Breast cancer risk in atomic bomb survivors from multi-model inference with incidence data 1958-1998

Comparison and multi-model inference of excess risks models for radiation-related solid cancer

In assessments of detrimental health risks from exposures to ionising radiation, many forms of risk to dose-response models are available in the literature. The usual practice is to base risk assessment on one specific model and ignore model uncertainty. The analysis illustrated here considers model uncertainty for the outcome all solid cancer incidence, when modelled as a function of colon organ dose, using the most recent publicly available data from the Life Span Study on atomic bomb survivors of Japan. Seven recent publications reporting all solid cancer risk models currently deemed plausible by the scientific community have been included in a model averaging procedure so that the main conclusions do not depend on just one type of model. The models have been estimated with different baselines and presented for males and females at various attained ages and ages at exposure, to obtain specially computed model-averaged Excess Relative Risks (ERR) and Excess Absolute Risks (EAR). Monte Carlo simulated estimation of uncertainty on excess risks was accounted for by applying realisations including correlations in the risk model parameters. Three models were found to weight the model-averaged risks most strongly depending on the baseline and information criteria used for the weighting. Fitting all excess risk models with the same baseline, one model dominates for both information criteria considered in this study. Based on the analysis presented here, it is generally recommended to take model uncertainty into account in future risk analyses.

Concepts of association between cancer and ionising radiation: accounting for specific biological mechanisms

The probability that an observed cancer was caused by radiation exposure is usually estimated using cancer rates and risk models from radioepidemiological cohorts and is called assigned share (AS). This definition implicitly assumes that an ongoing carcinogenic process is unaffected by the studied radiation exposure. However, there is strong evidence that radiation can also accelerate an existing clonal development towards cancer. In this work, we define different association measures that an observed cancer was newly induced, accelerated, or retarded. The measures were quantified exemplarily by Monte Carlo simulations that track the development of individual cells. Three biologically based two-stage clonal expansion (TSCE) models were applied. In the first model, radiation initiates cancer development, while in the other two, radiation has a promoting effect, i.e. radiation accelerates the clonal expansion of pre-cancerous cells. The parameters of the TSCE models were derived from breast cancer data from the atomic bomb survivors of Hiroshima and Nagasaki. For exposure at age 30, all three models resulted in similar estimates of AS at age 60. For the initiation model, estimates of association were nearly identical to AS. However, for the promotion models, the cancerous clonal development was frequently accelerated towards younger ages, resulting in associations substantially higher than AS. This work shows that the association between a given cancer and exposure in an affected person depends on the underlying biological mechanism and can be substantially larger than the AS derived from classic radioepidemiology.

Improving astronaut cancer risk assessment from space radiation with an ensemble model framework

A new approach to NASA space radiation risk modeling has successfully extended the current NASA probabilistic cancer risk model to an ensemble framework able to consider sub-model parameter uncertainty as well as model-form uncertainty associated with differing theoretical or empirical formalisms. Ensemble methodologies are already widely used in weather prediction, modeling of infectious disease outbreaks, and certain terrestrial radiation protection applications to better understand how uncertainty may influence risk decision-making. Applying ensemble methodologies to space radiation risk projections offers the potential to efficiently incorporate emerging research results, allow for the incorporation of future models, improve uncertainty quantification, and reduce the impact of subjective bias. Moreover, risk forecasting across an ensemble of multiple predictive models can provide stakeholders additional information on risk acceptance if current health/medical standards cannot be met for future space exploration missions, such as human missions to Mars. In this work, ensemble risk projections implementing multiple sub-models of radiation quality, dose and dose-rate effectiveness factors, excess risk, and latency are presented. Initial consensus methods for ensemble model weights and correlations to account for individual model bias are discussed. In these analyses, the ensemble forecast compares well to results from NASA's current operational cancer risk projection model used to assess permissible mission durations for astronauts. However, a large range of projected risk values are obtained at the upper 95th confidence level where models must extrapolate beyond available biological data sets. Closer agreement is seen at the median ± one sigma due to the inherent similarities in available models. Identification of potential new models, epidemiological data, and methods for statistical correlation between predictive ensemble members are discussed. Alternate ways of communicating risk and acceptable uncertainty with respect to NASA's current permissible exposure limits are explored.

