Atomic bomb survivor data
The most important evidence for radiation effects is generally recognized to be the data from atomic bomb survivors. E.g. BEIR VII Report (2005) states on p. 141:
The 2012 update to the data from atomic bomb survivors, (Ozasa, 2012) states on p. 234
Thus, these data do not support the linear no-threshold model, because of the significant curvature in the data. The reason for the curvature is discussed on p. 238
The atomic bomb survivor data, processed using the LNT model assumption, results in a dose-response shape that is inconsistent with the LNT model, as it has a significant curvature (see text and Figure above).
This is also apparently the conclusion of prominent LNT model supporters as indicated by their actions, of not using the latest atomic bomb survivor data for claiming cancer risk from low-dose radiation. E.g. in the 2014 debate in Medical Physics, a prominent proponent of the LNT model did not use these data to justify cancer risk from low-dose radiation whereas in the 2009 debate in Radiology the atomic bomb survivor data were the first data quoted. Also, in the 2014 review article in BJR, older atomic bomb survivor data were used to claim cancer risk from low-dose radiation by another prominent proponent of the LNT model. When challenged for using the older, outdated data, the author provided no justification for using the outdated data in his response.
When the most important data do not support a hypothesis, and many other data also do not support the hypothesis, the hypothesis should be rejected.
Whereas Ozasa et al. do not have an explanation for the reduction of cancers in this dose range of 0.3-0.7 Gy, there is a possible explanation using the radiation hormesis model (Doss, 2013).