Mediation Proportion

To the Editor: Sullivan et al recently presented a case–crossover study1 with interesting null findings, like in other Seattle studies of the same design.2,3 In contrast to the Boston study of Peters et al,4 the Seattle associations between ambient concentrations before onset of a myocardial infarction and ambient conditions on control days were substantially smaller. Unfortunately, this is yet another case–crossover study, out of more than 20 to date, that do not either provide or discuss the distribution of the relevant exposure term and its implications on statistical power.5 The exposure term in the case–crossover design is not the daily level of pollutants, but the difference between the ambient concentration on the event day and the concentration(s) on some control day(s). We have shown that this difference can be very small for a large fraction of event days, thereby seriously limiting the statistical power to refute the null hypothesis.5 The relevant distribution of these differences cannot be inferred from the usual tables showing the distribution of the daily levels (Table 2 in Sullivan et al1). We believe it is time for a change in reporting of case–crossover studies. Authors and reviewers alike should opt for a summary of the relevant exposure term. Otherwise, an important alternative explanation of null findings cannot be evaluated: insufficient statistical power. Sullivan et al provided a further example for the need to present findings using the relevant exposure metric. To assess the shape of the concentration–response function, they show risk estimates for quintiles of the ambient concentrations. However, a conceptually appropriate presentation would stratify risk estimates by quintiles of the relevant exposure term, as defined previously. This might provide different results. We acknowledge that the sample size was large in this study and that elaboration of the analyses in the appropriate exposure metric may simply confirm the results. We also appreciate the thorough discussion of the potential environmental causes of the null findings in Seattle. However, we believe that case–crossover studies should comply with longstanding traditions of good epidemiologic practice; in particular, they should describe the (design-relevant) exposure distribution and address statistical power. This is particularly important when trying to investigate regional differences in acute effects of air pollution.2–4 Nino Künzli Keck School of Medicine University of Southern California Los Angeles, CA [email protected] Christian Schindler Institute of Social and Preventive Medicine University Basel Basel, Switzerland