DOI: 10.1097/01.ede.0000165815.89253.25

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Issn Print: 1044-3983

Publication Date: 2005/07/01


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Case–Crossover Studies

Jeffrey Sullivan; Lianne Sheppard; Astrid Schreuder; Joel Kaufman

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Author Information: sulljh@u.washington.edu

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Drs. Künzli and Schindler1 raise an interesting point regarding the relevant exposure description in acute effect air pollution studies. We agree that it is helpful for the data description to include a summary of the exposure variation actually used in the analysis. Similar to time-series analyses, the convention in case–crossover papers has been to report on the unadjusted exposure distribution. This description ignores the fact that the calculation of the health effect estimate relies on a restricted exposure range. For case–crossover studies, the relevant exposure variability is restricted to within-referent windows.
In our study,2 the square root of the average within-referent window exposure variance was 10.9 μg/m3. This quantity ranged from 1.1 to 46.3 μg/m3 with an interquartile range (IQR) of 3.8–11.9 μg/m3. For time-series studies, the relevant exposure distribution is obtained after the smooth function of time has been removed. The equivalent calculation for case–crossover studies subtracts the mean for each referent window from all observations in that window. This summary yields an IQR of 7.9 μg/m3, compared with the unadjusted IQR of 10.6 μg/m3 shown in Table 2 of our paper. Although this description of exposure represents a smaller exposure variation than the data description reported in our paper, it does not change our analysis or results.
Our model assumed a linear dose–response. Thus, referent windows with average exposure of 25 μg/m3 contribute the same information as referent windows with average exposure of 5 μg/m3 provided they have identical exposure variability. We disagree with the suggestion by Künzli and Schindler that our Figure 1 presentation should have been indexed by some other metric than the PM quintile midrange. Because our model is linear, our presentation gives a visual check of the linear dose–response assumption. It also showed a direct comparison of our results with those for the Boston Onset Study.3
We also disagree with the assertion of Künzli and Schindler that insufficient statistical power may be an alternative explanation for the null findings in our study. Once study results have been obtained, confidence interval estimates should be used to assess study power.4,5 Our study's large sample size produced relatively narrow confidence interval estimates. For a 10-μg/m3 increase in PM 1-hour before myocardial infarction (MI) onset, we reported 1.05 as the upper limit of our confidence interval estimate. For risk of MI onset in Seattle, this finding can be interpreted as providing evidence against a short-term effect of fine PM larger than a relative risk of 1.05 for a 10-μg/m3 increase in PM.
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