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.

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.

Methods to account for uncertainties in exposure assessment in studies of environmental exposures.

BACKGROUND: Accurate exposure estimation in environmental epidemiological studies is crucial for health risk assessment. Failure to account for uncertainties in exposure estimation could lead to biased results in exposure-response analyses. Assessment of the effects of uncertainties in exposure estimation on risk estimates received a lot of attention in radiation epidemiology and in several studies of diet and air pollution. The objective of this narrative review is to examine the commonly used statistical approaches to account for exposure estimation errors in risk analyses and to suggest how each could be applied in environmental epidemiological studies. MAIN TEXT: We review two main error types in estimating exposures in epidemiological studies: shared and unshared errors and their subtypes. We describe the four main statistical approaches to adjust for exposure estimation uncertainties (regression calibration, simulation-extrapolation, Monte Carlo maximum likelihood and Bayesian model averaging) along with examples to give readers better understanding of their advantages and limitations. We also explain the advantages of using a 2-dimensional Monte-Carlo (2DMC) simulation method to quantify the effect of uncertainties in exposure estimates using full-likelihood methods. For exposures that are estimated independently between subjects and are more likely to introduce unshared errors, regression calibration and SIMEX methods are able to adequately account for exposure uncertainties in risk analyses. When an uncalibrated measuring device is used or estimation parameters with uncertain mean values are applied to a group of people, shared errors could potentially be large. In this case, Monte Carlo maximum likelihood and Bayesian model averaging methods based on estimates of exposure from the 2DMC simulations would work well. The majority of reviewed studies show relatively moderate changes (within 100%) in risk estimates after accounting for uncertainties in exposure estimates, except for the two studies which doubled/tripled naïve estimates. CONCLUSIONS: In this paper, we demonstrate various statistical methods to account for uncertain exposure estimates in risk analyses. The differences in the results of various adjustment methods could be due to various error structures in datasets and whether or not a proper statistical method was applied. Epidemiological studies of environmental exposures should include exposure-response analyses accounting for uncertainties in exposure estimates.

Organ-specific dose coefficients derived from Monte Carlo simulations for historical (1930s to 1960s) fluoroscopic and radiographic examinations of tuberculosis patients.

This work provides dose coefficients necessary to reconstruct doses used in epidemiological studies of tuberculosis patients treated from the 1930s through the 1960s, who were exposed to diagnostic imaging while undergoing treatment. We made use of averaged imaging parameters from measurement data, physician interviews, and available literature of the Canadian Fluoroscopy Cohort Study and, on occasion, from a similar study of tuberculosis patients from Massachusetts, United States, treated between 1925 and 1954. We used computational phantoms of the human anatomy and Monte Carlo radiation transport methods to compute dose coefficients that relate dose in air, at a point 20 cm away from the source, to absorbed dose in 58 organs. We selected five male and five female phantoms, based on the mean height and weight of Canadian tuberculosis patients in that era, for the 1-, 5-, 10-, 15-year old and adult ages. Using high-performance computers at the National Institutes of Health, we simulated 2,400 unique fluoroscopic and radiographic exposures by varying x-ray beam quality, field size, field shuttering, imaged anatomy, phantom orientation, and computational phantom. Compared with previous dose coefficients reported for this population, our dosimetry system uses improved anatomical phantoms constructed from computed tomography imaging datasets. The new set of dose coefficients includes tissues that were not previously assessed, in particular, for tissues outside the x-ray field or for pediatric patients. In addition, we provide dose coefficients for radiography and for fluoroscopic procedures not previously assessed in the dosimetry of this cohort (i.e. pneumoperitoneum and chest aspirations). These new dose coefficients would allow a comprehensive assessment of exposures in the cohort. In addition to providing newly derived dose coefficients, we believe the automation and methods developed to complete these dosimetry calculations are generalizable and can be applied to other epidemiological studies interested in an exposure assessment from medical x-ray imaging. These epidemiological studies provide important data for assessing health risks of radiation exposure to help inform the current system of radiological protection and efforts to optimize the use of radiation in medical studies.

