You may be interested in the work of the US NCRP SC 1-25 "Recent Epidemiologic Studies and Implications for the Linear-Nonthreshold Model", of which Commentary will come out late this year.
Several types of human cancers (e.g., skin cancer and bone sarcoma in Japanese atomic bomb survivors) do not exhibit a linear dose response, but this does not "contradict" the LNT model because LNT is the model simplified for all types (but not each type) of cancers for radiation protection purposes.
Provided below is more information on my aforementioned description in Japanese atomic bomb survivors.
For non-melanoma skin cancer incidence from 1958-1998, the 2007 paper reported that the spline model with a change in slope at 1 Gy fit the data better than a pure linear model ( https://www.ncbi.nlm.nih.gov/pubmed/17722996 ). For skin basal cell carcinoma incidence from 1958-1996, the 2014 paper reported that there was a significant linear risk with a threshold of 0.63 Gy ( https://www.ncbi.nlm.nih.gov/pubmed/24754560 ).
For bone sarcoma incidence from 1958-2001, the 2011 paper reported that a threshold of 0.85 Gy (95% confidence intervals: 0.12, 1.85 Gy) existed, above which there was a linear dose–response relationship ( https://www.ncbi.nlm.nih.gov/pubmed/21984980 ).
You may also be interested in the following papers that discusses potential thresholds in cancer for acute exposure (particularly discussing if the addition of a threshold term improves the fit to the dose response model for incidence or mortality in atomic bomb survivors, https://www.ncbi.nlm.nih.gov/pubmed/9721832 ) and protracted internal exposure (particularly discussing "virtual" threshold for cancer in bone, bone marrow and lungs, https://www.ncbi.nlm.nih.gov/pubmed/26063349 ).
Jeffry A. Siegel, Charles W. Pennington, and Bill Sacks
Subjecting Radiologic Imaging to the Linear No-Threshold Hypothesis: A Non Sequitur of Non-Trivial Proportion
J Nucl Med 2017 58:1-6 published ahead of print August 4, 2016 (10.2967/jnumed.116.180182).
...S P E C I A L C O N T R I B U T I O N S Jeffry A. Siegel1, Charles W. Pennington2, and Bill Sacks3 1Nuclear Physics Enterprises, Marlton, New Jersey; 2NAC International (retired), Norcross, Georgia, and executive nuclear energy consultant, Alpharetta, Georgia; and 3U.S. Food and Drug Administration ~~~
And a followup Letters to the Editor
Jeffry A. Siegel and Bill Sacks
Eliminating the Use of the Linear No-Threshold Assumption In Medical Imaging
J Nucl Med jnumed.117.189928 published ahead of print February 16, 2017 (10.2967/jnumed.117.189928).
...Eliminating the Use of the Linear-No-Threshold Assumption In Medical Imaging TO THE EDITOR: We thank the Journal for requesting our “Special Contribution” article advocating rejection of the linear no-threshold (LNT) assumption in medical imaging (1). We note that all valid evidence favors either ~~~
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From the view point of the shape of the dose response curve, various low dose phenomena such as hormesis, adaptive responses, bystander effects and other non-targeted effects do not follow the linear relationship. However, this may not necessarily contradict the LNT model for radiation protection purposes. This is because there is no firm evidence that other models are more plausibly better than the LNT model; however, discussion on alternative models is very important and surely necessary.
The latest report on the solid cancer incidence data in atomic bomb survivors has been published. https://www.ncbi.nlm.nih.gov/pubmed/28319463
The sex averaged dose response now exhibits an significant upward curvature (p = 0.03) in a linear quadratic model assuming the common curvature for males and females that was estimated to be 0.22 per Gy [95% confidence intervals (CIs): 0.01 to 0.60]. For this, the shape of the dose response was significantly different between sexes, such that the dose response was linear for females, but exhibited an significant upward curvature for males.
A threshold was not significant. For females, the estimated threshold of 0.08 Gy was not different from 0, and the upper bound of the 95% CI was 0.2 Gy. For males, the best estimate of 0.75 Gy was not different from 0, and the upper bound of the 95% CI was 0.8 Gy.
To address whether recent epidemiological studies support the linear non-threshold model for use in radiation protection, the US National Council on Radiation Protection and Measurements (NCRP) established the Scientific Committee 1-25 (SC 1-25) "Recent Epidemiologic Studies and Implications for the Linear-Nonthreshold Model" in late 2015 under Program Area Committee 1 (PAC1).
As aforementioned, the NCRP SC 1-25 "Recent Epidemiologic Studies and Implications for the Linear-Nonthreshold Model" is reviewing recent epidemiological studies focusing on dose-response models, including threshold, and the relevance to radiation protection, and working on the draft of a commentary.
The final form will be published as the NCRP Commentary later this year, but the outline of the SC 1-25 draft has just been published online. https://www.ncbi.nlm.nih.gov/pubmed/28532210
The US National Council on Radiation Protection and Measurements (NCRP) has just started public consultation for the draft Commentary “Implications of Recent Epidemiologic Studies for the Linear-Nonthreshold Model and Radiation Protection” prepared by Scientific Committee 1-25 (SC 1-25) under Program Area Committee 1 (PAC 1). Please see “Documents in Review” at http://ncrponline.org/ to download the draft and post comments (due 16 October 2017). The information on SC 1-25 “Recent Epidemiologic Studies and Implications for the Linear-Nonthreshold Model” is available at http://ncrponline.org/program-areas/sc-1-25-recent-epidemiologic-studies-and-implications-for-the-linear-nonthreshold-model/ . The information on PAC 1 “Basic Criteria, Epidemiology, Radiobiology, and Risk” is available at http://ncrponline.org/program-areas/pac-1-basic-criteria-epidemiology-radiobiology-and-risk/ .