Mammary Chain Irradiation in Left-Sided Breast Cancer: Can We Reduce the Risk of Secondary Cancer and Ischaemic Heart Disease with Modern Intensity-Modulated Radiotherapy Techniques?

Introduction

The aim of the present study was to estimate the impact of the addition of internal mammary chain (IMC) irradiation in node-positive left-sided breast cancer (BC) patients undergoing regional nodal irradiation (RNI) and comparatively evaluate excess relative and absolute risks of radiation-induced lung cancer/BC and ischaemic heart disease for intensity-modulated radiotherapy (IMRT) versus 3D conformal radiotherapy (3D-CRT).

Methods

Four treatment plans were created (3D-CRT and IMRT -/+ IMC) for each of the 10 evaluated patients, and estimates of excess relative risk (ERR) and 10-year excess absolute risk (EAR) were calculated for radiation-induced lung cancer/BC and coronary events using linear, linear-exponential and plateau models.

Results

The addition of IMC irradiation to RNI significantly increased the dose exposure of the heart, lung and contralateral breast using both techniques, increasing ERR for secondary lung cancer (58 vs. 44%, p = 0.002), contralateral BC (49 vs. 31%, p = 0.002) and ischaemic heart disease (41 vs. 27%, p = 0.002, IMRT plans). IMRT significantly reduced the mean cardiac dose and mean lung dose as compared to 3D-CRT, decreasing ERR for major coronary events (64% 3D-CRT vs. 41% IMRT, p = 0.002) and ERR for secondary lung cancer (75 vs. 58%, p = 0.004) in IMC irradiation, without a significant impact on secondary contralateral BC risks.

Conclusion

Although IMC irradiation has been shown to increase survival rates in node-positive BC patients, it increased dose exposure of organs at risk in left-sided BC, resulting in significantly increased risks for secondary lung cancer/contralateral BC and ischaemic heart disease. In this setting, the adoption of IMRT seems advantageous when compared to 3D-CRT.

ProZES: the methodology and software tool for assessment of assigned share of radiation in probability of cancer occurrence

ProZES is a software tool for estimating the probability that a given cancer was caused by preceding exposure to ionising radiation. ProZES calculates this probability, the assigned share, for solid cancers and hematopoietic malignant diseases, in cases of exposures to low-LET radiation, and for lung cancer in cases of exposure to radon. User-specified inputs include birth year, sex, type of diagnosed cancer, age at diagnosis, radiation exposure history and characteristics, and smoking behaviour for lung cancer. Cancer risk models are an essential part of ProZES. Linking disease and exposure to radiation involves several methodological aspects, and assessment of uncertainties received particular attention. ProZES systematically uses the principle of multi-model inference. Models of radiation risk were either newly developed or critically re-evaluated for ProZES, including dedicated models for frequent types of cancer and, for less common diseases, models for groups of functionally similar cancer sites. The low-LET models originate mostly from the study of atomic bomb survivors in Hiroshima and Nagasaki. Risks predicted by these models are adjusted to be applicable to the population of Germany and to different time periods. Adjustment factors for low dose rates and for a reduced risk during the minimum latency time between exposure and cancer are also applied. The development of the methodology and software was initiated and supported by the German Federal Ministry for the Environment, Nature Conservation and Nuclear Safety (BMU) taking up advice by the German Commission on Radiological Protection (SSK, Strahlenschutzkommission). These provide the scientific basis to support decision making on compensation claims regarding malignancies following occupational exposure to radiation in Germany.

Biologically-based modeling of radiation risk and biomarker prevalence for papillary thyroid cancer in Japanese a-bomb survivors 1958-2005

PURPOSE

Thyroid cancer of papillary histology (PTC) is the dominant type in radio-epidemiological cohorts established after nuclear accidents or warfare. Studies on post-Chernobyl PTC and on thyroid cancer in the life span study (LSS) of Japanese a-bomb survivors consistently revealed high radiation risk after exposure during childhood and adolescence. For post-Chernobyl risk assessment overexpression of the CLIP2 gene was proposed as molecular biomarker to separate radiogenic from sporadic PTC. Based on such binary marker a biologically-based risk model of PTC carcinogenesis has been developed for observational Chernobyl data. The model featured two independent molecular pathways of disease development, of which one was associated with radiation exposure. To gain credibility the concept for a mechanistic risk model must be based on general biological features which transcend findings in a single cohort. The purpose of the present study is therefore to demonstrate portability of the model concept by application to PTC incidence data in the LSS. By exploiting the molecular two-path concept we improve the determination of the probability of radiation causing cancer (POC).

