**Introduction:** In “Keeping ICRP Recommendations Fit for Purpose”, LNT model is described as “LNT is the most appropriate evidence-based assumption to use for radiological protection purposes (p.10).” According to our critical literature survey on radiological epidemiology, some limitations were identified: (1) aggregation of individual level data, (2) model formulation, (3) model estimation, (4) model selection, (5) results interpretation. In this paper we focus (4) model selection and demonstrate LNT was the best model.

**Data and Method:** Using “Life Span Study Report 14. Cancer and non-cancer disease mortality data, 1950-2003”, solid cancer mortality was re-analyzed. In addition to the L, Q, LQ, hadn searched threshold model, kinked–at-2Gy model that assumes LQ for less than 2Gy and L for larger than 2 Gy, and Linear model with threshold as a parameter were estimated. Following [3], Poisson regression model was applied and model fit was compared with AIC and BIC.

**Results:** Among estimated models, Linear (BIC=18317.9) and grid search threshold at 20mSv (BIC=18318.1) was selected as the best models. Directly estimated threshold was -23.2 mSv and it was statistically insignificant (z=-0.087,p>0.1). Model fit of kinked-at-2Gy was poorer than these models (BIC=18321.2).

**Conclusion:** Based on these results, we can conclude LNT model is the best model for a-bomb survivor solid cancer mortality. According to our literature survey, LNT is supported Description of LNT model in “Keeping ICRP Recommendations Fit for Purpose” should be modified accordingly: “LNT is the scientifically supported model, it is reasonable LNT to use for radiological protection purposes.”

*Keywords: **LNT; Radiation epidemiology; Poisson regression; Re-analysis*

Yutaka Hamaoka

Thank you for comment and question. According to Table 1 in LSS14 paper, https://www.rerf.or.jp/uploads/2017/08/rr1104-1.pdf, among 86611 subjects, 38509 and 29961 subjects are concentrated at <0.005 Gy and 0.1

Bernd Lorenz

there is no proof for LNT. What you demonstrate here is a self-fulfilling prophecy.. The data from LSS do not allow conclusions about low and very low doses. LNT has to be questioned as it leads to lower and lower doses without benefit.

Cameron JeffriesSouth Australia Medical Imaging

Bernd I was wondering how to express the idea of assuming exposure to radiation from an atomic bomb is representative of radiation exposure for other people.

Yutaka Hamaoka

A-bomb cohort was designed based on 1950 national census and includes all sex and ages, thus I believe it is less biased compared with nuclear worker, medical worker, and patients studies. Please refer https://www.rerf.or.jp/uploads/2017/09/briefdescript_e.pdf

Exposure situation seems to be different, but according to my knowledge, obtained ERR for solid cancer mortality are similar among a-bomb (0.47), Techa river (0.61), and nuclear worker (0.47). Richardson,et al. (2015)

Risk of cancer from occupational exposure to ionising radiation: retrospective cohort study of workers in France, the United Kingdom, and the United States (INWORKS). Bmj 351, h5359. Schonfeld et al. (2013)

Solid Cancer Mortality in the Techa River Cohort (1950-2007). Radiation Research 179, 183-189.

Dose of a-bomb survivor is “additional” dose by atomic bomb that varies among subjects. On the contrary, background dose that is common among all subjects will not affect slope of dose-response relationship.

Cameron JeffriesSouth Australia Medical Imaging

Background radiation dose in Japan is estimated to be 2.2 mSv per year. ~150 mSv over 70 years. This raises two questions; is a model threshold of -23.5 mSv telling us there is a threshold in the background radiation? Does LSS have the statistical power to measure an effect from 0.05 mSv out of ~150 mSv lifetime?

This is very much a question about everyone being exposed to background radiation. ~44% of the cohort with a dose of 0.005 mSv or below. (sorry, i was wrong about this number in my last comment). Certainly the LSS is representative of solid cancers in atomic bomb survivors, as per the conclusion. Should we assume this is the same for non-exposed persons? is it statisticall possible to see a difference between 154 mSv and 154.005 mSv?

Yutaka Hamaoka

"Thank you for comment and question again. Lowest dose category is <0.005 Gy or <5mGy. Directly estimated -23mSv was insignificant (z=-0.087,p>0.1) that supports no threshold model. To clarify nature of exposure, subject id (i) is added to our risk model.

Risk_i ~background + beta *dose_i (A)

As we see, background is common among subjects and it does not affect relationship between dose and Risk (beta). Here, dose is continuous variable, thus I believe statistical power of “regression coefficient (beta)” should be discussed rather than that of “difference in proportion of two groups (for example, background vs background + x )”. I’m not sure how to calculate power of Poisson multiple regression coefficient, estimated beta in LSS14 is highly significant (please refer Table 3 in LSS 14 paper, P<0.001 for both male and female solid cancer). It should have enough power.

If you prefer grouping, you can define a dummy variable d;

d_i =0 for dose_i <x,

d=1_i for dose_i >=x

Then put it in the risk model.

Risk_i ~background + beta *d_i

Apparently smaller x leads to lower statistical power.

In addition, please notice grouping neglect value of dose: if we set x=1mSv, for subjects whose dose exceed 1 mSv including 5mSv, 100mSv or even 4Gy, d_i=1. Of course you can limit upper bound by adding dummy variable(s), for example, d1==1 if x<1, d=0 otherwise. d2 =1 if x>=1 & x<20, d2 =0 other wise. d3 =1 if x>=20, dx3 =0 other wise

In such case our model should be , Risk_i ~background + beta2 *d2_i + beta3 *d3_i

In LSS14, 22 dose category dummy model was estimated (point estimates and CIs are plotted in Fig 4 of LSS14).

Although, model fit was not discussed in the paper, according to my re-analysis, AIC of the model is 18318 and larger than that of LNT model (18307)or we can conclude LNT fits better (see my presentation Table Results of Estimation: Model5 and Model 1) .We can assume any dose-response, but the best must be selected based on AIC or BIC.

LSS14: Ozasa et al. (2012) Studies of the Mortality of Atomic Bomb Survivors, Report 14, 1950–2003: An Overview of Cancer and Noncancer Diseases. Radiation Research 177, 229-243.

Thank you for the presentation. How did you account for background radiation exposure?