A mathematical model of antibody-dependent cellular cytotoxicity (ADCC).

Immunotherapies exploit the immune system to target and kill cancer cells, while sparing healthy tissue. Antibody therapies, an important class of immunotherapies, involve the binding to specific antigens on the surface of the tumour cells of antibodies that activate natural killer (NK) cells to kill the tumour cells. Preclinical assessment of molecules that may cause antibody-dependent cellular cytotoxicity (ADCC) involves co-culturing cancer cells, NK cells and antibody in vitro for several hours and measuring subsequent levels of tumour cell lysis. Here we develop a mathematical model of such an in vitro ADCC assay, formulated as a system of time-dependent ordinary differential equations and in which NK cells kill cancer cells at a rate which depends on the amount of antibody bound to each cancer cell. Numerical simulations generated using experimentally-based parameter estimates reveal that the system evolves on two timescales: a fast timescale on which antibodies bind to receptors on the surface of the tumour cells, and NK cells form complexes with the cancer cells, and a longer time-scale on which the NK cells kill the cancer cells. We construct approximate model solutions on each timescale, and show that they are in good agreement with numerical simulations of the full system. Our results show how the processes involved in ADCC change as the initial concentration of antibody and NK-cancer cell ratio are varied. We use these results to explain what information about the tumour cell kill rate can be extracted from the cytotoxicity assays.

Bayesian dose-response analysis for epidemiological studies with complex uncertainty in dose estimation.

Most conventional risk analysis methods rely on a single best estimate of exposure per person, which does not allow for adjustment for exposure-related uncertainty. Here, we propose a Bayesian model averaging method to properly quantify the relationship between radiation dose and disease outcomes by accounting for shared and unshared uncertainty in estimated dose. Our Bayesian risk analysis method utilizes multiple realizations of sets (vectors) of doses generated by a two-dimensional Monte Carlo simulation method that properly separates shared and unshared errors in dose estimation. The exposure model used in this work is taken from a study of the risk of thyroid nodules among a cohort of 2376 subjects who were exposed to fallout from nuclear testing in Kazakhstan. We assessed the performance of our method through an extensive series of simulations and comparisons against conventional regression risk analysis methods. When the estimated doses contain relatively small amounts of uncertainty, the Bayesian method using multiple a priori plausible draws of dose vectors gave similar results to the conventional regression-based methods of dose-response analysis. However, when large and complex mixtures of shared and unshared uncertainties are present, the Bayesian method using multiple dose vectors had significantly lower relative bias than conventional regression-based risk analysis methods and better coverage, that is, a markedly increased capability to include the true risk coefficient within the 95% credible interval of the Bayesian-based risk estimate. An evaluation of the dose-response using our method is presented for an epidemiological study of thyroid disease following radiation exposure.

Uncertainties in estimating health risks associated with exposure to ionising radiation.

The information for the present discussion on the uncertainties associated with estimation of radiation risks and probability of disease causation was assembled for the recently published NCRP Report No. 171 on this topic. This memorandum provides a timely overview of the topic, given that quantitative uncertainty analysis is the state of the art in health risk assessment and given its potential importance to developments in radiation protection. Over the past decade the increasing volume of epidemiology data and the supporting radiobiology findings have aided in the reduction of uncertainty in the risk estimates derived. However, it is equally apparent that there remain significant uncertainties related to dose assessment, low dose and low dose-rate extrapolation approaches (e.g. the selection of an appropriate dose and dose-rate effectiveness factor), the biological effectiveness where considerations of the health effects of high-LET and lower-energy low-LET radiations are required and the transfer of risks from a population for which health effects data are available to one for which such data are not available. The impact of radiation on human health has focused in recent years on cancer, although there has been a decided increase in the data for noncancer effects together with more reliable estimates of the risk following radiation exposure, even at relatively low doses (notably for cataracts and cardiovascular disease). New approaches for the estimation of hereditary risk have been developed with the use of human data whenever feasible, although the current estimates of heritable radiation effects still are based on mouse data because of an absence of effects in human studies. Uncertainties associated with estimation of these different types of health effects are discussed in a qualitative and semi-quantitative manner as appropriate. The way forward would seem to require additional epidemiological studies, especially studies of low dose and low dose-rate occupational and perhaps environmental exposures and for exposures to x rays and high-LET radiations used in medicine. The development of models for more reliably combining the epidemiology data with experimental laboratory animal and cellular data can enhance the overall risk assessment approach by providing biologically refined data to strengthen the estimation of effects at low doses as opposed to the sole use of mathematical models of epidemiological data that are primarily driven by medium/high doses. NASA's approach to radiation protection for astronauts, although a unique occupational group, indicates the possible applicability of estimates of risk and their uncertainty in a broader context for developing recommendations on: (1) dose limits for occupational exposure and exposure of members of the public; (2) criteria to limit exposures of workers and members of the public to radon and its short-lived decay products; and (3) the dosimetric quantity (effective dose) used in radiation protection.

