in the entire sample of N = 160 subjects.

Among adults, the linear model for individual lung function decline provides a good approximation to the actual shape of the decay curve over a period of 4 to 6 yr (8). Assuming a 5-yr linear relation among 11 measurements, we estimated the variation around the fitted regression line for each individual j (^ ²_j) and the average variation around the regression line for all study subjects. We also estimated the FEV₁ slope for individual j (^ _j), and obtained the average of ^ _j values, giving the average slope ( ^) for N individuals; µ = ^ is the unbiased estimator of µ (the mean of an infinite population of individuals).

For all 160 subjects, the individual spirometry tests were numbered 1 through 11, from the first to the last test during the 5 yr of follow-up. We used all combinations of data with equal spacing between tests and at least three measurements. Within the 5-yr study, there are 17 separate combinations of D and P (see Table 2), and a total of 72 possible combinations of equally spaced tests with at least 3 measurements, that is, 6 monthly, yearly, or at the beginning, middle, and end of the study. For example, there are five available combinations of tests for D = 3 yr and P = 3 tests, including tests 1-4-7, 2-5-8, 3-6-9, 4-7-10, and 5-8-11; similarly, there are three different combinations of tests available for D = 4 and P = 9; and so forth. We computed the maximum error values using within- and between-subject variation (^ ² and ^ ²) obtained from the full sample of N = 160 individuals, and the corresponding study duration (D) and the number of spirometry measurements (P) for all 72 available combinations of tests. We then grouped the combinations of tests into sets (with same D and P, but different test numbers); and report the average maximum error value e_max for each set (see Table 2). For assessing the sample size effect, we computed the e_max for sample sizes of N = 30, 50, and 100, using the values of ^ ² and ² obtained from the cohort of N = 160 individuals. All the calculations for parameters of ^ _j, ², ^ ², and the maximum error values were conducted by using SAS (Cary, NC) software (9) (see Appendix for a detailed explanation of the formulas used).

Estimating the Detectable Difference in FEV₁

Suppose we want to detect a difference of  units between the average rates of change in two groups. Using Schlesselman's formula 14 (5), {^ ² + 12(P  1)^ ²/[D²P(P + 1)]}/N = ²/[2(Z + Z)²], we are able to estimate the magnitude of  units under the following assumptions. Suppose we want to detect the difference at the significant level of  = 0.05 (Z = 1.64), using a one-sided test of significance, and  = 0.20 (80% power, Z = 0.84). We calculated the anticipated detectable differences in FEV₁ by substituting the values of P and D, and the corresponding values of ^ ² and ^ ² presented in Table 2, for a fixed sample size of N = 30, 50, 100, and 160 for each group, respectively. (For a two-sided test of significance, Z should be replaced by Z_/2, and Z_/2 = 1.96.)

Estimating the Number of Subjects Needed

On the basis of the above formula (Schlesselman's formula 14 [5]), we calculated the anticipated number of subjects requested in each group to detect a difference in average FEV₁ between two groups for any fixed  units. The sample size estimation was made by using the corresponding values of ^ ² and ^ ² obtained from the full sample of N = 160 for various available values of D and P, at  = 0.05 and 80% power, using a one-sided test of significance.

	RESULTS

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Table 1 gives the characteristics for the original study cohort as a whole by the number of spirometry tests completed. In the present analysis, we included 160 participants who had completed all 11 spirometry measurements. The average age at baseline was about 39 yr (ranged from 25 to 65 yr); 24% were current smokers and 44% were nonsmokers at the initial survey. The mean FEV₁ at baseline was 4.18 L, and 3.85 L at the last survey. A greater proportion of miners than nonminers participated in all 11 spirometry tests (59 versus 42%, p < 0.001). Otherwise, there were no significant differences in the baseline characteristics of those who were included in the study group (N = 160) versus those who were excluded from the current analyses (N = 251).

We calculated the within- and between-subject variations (^ ² and ^ ²), and the maximum error values for all 72 available combinations of tests with study duration (D) varied from 1 to 5 yr and the number of measurements (P) from 3 to 11; and then grouped the results into 17 sets with the same D and P. Table 2 presents means of ^ ² and ^ ², by various available values of D and P, for N = 160. Table 3 summarizes the maximum error values for the 17 available sets of P and D, when N = 30, 50, 100, and 160 subjects. The results indicated that the longer the study durations and the larger the sample sizes, the smaller the maximum errors. However, within the same study durations, testing every 6 or 12 mo resulted in similar maximum error values. When designing longitudinal spirometry studies, several combinations of D, P, and N are available that can achieve a desired value of maximum error. For example, to design a study in which the error in the estimation of FEV₁ slope is intended to be less than or equal to 11.7 ml/yr (i.e., the length of the CI = 23.4 ml/yr), the investigator could choose 16 options (as highlighted) from Table 3, including between N = 100, D = 5, P = 11 and N = 160, D = 3, P = 7. 

Table 4 illustrates the size of the anticipated difference in average FEV₁ slope between two groups to be detected at  = 0.05 and 80% power level when sample sizes are N = 30, 50, 100, and 160 for each of the two groups. For example, if the anticipated difference in FEV₁ between two groups is 25-30 ml/yr, then the study design would have nine options (as highlighted) from Table 4, including between N = 30, D = 5, P = 11 and N = 160, D = 2.5, P = 6. Again, with a longer study duration and a larger sample size, a smaller difference can be detected. However, with the same study duration and sample size, as the testing frequency increases the changes in detectable FEV₁ are relatively small. For longer follow-up duration and larger sample size, annual measurements are unnecessarily frequent.

