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To the Editor:
In their commentary on the Swedish childhood cancer study, 1 Jaffa et al. conclude that compared with contemporary measurements, historical calculations are an inferior surrogate for magnetic field exposure. 2 First, they show that there is a considerable calculation error (about 21%) in historical calculations, and that this error is substantially larger than the magnitude of temporal changes during the study period. Second, they suggest that “there appears to be some form of differential misclassification” in the study that is biasing the effect estimate away from the null. They reach this conclusion by comparing subjects living in single-family homes with those living in apartments and observing that although there is better agreement between measurements and calculations for single-family homes, there is larger disagreement between effect estimates for these metrics.
Feychting and Ahlbom, in their counter-commentary, correctly argue that in a population with a low prevalence of highly exposed subjects, high specificity of the exposure estimation method is necessary to estimate the effects of the exposure accurately, and low sensitivity does not substantially change the effect estimate. 3 Jaffa et al. respond that these points do not seem to address fully their main argument that a better agreement between two metrics associated with a larger disagreement between effect estimates for those metrics cannot be a result of non-differential misclassification. 4
While we agree with Jaffa et al. that historical calculations may result in substantial errors in exposure estimates, their conclusion regarding non-differential misclassification does not hold in all situations. Using two hypothetical numerical examples (Table 1), we show that the seeming paradox of a better agreement between two metrics associated with a larger disagreement between effect estimates could easily occur as a result of non-differential misclassification. This result can occur because marginal agreement and the magnitude of bias not only depend on whether misclassification is differential or non-differential, but also are greatly influenced by the sensitivity and specificity of the metric and the prevalence of the exposure. For simplicity, in our examples, exposure is associated with a twofold increase in risk, misclassification is non-differential, and exposure is classified into two levels.
The first example compares two metrics: one with high specificity and low sensitivity (A), the second with both high sensitivity and high specificity (B). Although metric B has higher overall agreement (95%vs 90%), it results in a larger deviation from the true odds ratio of 2.
As in the Swedish study, the second example involves two populations with different exposure prevalence and compares two exposure metrics which, in the absence of a “gold standard” (in the real world, the true classification would not be known), are compared with each other. In this example, a better agreement between metrics in population 1 (90%vs 80% for population 2) results in a larger discrepancy in effect estimates.
In our examples, which are purely hypothetical, we assume that there is a real association between exposure and disease; this might not be the case for exposure to EMF and childhood cancers. The sensitivity and specificity values used are only illustrative and may not reflect the situation in the Swedish study.
The examples could be modified to show more complicated scenarios, or ones more closely resembling those in the Swedish study (eg, three exposure levels, more disparate effect estimates, etc.). Our purpose, however, is only to show that the seeming paradox of better agreement between metrics associated with larger disagreement between effect estimates is not necessarily a result of differential misclassification.
1. Feychting M, Ahlbom A. Magnetic fields and cancer in children residing near Swedish high-voltage power lines. Am J Epidemiol 1993; 138: 467–481.
2. Jaffa KC, Kim H, Aldrich TE. The relative merits of contemporary measurements and historical calculated fields in the Swedish childhood cancer study. Epidemiology 2000; 11: 353–356.
3. Feychting M, Ahlbom A. With regard to the relative merits of contemporary measurements and historical calculated fields in the Swedish childhood cancer study. Epidemiology 2000; 11: 357–358.
4. Jaffa KC, Kim H, Aldrich TE. Measuring electromagnetic fields. Epidemiology 2000; 11: 359–360.