Shape of the dose-response relationship and its impact on leukemia risk

The most striking result of the German KiKK study is a more than two-fold increase in leukemia risk in young children living near German nuclear power plants (NPPs). The statistical significance of this finding is such that a chance result can be largely ruled out. No other potential risk factors were identified in the KiKK study that could explain this finding. The result, however, is in conflict with the assertion by radiation protection authorities that the estimated doses from nuclear power plants were at least a factor of 1000 too low to produce the observed effect.

A number of scientists have pointed out that official dose calculations often use inadequate propagation models and very low dose coefficients for internal emitters which, together, could account for a possible underestimation of doses by a factor 10 to 100. But we need to explain a difference of a factor of 1000. What did we overlook?

A common assumption is that a 100% increase in effect requires a 100% increase in dose. This, however, is not true if the dose-response is non-linear. In addition, residents near NPPs are exposed to widely fluctuating dose rates over the year and not to a constant low dose rate. With a curvilinear dose-response, the effect will be determined not by the average dose but by the dose from emission peaks. This means close examination should be made of emission peaks, eg those resulting from the opening of reactors during refuelling.

To date, we do not know the shape of the dose-response curve for prenatal leukaemia induction. But after the Chernobyl accident, a significant increase of perinatal mortality was found in Germany and the risk depended on the dose to the power of 3.5, ie there was a curvilinear, not linear, dose-response relationship [1].

Assuming that the dose-response for in utero leukemia induction is curvilinear with also a power of dose of 3.5, a 10% increase of dose, eg an increase from 1 mSv per year to 1.1 mSv per year, would yield a 40% increase in leukemia risk. And if the emissions are not constant but characterised by peaks, the resulting effect will be even greater. If the whole annual dose is delivered during the month of refuelling, a 10% increase in annual dose will translate into a 120% increase in leukaemia risk. This will be shown in the following.

With a background dose rate of 1 mSv per year (ie 0.083 mSv per month) the total dose rate during the month of refuelling will be 0.1 + 0.083 = 0.183 mSv per month. Expressed per year, this is a rate of 2.2 mSv per year. For the rest of the year, the dose rate would remain unchanged at 1 mSv per year. Assuming a dose-risk relationship where risk is proportional to dose to the power of 3.5, the radiation risk would be 2.2^3.5 = 15.8 times greater during the refuelling month, than the risk during the rest of the year. Therefore the increase in radiation risk over the whole year would be a factor of (15.8 x 0.083) + (1 x 0.917) = 2.23.

A curvilinear dose-response would be a consequence of the reasonable assumptions that individual doses and radiosensitivities are randomly distributed in a population. As can be shown, the mathematical form of the resulting dose-response relationship is a cumulative lognormal distribution function which, at low dose values, has a strongly curvilinear shape [2]. Such a non-linear shape, together with corrected dose estimates, have the potential to explain the doubling of leukaemia rates observed near German NPPs.

1 Körblein A, Küchenhoff H. Perinatal Mortality in Germany following the Chernobyl accident. Radiat Environ Biophys 1997; 36 (1): 3-7, available at:

2 Körblein A. Einfluss der Form der Dosis-Wirkungsbeziehung auf das Leukämierisiko (in German).
Strahlentelex 2008;524:8-10.

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