MATERIALS AND METHODS

The current analysis uses thyroid cancer incidence data of the LSS with thyroid cancer diagnoses and papillary histology (n = 292) from the follow-up period between 1958 and 2005. Risk analysis was performed with both descriptive and biologically-based models.

RESULTS

Judged by goodness-of-fit all applied models described the data almost equally well. They yielded similar risk estimates in cohorts post-Chernobyl and LSS. The preferred mechanistic model was selected by biological plausibility. It reflected important features of an imperfect radiation marker which are not easily addressed by descriptive models. Precise model predictions of marker prevalence in strata of epidemiological covariables can be tested by molecular measurements. Application of the radiation-related molecular pathway from our preferred model in retrospective risk assessment decreases the threshold dose for 50% POC from 0.33 (95% confidence interval (CI) 0.18; 0.64) Gy to 0.04 (95% CI 0.01; 0.19) Gy for females and from 0.43 (95% CI 0.17; 1.84) Gy to 0.19 (95% CI 0.05; 1.00) Gy for males. These improvements are still not sufficient to separate radiation-induced from sporadic PTC cases at very low doses <0.015 Gy typical for the Fukushima accident.

CONCLUSIONS

Successful application of our preferred mechanistic model to LSS incidence data confirms and improves the biological two-path concept of radiation-induced PTC. Model predictions suggest further molecular validation studies to consolidate the basis of biologically-based risk estimation.

Effect of Diets, Familial History, and Alternative Therapies on Genomic Instability of Breast Cancer Patients

This study evaluates a correlation between family history, micronutrients intake, and alternative therapies with genetic instability, before and during breast cancer treatment. For this study, a total of 150 women were selected. Among those, 50 women were breast cancer patients on chemotherapy, while 50 breast cancer patients were on radiotherapy, and 50 were healthy females. All the participants signed the informed consent form and answered the public health questionnaire. Samples of buccal epithelial and peripheral blood cells were collected and analyzed through micronucleus and comet assays. The cells were evaluated for apoptosis and DNA damage. Results showed the association of patients' family history with an increase in toxicogenetic damage before and during cancer therapy. On the other hand, patients with late-onset cancer also presented genetic instability before and during therapy, along with those who did not take sufficient vegetables and alternative therapies. A positive correlation was observed between the genetic instability and alternative therapies, while inverse correlation was recorded with the vegetable consumption. Results clearly explain that the nutritional aspects and alternative therapies influence the genetic instability before and during cancer therapies especially in radiotherapy treated patients. Our data could be used for the monitoring therapies and management of breast cancer patients.

Dose-responses for mortality from cerebrovascular and heart diseases in atomic bomb survivors: 1950-2003

The scientific community faces important discussions on the validity of the linear no-threshold (LNT) model for radiation-associated cardiovascular diseases at low and moderate doses. In the present study, mortalities from cerebrovascular diseases (CeVD) and heart diseases from the latest data on atomic bomb survivors were analyzed. The analysis was performed with several radio-biologically motivated linear and nonlinear dose-response models. For each detrimental health outcome one set of models was identified that all fitted the data about equally well. This set was used for multi-model inference (MMI), a statistical method of superposing different models to allow risk estimates to be based on several plausible dose-response models rather than just relying on a single model of choice. MMI provides a more accurate determination of the dose response and a more comprehensive characterization of uncertainties. It was found that for CeVD, the dose-response curve from MMI is located below the linear no-threshold model at low and medium doses (0-1.4 Gy). At higher doses MMI predicts a higher risk compared to the LNT model. A sublinear dose-response was also found for heart diseases (0-3 Gy). The analyses provide no conclusive answer to the question whether there is a radiation risk below 0.75 Gy for CeVD and 2.6 Gy for heart diseases. MMI suggests that the dose-response curves for CeVD and heart diseases in the Lifespan Study are sublinear at low and moderate doses. This has relevance for radiotherapy treatment planning and for international radiation protection practices in general.

