Abstract
The Wertheimer–Leeper (W–L) wire code is a construct used as a surrogate indicator of residential exposure to electromagnetic fields. However, little is known about how changes in electrical distribution systems affect wire code assignment. The wire code was determined for 150 homes in the Seattle, WA, area twice, 9–11 years apart. For each home, the authors evaluated whether the electrical configuration around the home and the wire code changed between the two time points. The effect of wire code misclassification on observable odds ratios was evaluated, given hypothetical true control distributions and two different dose–response curves. There was an electrical configuration change for 77 (51.3%) homes, which resulted in a wire code change for 29 (19.3%) homes. Eight (5.3%) other homes had a wire code change due to mapping errors or methodological inconsistencies. Misclassification masked the shape of a threshold (nonlinear) dose–response curve and changed the slope of a linear dose–response curve. Although the wire code detected less than half of electrical configuration changes, misclassification of exposure over time may change odds ratios and mask possible dose–response relationships.
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Acknowledgements
This research was supported by grant no. R01CA55844 from the National Cancer Institute. Shelley S. Tworoger was supported, in part, by the National Institutes of Environmental Health Sciences (NIEHS, NIH) Training grant T32EF07262. The authors thank the following individuals for their valuable contributions to this work: Norma Logan, project management; Elizabeth Carosso, data management; Neil Callahan, Yves Jaques and Cathy Kirkwood, data collection; and Peggy Adams Myers, contract administration. The authors also particularly thank Mark Reames, who was involved in data collection and helped with the visual map inspections.
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Appendix
Appendix
Determining observable case–control exposure distributions and odds ratios from a hypothesized, true distribution and odds ratios, accounting for misclassification
Let,
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VL=VLCC
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OL=OLCC
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OH=OHCC
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VH=VHCC
(A) Choose parameter definitions:
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OROL=odds ratio, OLCC versus VLCC
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OROH=odds ratio, OHCC versus VLCC
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ORVH=odds ratio, VHCC versus VLCC
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n=number of controls
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PVL=proportion of controls, VLCC
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POL=proportion of controls, OLCC
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POH=proportion of controls, OHCC
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PVH=proportion of controls, VHCC
(B) Determine the true number of controls in each category:
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NCo,VL=number of controls, VLCC=n*PVL
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NCo,OL=number of controls, OLCC=n*POL
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NCo,OH=number of controls, OHCC=n*POH
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NCo,VH=number of controls, VHCC=n*PVH
(C) Determine the true number of cases in each category:
Let,
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x=OROL(NCo,OL/NCo,VL)
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y=OROH(NCo,OH/NCo,VL)
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z=ORVH(NCo,VH/NCo,VL)
Then,
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NCa,VL=number of cases, VLCC=n/(1+x+y+z)
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NCa,OL=number of cases, OLCC=NCa,VL*x
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NCa,OH=number of cases, OHCC=NCa,VL*y
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NCa,VH=number of cases, VHCC=NCa,VL*z
(D) Determine the observable number of controls, using the misclassification matrix \(\overline{M}\) and the true case and control distributions, \(\overline{A}\) and \(\overline{B}\), respectively. Let:
where Ci,j is the proportion of those with true exposure category j (from the original study) classified as exposure category i in the validity study.
Then, the observable case and control distributions are \(\overline{C}\); and \(\overline{D}\), respectively, where:
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TWOROGER, S., DAVIS, S., SCHWARTZ, S. et al. Stability of Wertheimer–Leeper wire codes as a measure of exposure to residential magnetic fields over a 9- to 11-year interval. J Expo Sci Environ Epidemiol 12, 448–454 (2002). https://doi.org/10.1038/sj.jea.7500246
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DOI: https://doi.org/10.1038/sj.jea.7500246