Frequentist model averaging for analysis of dose-response in epidemiologic studies with complex exposure uncertainty.

In epidemiologic studies, association estimates of an exposure with disease outcomes are often biased when the uncertainties of exposure are ignored. Consequently, corresponding confidence intervals (CIs) will not have correct coverage. This issue is particularly problematic when exposures must be reconstructed from physical measurements, for example, for environmental or occupational radiation doses that were received by a study population for which radiation doses cannot be measured directly. To incorporate complex uncertainties in reconstructed exposures, the two-dimensional Monte Carlo (2DMC) dose estimation method has been proposed and used in various dose reconstruction efforts. The 2DMC method generates multiple exposure realizations from dosimetry models that incorporate various sources of errors to reflect the uncertainty of the dose distribution as well as the uncertainties in individual doses in the exposed population. Traditional measurement-error model approaches, typically based on using mean doses in the dose-exposure analysis, do not fully account exposure uncertainties. A recently developed statistical approach that overcomes many of these limitations by analyzing multiple exposure realizations in relation to disease risk is Bayesian model averaging (BMA). The analytic advantage of the BMA is its ability to better accommodate complex exposure uncertainty in the risk estimation, but a practical. Drawback is its significant computational complexity. In this present paper, we propose a novel frequentist model averaging (FMA) approach which has all the analytical advantages of the BMA method but is much simpler to implement and computationally faster. We show in simulations that, like BMA, FMA yields 95% confidence intervals for association parameters that close to 95% coverage rate. In simulations, the FMA has shorter length of CIs than those of another frequentist approach, the corrected information matrix (CIM) method. We illustrate the similarities in performance of BMA and FMA from a study of exposures from radioactive fallout in Kazakhstan.

RadRAT: a radiation risk assessment tool for lifetime cancer risk projection.

Risk projection methods allow for timely assessment of the potential magnitude of radiation-related cancer risks following low-dose radiation exposures. The estimation of such risks directly through observational studies would generally require infeasibly large studies and long-term follow-up to achieve reasonable statistical power. We developed an online radiation risk assessment tool (RadRAT) which can be used to estimate the lifetime risk of radiation-related cancer with uncertainty intervals following a user-specified exposure history (https://irep.nci.nih.gov/radrat). The uncertainty intervals constitute a key component of the program because of the various assumptions that are involved in such calculations. The risk models used in RadRAT are broadly based on those developed by the BEIR VII committee for estimating lifetime risk following low-dose radiation exposure of the US population for eleven site-specific cancers. We developed new risk models for seven additional cancer sites, oral, oesophagus, gallbladder, pancreas, rectum, kidney and brain/central nervous system (CNS) cancers, using data from Japanese atomic bomb survivors. The lifetime risk estimates are slightly higher for RadRAT than for BEIR VII across all exposure ages mostly because the weighting of the excess relative risk and excess absolute risk models was conducted on an arithmetic rather than a logarithmic scale. The calculator can be used to estimate lifetime cancer risk from both uniform and non-uniform doses that are acute or chronic. It is most appropriate for low-LET radiation doses < 1 Gy, and for individuals with life-expectancy and cancer rates similar to the general population in the US.