Correlations between Risk Factors for Breast Cancer and Genetic Instability in Cancer Patients-A Clinical Perspective Study

Molecular epidemiological studies have identified several risk factors linking to the genes and external factors in the pathogenesis of breast cancer. In this sense, genetic instability caused by DNA damage and DNA repair inefficiencies are important molecular events for the diagnosis and prognosis of therapies. Therefore, the objective of this study was to analyze correlation between sociocultural, occupational, and lifestyle risk factors with levels of genetic instability in non-neoplastic cells of breast cancer patients. Total 150 individuals were included in the study that included 50 breast cancer patients submitted to chemotherapy (QT), 50 breast cancer patients submitted to radiotherapy (RT), and 50 healthy women without any cancer. Cytogenetic biomarkers for apoptosis and DNA damage were evaluated in samples of buccal epithelial and peripheral blood cells through micronuclei and comet assay tests. Elder age patients (61-80 years) had higher levels of apoptosis (catriolysis by karyolysis) and DNA damage at the diagnosis (baseline damage) with increased cell damage during QT and especially during RT. We also reported the increased frequencies of cytogenetic biomarkers in patients who were exposed to ionizing radiation as well as for alcoholism and smoking. QT and RT induced high levels of fragmentation (karyorrhexis) and nuclear dissolution (karyolysis) and DNA damage. Correlations were observed between age and karyorrhexis at diagnosis; smoking and karyolysis during RT; and radiation and karyolysis during QT. These correlations indicate that risk factors may also influence the genetic instability in non-neoplastic cells caused to the patients during cancer therapies.

Mechanistic study on lung cancer mortality after radon exposure in the Wismut cohort supports important role of clonal expansion in lung carcinogenesis

Lung cancer mortality after radon exposure in the Wismut cohort was analyzed using the two-stage clonal expansion (TSCE) model. A total of 2996 lung cancer deaths among the 58,695 male workers were observed during the follow-up period between 1946 and 2003. Adjustment to silica exposure was performed to find a more accurate estimation of the risk of radon exposure. An additional analysis with the descriptive excess relative risk (ERR) model was carried out for comparison. The TSCE model that best describes the data is nonlinear in the clonal expansion with radon exposure and has a saturation level at an exposure rate of [Formula: see text]. The excess relative risk decreases with age and shows an inverse exposure rate effect. In comparison with the ERR model, the TSCE model predicts a considerably larger risk for low exposures rates below [Formula: see text]. Comparison to other mechanistic studies of lung cancer after exposure to alpha particles using the TSCE model reveals an extraordinary consistency in the main features of the exposure response, given the diversity in the characteristics of the cohorts and the exposure across different studies. This suggests that a nonlinear response mechanism in the clonal expansion, with some level of saturation at large exposure rates, may be playing a crucial role in the development of lung cancer after alpha particle irradiation.

Simulating Space Radiation-Induced Breast Tumor Incidence Using Automata

Estimating cancer risk from space radiation has been an ongoing challenge for decades primarily because most of the reported epidemiological data on radiation-induced risks are derived from studies of atomic bomb survivors who were exposed to an acute dose of gamma rays instead of chronic high-LET cosmic radiation. In this study, we introduce a formalism using cellular automata to model the long-term effects of ionizing radiation in human breast for different radiation qualities. We first validated and tuned parameters for an automata-based two-stage clonal expansion model simulating the age dependence of spontaneous breast cancer incidence in an unexposed U.S.

POPULATION

We then tested the impact of radiation perturbation in the model by modifying parameters to reflect both targeted and nontargeted radiation effects. Targeted effects (TE) reflect the immediate impact of radiation on a cell's DNA with classic end points being gene mutations and cell death. They are well known and are directly derived from experimental data. In contrast, nontargeted effects (NTE) are persistent and affect both damaged and undamaged cells, are nonlinear with dose and are not well characterized in the literature. In this study, we introduced TE in our model and compared predictions against epidemiologic data of the atomic bomb survivor cohort. TE alone are not sufficient for inducing enough cancer. NTE independent of dose and lasting ∼100 days postirradiation need to be added to accurately predict dose dependence of breast cancer induced by gamma rays. Finally, by integrating experimental relative biological effectiveness (RBE) for TE and keeping NTE (i.e., radiation-induced genomic instability) constant with dose and LET, the model predicts that RBE for breast cancer induced by cosmic radiation would be maximum at 220 keV/μm. This approach lays the groundwork for further investigation into the impact of chronic low-dose exposure, inter-individual variation and more complex space radiation scenarios.

