For 30 years, there have been suggestions that extremely low frequency magnetic fields such as those are produced by electric power systems may be associated with elevated risks of childhood leukemia. These suggestions are driven by epidemiological evidence, and it has been common to characterize that evidence as showing a threshold effect, with no increase in risk below a threshold, often 0.3 or 0.4 μT, and a constant risk above it. Such a threshold would, however, be biologically unlikely. We tested alternative dose-response relationships quantitatively. We obtained five exposure data sets, applied several candidate dose-response relationships to each one, and performed a regression analysis to see how well they fit each of the three epidemiological data sets. Threshold dose-response relationships performed only moderately. Linear relationships were generally even poorer. The fit was improved by adding quadratic terms or performing non-linear regression. There are limitations in our analysis, stemming from the available data, but addressing this issue in a data-based, quantitative manner should improve understanding, allow better calculations to be made of attributable numbers, and hence ultimately inform public policy making.