Table 5 provides estimates of the number of subjects needed in each of two groups to detect a fixed difference in FEV₁ between the groups at a significance level of 0.05 with 80% power. For example, a study is planned for lung function in two groups of employees: those exposed to a chemical dust and those not exposed, in which FEV₁ will be measured every 6 mo for 3 yr. If the exposure is estimated to result in a mean difference in FEV₁ slope of at least 30 ml/yr between the exposed group and the unexposed group, Table 5 suggests that, to detect this effect, the sample size should be about 76 subjects in each group, as highlighted.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The rate of change in spirometric lung function is widely used as an outcome variable in investigating the possible hazard of specific exposures. The usefulness of FEV₁ measurements in assessing the adverse effects of environmental exposures or disease processes is critically dependent on the intrinsic variability in the measurement. Many sources of variation can be controlled by assuring adequate training of personnel administering the tests, by selecting equipment that has been tested by accepted procedures, and by adhering to recommended test methodologies and procedures (10, 11).

After these sources of measurement variation have been controlled, the "error" term in estimating group mean FEV₁ slopes can be minimized by increasing the number of subjects (N), the duration of follow-up (D), and/or the frequency of measurements (P). Because longitudinal studies are labor intensive and time consuming, investigators aim to select efficient design strategies that can reliably detect the anticipated effects.

Statistical techniques have previously been suggested in planning and in evaluating longitudinal study design choices, such as frequency of measurement and study duration. In 1974, Berry estimated the standard deviation of the FEV₁ between occasions (within-subject variation) to be 0.12 L, based on several previous studies. By substituting this single value of 0.12 L as the between-occasion standard deviation into the formula given by Schlesselman (5) [Eq. (6)], Berry produced a table of the standard errors (L/yr) of the FEV₁ slope for study durations ranging from 1 to 10 yr and intervals between tests of 1, 3, 6, and 12 mo (4). The results provided information on trends for precision in the estimation of FEV₁, and suggested that for shorter follow-up periods, the estimation error predominates, whereas for longer periods of follow-up it is negligible.

Our study indicates similar conclusions: that longer study durations and larger sample sizes give smaller maximum errors; whereas within the same study durations, testing every 6 or 12 mo results in similar e_max values. However, in the current study, based on actual longitudinal spirometry tests performed with ATS-recommended equipment and procedures, we were able to calculate the within-subject and between-subject variation, ^ ² and ^ ², corresponding to a range of specific combinations of study duration and measurement frequency. Tables are reported for the maximum error (e_max), a single indicator for assessing the precision of estimation for FEV₁ slope. E_max values integrate the effects of D, P, N, and inter- and intrasubject variability, and offer unique guidance for investigators in selecting among various study designs. Tables are also presented for predicting the magnitude of differences in FEV₁ between two groups that can be reliably detected, and for estimating the number of subjects needed in each of two groups for reliably detecting anticipated differences in FEV₁.

This study and the study by Berry (4) provide tables recommending the number of subjects required in each of two groups for a longitudinal study of FEV₁; however, the results are quite different. For example, Table VI in Berry (4) indicates that a 2-yr study with three test points would require 153 subjects in each of two groups to have sufficient power to detect a 30-ml/yr difference, whereas our study predicts the need for 229 subjects, a 50% increase. For a 5-yr study, our results suggest the need for 27 subjects, whereas Berry indicated 37 were needed. In contrast, for a 4-yr study, results from this study and those of Berry are similar (requiring 42 versus 45 subjects for 6-monthly measurements, and 54 versus 53 subjects for yearly testing). One of the reasons for the differences might be related to the values of within- and between-subject variation being used in the estimation. Berry used single values of ^ and ^   for different combinations of study duration and measurement frequency, rather than values from actual test results, as in the current study. Schlesselman commented that actual longitudinal data were needed to use these statistical techniques, and avoids speculation about the size of ^ ² (5).

Certain cautions should be observed in using the tables to evaluate various study designs, because results from studies that use different methods or populations may not be fully comparable. First, the linear function for individual lung function decline provides a good approximation to the actual shape of the FEV₁ decay curve for periods up to 4 to 6 yr. The adequacy of this approximation will decrease as the length of follow-up increases, but should still remain good for adults under 60 yr of age (8). For longer studies, basing statistical analyses solely on linear trends should be satisfactory as a first approximation, but may be insufficient for a more refined analysis, in which a second degree polynomial or other, more complicated curves may be appropriate. Second, an increase in within-subject variability in FEV₁ has been observed among patients, compared with the general population (12). This might have implications for longitudinal study errors, particularly among current and former smokers, which represented about 55% of our study population. Among a currently working population, some investigators have found that smoking status has little effect on the standard deviation of FEV₁ slopes (13). However, the applicability of our results to studies of populations with a high proportion of respiratory illness is not clear. Finally, in our study, testing was done throughout the 5-yr period according to ATS recommendations, by trained and motivated technicians, with ongoing quality assurance, and using an accurate volume spirometer. The results will be most suitable for studies using similar methods.

In summary, the results of this investigation provide guidance to researchers in selecting for longitudinal field spirometry studies a practical and efficient design that will result in acceptable values of maximum error and adequate power to detect anticipated differences in FEV₁ slopes between two groups. The tables should be most useful for studies involving other middle-aged (25 to 65 yr), white, male working populations, with a similar proportion of smokers. It is anticipated that data from other longitudinal spirometry studies will be analyzed in a similar fashion, in order to provide data relevant to other populations.