Breast cancer risk and possible mechanisms of radiation-induced genomic instability in the Swedish hemangioma cohort after reanalyzed dosimetry

The cohort of 17,200 female Swedish hemangioma patients, who had been exposed to ionizing radiation because of skin hemangioma, was analyzed for breast cancer incidence with descriptive excess relative risk models and mechanistic models of carcinogenesis. The dosimetry system has recently been updated, leading to substantially reduced doses for the most highly exposed part of the Stockholm cohort. The follow-up includes persons until December 2009 with 877 breast cancer cases. All models agree on the risk estimates. The excess relative and excess absolute risk at the age of 50 years are 0.48 Gy(-1) (95% CI 0.28; 0.69) and 10.4 (10(4)PYR Gy)(-1) (95% CI 6.1; 14.4) (95% CI 6.1; 14.4), respectively. These risk estimates are about a factor of 2 higher than previous analyses of this cohort as a consequence of the re-evaluation of the dosimetry system. Explicit models incorporating effects of genomic instability were developed and applied to the hemangioma cohort. It was found that a radiation-induced transition towards genomic instability was highly significant. The models indicate that the main effect of radiation-induced genomic instability is to increase the rate of transition of non-initiated cells to initiated cells with a proliferative advantage. The magnitude of such an acceleration cannot be inferred from epidemiological data alone, but must be complemented by radiobiological measurements.

Genomic instability and radiation risk in molecular pathways to colon cancer

Colon cancer is caused by multiple genomic alterations which lead to genomic instability (GI). GI appears in molecular pathways of microsatellite instability (MSI) and chromosomal instability (CIN) with clinically observed case shares of about 15–20% and 80–85%. Radiation enhances the colon cancer risk by inducing GI, but little is known about different outcomes for MSI and CIN. Computer-based modelling can facilitate the understanding of the phenomena named above. Comprehensive biological models, which combine the two main molecular pathways to colon cancer, are fitted to incidence data of Japanese a-bomb survivors. The preferred model is selected according to statistical criteria and biological plausibility. Imprints of cell-based processes in the succession from adenoma to carcinoma are identified by the model from age dependences and secular trends of the incidence data. Model parameters show remarkable compliance with mutation rates and growth rates for adenoma, which has been reported over the last fifteen years. Model results suggest that CIN begins during fission of intestinal crypts. Chromosomal aberrations are generated at a markedly elevated rate which favors the accelerated growth of premalignant adenoma. Possibly driven by a trend of Westernization in the Japanese diet, incidence rates for the CIN pathway increased notably in subsequent birth cohorts, whereas rates pertaining to MSI remained constant. An imbalance between number of CIN and MSI cases began to emerge in the 1980s, whereas in previous decades the number of cases was almost equal. The CIN pathway exhibits a strong radio-sensitivity, probably more intensive in men. Among young birth cohorts of both sexes the excess absolute radiation risk related to CIN is larger by an order of magnitude compared to the MSI-related risk. Observance of pathway-specific risks improves the determination of the probability of causation for radiation-induced colon cancer in individual patients, if their exposure histories are known.

Independent analysis of the radiation risk for leukaemia in children and adults with mortality data (1950-2003) of Japanese A-bomb survivors

A recent analysis of leukaemia mortality in Japanese A-bomb survivors has applied descriptive models, collected together from previous studies, to derive a joint excess relative risk estimate (ERR) by multi-model inference (MMI) (Walsh and Kaiser in Radiat Environ Biophys 50:21-35, 2011). The models use a linear-quadratic dose response with differing dose effect modifiers. In the present study, a set of more than 40 models has been submitted to a rigorous statistical selection procedure which fosters the parsimonious deployment of model parameters based on pairwise likelihood ratio tests. Nested models were consequently excluded from risk assessment. The set comprises models of the excess absolute risk (EAR) and two types of non-standard ERR models with sigmoidal responses or two line spline functions with a changing slope at a break point. Due to clearly higher values of the Akaike Information Criterion, none of the EAR models has been selected, but two non-standard ERR models qualified for MMI. The preferred ERR model applies a purely quadratic dose response which is slightly damped by an exponential factor at high doses and modified by a power function for attained age. Compared to the previous analysis, the present study reports similar point estimates and confidence intervals (CI) of the ERR from MMI for doses between 0.5 and 2.5 Sv. However, at lower doses, the point estimates are markedly reduced by factors between two and five, although the reduction was not statistically significant. The 2.5 % percentiles of the ERR from the preferred quadratic-exponential model did not fall below zero risk in exposure scenarios for children, adolescents and adults at very low doses down to 10 mSv. Yet, MMI produced risk estimates with a positive 2.5 % percentile only above doses of some 300 mSv. Compared to CI from a single model of choice, CI from MMI are broadened in cohort strata with low statistical power by a combination of risk extrapolations from several models. Reverting to MMI can relieve the dilemma of needing to choose between models with largely different consequences for risk assessment in public health.

