The authors respond:
We thank Vedal and Sheppard1 for their comments.
We understand that inclusion of ratios in regression models can cause spurious correlations; however, we do not think that this is the case with our data. The ratio, FEF25–75/FVC, has a physiological interpretation as the reciprocal of one half the time constant of the lung—a measure of airway size. Moreover, we have demonstrated2 that FEF25–75/FVC is highly correlated with another parameter that reflects airway size, Vmax50/Pst(L)50 (maximum instantaneous flow at the 50% volume point divided by static elastic recoil at 50% of lung volume). Mead showed that Vmax50/Pst(L)50 was inversely related to vital capacity,3 a phenomenon termed dysanapsis4 to reflect the disproportionate relation between airway size and lung volumes. Note that Vmax50/Pst(L)50 does not include FVC. We found the same inverse relation between FVC and FEF25–75/FVC2 and showed that this ratio is inversely related to bronchial responsiveness,2 a characteristic that is related, in part, to airway size. We noted in the paper5 that the FEF25–75/FVC ratio is a heritable physiological trait.6 Thus, we feel that this ratio has a sound physiological basis, and its relation to lung function response to ozone presented in our paper is not the result of a spurious correlation, but reflects the impact of airway size. Moreover, with respect to the Krommal paper (scenario 3),7 we are not interested in the individual components of FEF25–75/FVC; rather, as stated previously, we were interested in the single estimate of this term given its interpretation of a measure of airway size. We understand that inclusion of the interaction term of O3 and FEF25–75/FVC without FEF25–75/FVC would likely inflate the magnitude of the coefficient for the interaction term. Given the large t-statistics associated with the interaction, it is not likely that our inferences with respect to the interaction are invalid.
We note in the paper5 that we carried out an analysis of the data from our original publication8 exactly as we did with current data. The coefficients we found were identical to those reported for the new data. The previous analysis did show a main effect of ozone on lung function. The 2 populations differed substantially in their racial/ethnic distribution, and we did not see this main effect in the current data. This issue of dysanapsis is relevant to racial differences, because Asians and blacks tend to have smaller lung volumes than whites after standardization for age, weight, and body size.4 Correction for differences in airway size made the 2 populations comparable.
The characterization of our approach to the evaluation of FVC as “nonstandard” is misleading. The American Thoracic Society guidelines to which Vidal and Sheppard refer were written for adults and are not necessarily applicable to younger ages.9,10 We have shown that, in the age group reported, FVC is not related to duration of the maneuver.11 The guidelines cited by Vidal and Sheppard state that “no change in volume for at least one second or (our italics) a reasonable expiratory time” is part of the criterion and that “In a normal young subject, this would be before the completion of the breath—usually (sic) less than a 6-second maneuver.”12 All of the maneuvers that were less than 6 seconds in our data, which includes the few that were 2 seconds, met the end-of-test criteria of the spirometer software. Therefore, we feel confident that our FVC measures are accurate.
We did not analyze FVC in the current data set. Our previous analysis11 showed that there was no suggestion of an association between estimated lifetime exposure to ozone and FVC (see Table 16).
University of California, Berkeley
Berkeley School of Public Health
University of California, San Francisco
Berkeley School of Public Health
Sonoma Technology, Inc.
Keck School of Medicine
University of Southern California
Los Angeles, California
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2. Tager IB, Weiss ST, Munoz A, et al. Determinants of response to eucapneic hyperventilation with cold air in a population-based study. Am Rev Respir Dis
3. Mead J. Dysanapsis in normal lungs assessed by the relationship between maximal flow, static recoil, and vital capacity. Am Rev Respir Dis
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11. Tager IB, Küenzli N, Ngo L, et al. A Pilot Study to Assess the Reliability of Estimates of Lifetime Exposure to Ambient Ozone Derived From Questionnaires and Ambient Monitoring Data
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12. American Thoracic Society. Standardization of spirometry—1994 update. Am J Respir Crit Care Med