Dose Estimation for Exposure to Radioactive Fallout from Nuclear Detonations.

ABSTRACT: In recent years, the prospects that a nuclear device might be detonated due to a regional or global political conflict, by violation of present nuclear weapons test ban agreements, or due to an act of terrorism, has increased. Thus, the need exists for a well conceptualized, well described, and internally consistent methodology for dose estimation that takes full advantage of the experience gained over the last 70 y in both measurement technology and dose assessment methodology. Here, the models, rationale, and data needed for a detailed state-of-the-art dose assessment for exposure to radioactive fallout from nuclear detonations discussed in five companion papers are summarized. These five papers present methods and data for estimating radionuclide deposition of fallout radionuclides, internal and external dose from the deposited fallout, and discussion of the uncertainties in the assessed doses. In addition, this paper includes a brief discussion of secondary issues related to assessments of radiation dose from fallout. The intention of this work is to provide a usable and consistent methodology for both prospective and retrospective assessments of exposure from radioactive fallout from a nuclear detonation.

A Methodology for Estimating External Doses to Individuals and Populations Exposed to Radioactive Fallout from Nuclear Detonations.

ABSTRACT: A methodology of assessment of the doses from external irradiation resulting from the ground deposition of radioactive debris (fallout) from a nuclear detonation is proposed in this paper. The input data used to apply this methodology for a particular location are the outdoor exposure rate at any time after deposition of fallout and the time-of-arrival of fallout, as indicated and discussed in a companion paper titled "A Method for Estimating the Deposition Density of Fallout on the Ground and on Vegetation from a Low-yield Low-altitude Nuclear Detonation." Example doses are estimated for several age categories and for all radiosensitive organs and tissues identified in the most recent ICRP publications. Doses are calculated for the first year after the detonation, when more than 90% of the external dose is delivered for populations close to the detonation site over a time period of 70 y, which is intended to represent the lifetime dose. Modeled doses in their simplest form assume no environmental remediation, though modifications can be introduced. Two types of dose assessment are considered: (1) initial, for a rapid but only approximate dose estimation soon after the nuclear detonation; and (2) improved, for a later, more accurate, dose assessment following the analysis of post-detonation measurements of radiation exposure and fallout deposition and the access of information on the lifestyle of the exposed population.

A Methodology for Calculation of Internal Dose Following Exposure to Radioactive Fallout from the Detonation of a Nuclear Fission Device.

ABSTRACT: The purpose of this paper is to provide a methodology for the calculation of internal doses of radiation following exposure to radioactive fallout from the detonation of a nuclear fission device. Reliance is on methodology previously published in the open literature or in reports not readily available, though some new analysis is also included. Herein, we present two methodologic variations: one simpler to implement, the other more difficult but more flexible. The intention is to provide in one place a comprehensive methodology. Pathways considered are (1) the ingestion of vegetables and fruits contaminated by fallout directly, (2) the ingestion of vegetables and fruits contaminated by continuing deposition by rain- or irrigation-splash and resuspension, (3) the ingestion of vegetables and fruits contaminated by absorption of radionuclides by roots after tillage of soil, (4) the non-equilibrium transfer of short-lived radionuclides through the cow-milk and goat-milk food chains, (5) the equilibrium transfer of long lived radionuclides through milk and meat food chains, and (6) inhalation of descending fallout. Uncertainty in calculated results is considered. This is one of six companion papers that describe a comprehensive methodology for assessing both external and internal dose following exposures to fallout from a nuclear detonation. Input required to implement the dose-estimation model for any particular location consists of an estimate of the post-detonation external gamma-exposure rate and an estimate of the time of arrival of the fallout cloud. The additional data required to make such calculations are included in the six companion papers.

Parameter Values for Estimation of Internal Doses from Ingestion of Radioactive Fallout from Nuclear Detonations.

