What does the evidence say?

Radiation exposure over extended periods of time (several years)

Figure legend:

LNT model Prediction - Using BEIR VII Report radiation cancer risk factors (NRC, 2006)

Taiwan - Residents of radio-contaminated apartments in Taiwan (Hwang, 2006)

NSWS - Radiation workers in Nuclear Shipyard Worker Study (Sponsler, 2005)

British Radiologists - British Radiologists who entered service during the period 1955-1979 (Berrington, 2001)

Mayak - Evacuated residents of villages near Mayak Nulcear Weapons Facility (Kostyuchenko, 1994)

Conclusion: Radiation exposure over extended periods of time did not increase but reduced cancers, contradicting the LNT model.

Repeated low-dose radiation treatments to cancer patients

Links to references: (Pollycove, 2007)

Conclusion: Repeated low-dose radiation treatments to cancer patients did not increase but reduced cancers, contradicting the LNT model.

Instantaneous Low-dose radiation Exposures

Most important data from atomic bomb survivors.
These data are routinely quoted to support the LNT model.

Links to references: (Preston, 2003) (Ozasa, 2012)

The atomic bomb survivor data have been analyzed using the LNT model shape for dose-response in order to extract the ERRs. The resulting shape of dose-response appeared to be consistent with the LNT model in 2003. With more follow-up, in update publised in 2012, the shape is not consistent with the LNT model because of the curvature in the data.

Conclusion:

Major change in atomic bomb survivor data in 2012.
Reduction of cancers as the radiation dose increases from 0.25 Gy to 0.5 Gy (significant curvature) cannot be explained with the LNT model.

Explanation of curvature using Radiation Hormesis model.

If radiation hormesis were valid, the survivors in the lowest dose bins would have reduced cancers. However, the data from these bins were used in the fitting process to determine the baseline cancer rates, and so the baseline cancer rates would have a negative bias. Correcting for this negative bias, the dose-response curve attains the J-shape shown in the graph below consistent with radiation hormesis.