A method for determining weights for excess relative risk and excess absolute risk when applied in the calculation of lifetime risk of cancer from radiation exposure

Radiation-related risks of cancer can be transported from one population to another population at risk, for the purpose of calculating lifetime risks from radiation exposure. Transfer via excess relative risks (ERR) or excess absolute risks (EAR) or a mixture of both (i.e., from the life span study (LSS) of Japanese atomic bomb survivors) has been done in the past based on qualitative weighting. Consequently, the values of the weights applied and the method of application of the weights (i.e., as additive or geometric weighted means) have varied both between reports produced at different times by the same regulatory body and also between reports produced at similar times by different regulatory bodies. Since the gender and age patterns are often markedly different between EAR and ERR models, it is useful to have an evidence-based method for determining the relative goodness of fit of such models to the data. This paper identifies a method, using Akaike model weights, which could aid expert judgment and be applied to help to achieve consistency of approach and quantitative evidence-based results in future health risk assessments. The results of applying this method to recent LSS cancer incidence models are that the relative EAR weighting by cancer solid cancer site, on a scale of 0-1, is zero for breast and colon, 0.02 for all solid, 0.03 for lung, 0.08 for liver, 0.15 for thyroid, 0.18 for bladder and 0.93 for stomach. The EAR weighting for female breast cancer increases from 0 to 0.3, if a generally observed change in the trend between female age-specific breast cancer incidence rates and attained age, associated with menopause, is accounted for in the EAR model. Application of this method to preferred models from a study of multi-model inference from many models fitted to the LSS leukemia mortality data, results in an EAR weighting of 0. From these results it can be seen that lifetime risk transfer is most highly weighted by EAR only for stomach cancer. However, the generalization and interpretation of radiation effect estimates based on the LSS cancer data, when projected to other populations, are particularly uncertain if considerable differences exist between site-specific baseline rates in the LSS and the other populations of interest. Definitive conclusions, regarding the appropriate method for transporting cancer risks, are limited by a lack of knowledge in several areas including unknown factors and uncertainties in biological mechanisms and genetic and environmental risk factors for carcinogenesis; uncertainties in radiation dosimetry; and insufficient statistical power and/or incomplete follow-up in data from radio-epidemiological studies.

Dose-responses from multi-model inference for the non-cancer disease mortality of atomic bomb survivors

The non-cancer mortality data for cerebrovascular disease (CVD) and cardiovascular diseases from Report 13 on the atomic bomb survivors published by the Radiation Effects Research Foundation were analysed to investigate the dose-response for the influence of radiation on these detrimental health effects. Various parametric and categorical models (such as linear-no-threshold (LNT) and a number of threshold and step models) were analysed with a statistical selection protocol that rated the model description of the data. Instead of applying the usual approach of identifying one preferred model for each data set, a set of plausible models was applied, and a sub-set of non-nested models was identified that all fitted the data about equally well. Subsequently, this sub-set of non-nested models was used to perform multi-model inference (MMI), an innovative method of mathematically combining different models to allow risk estimates to be based on several plausible dose-response models rather than just relying on a single model of choice. This procedure thereby produces more reliable risk estimates based on a more comprehensive appraisal of model uncertainties. For CVD, MMI yielded a weak dose-response (with a risk estimate of about one-third of the LNT model) below a step at 0.6 Gy and a stronger dose-response at higher doses. The calculated risk estimates are consistent with zero risk below this threshold-dose. For mortalities related to cardiovascular diseases, an LNT-type dose-response was found with risk estimates consistent with zero risk below 2.2 Gy based on 90% confidence intervals. The MMI approach described here resolves a dilemma in practical radiation protection when one is forced to select between models with profoundly different dose-responses for risk estimates.