ABSTRACT: This paper suggests values or probability distributions for a variety of parameters used in estimating internal doses from radioactive fallout due to ingestion of food. Parameters include those needed to assess the interception and initial retention of radionuclides by vegetation, translocation of deposited radionuclides to edible plant parts, root uptake by plants, transfer of radionuclides from vegetation into milk and meat, transfer of radionuclides into non-agricultural plants and wildlife, and transfer from food and drinking water to mother's milk (human breast milk). The paper includes discussions of the weathering half-life for contamination on plant surfaces, biological half-lives of organisms, food processing (culinary factors), and contamination of drinking water. As appropriate, and as information exists, parameter values or distributions are specific for elements, chemical forms, plant types, or other relevant characteristics. Information has been obtained from the open literature and from publications of the International Atomic Energy Agency. These values and probability distributions are intended to be generic; they should be reviewed for applicability to a given location, time period, or season of the year, as appropriate. In particular, agricultural practices and dietary habits may vary considerably both with geography and over time in a given location.

Fluoroscopy X-Ray Organ-Specific Dosimetry System (FLUXOR) for Estimation of Organ Doses and Their Uncertainties in the Canadian Fluoroscopy Cohort Study.

As part of ongoing efforts to assess lifespan disease mortality and incidence in 63,715 patients from the Canadian Fluoroscopy Cohort Study (CFCS) who were treated for tuberculosis between 1930 and 1969, we developed a new FLUoroscopy X-ray ORgan-specific dosimetry system (FLUXOR) to estimate radiation doses to various organs and tissues. Approximately 45% of patients received medical procedures accompanied by fluoroscopy, including artificial pneumothorax (air in pleural cavity to collapse of lungs), pneumoperitoneum (air in peritoneal cavity), aspiration of fluid from pleural cavity and gastrointestinal series. In addition, patients received chest radiographs for purposes of diagnosis and monitoring of disease status. FLUXOR utilizes age-, sex- and body size-dependent dose coefficients for fluoroscopy and radiography exams, estimated using radiation transport simulations in up-to-date computational hybrid anthropomorphic phantoms. The phantoms include an updated heart model, and were adjusted to match the estimated mean height and body mass of tuberculosis patients in Canada during the relevant time period. Patient-specific data (machine settings, exposure duration, patient orientation) used during individual fluoroscopy or radiography exams were not recorded. Doses to patients were based on parameter values inferred from interviews with 91 physicians practicing at the time, historical literature, and estimated number of procedures from patient records. FLUXOR uses probability distributions to represent the uncertainty in the unknown true, average value of each dosimetry parameter. Uncertainties were shared across all patients within specific subgroups of the cohort, defined by age at treatment, sex, type of procedure, time period of exams and region (Nova Scotia or other provinces). Monte Carlo techniques were used to propagate uncertainties, by sampling alternative average values for each parameter. Alternative average doses per exam were estimated for patients in each subgroup, with the total average dose per individual determined by the number of exams received. This process was repeated to produce alternative cohort vectors of average organ doses per patient. This article presents estimates of doses to lungs, female breast, active bone marrow and heart wall. Means and 95% confidence intervals (CI) of average organ doses across all 63,715 patients were 320 (160, 560) mGy to lungs, 250 (120, 450) mGy to female breast, 190 (100, 340) mGy to heart wall and 92 (47, 160) mGy to active bone marrow. Approximately 60% of all patients had average doses to the four studied organs of less than 10 mGy, 10% received between 10 and 100 mGy, 25% between 100 and 1,000 mGy, and 5% above 1,000 mGy. Pneumothorax was the medical procedure that accounted for the largest contribution to cohort average doses. The major contributors to uncertainty in estimated doses per procedure for the four organs of interest are the uncertainties in exposure duration, tube voltage, tube output, and patient orientation relative to the X-ray tube, with the uncertainty in exposure duration being most often the dominant source. Uncertainty in patient orientation was important for doses to female breast, and, to a lesser degree, for doses to heart wall. The uncertainty in number of exams was an important contributor to uncertainty for ∼30% of patients. The estimated organ doses and their uncertainties will be used for analyses of incidence and mortality of cancer and non-cancer diseases. The CFCS cohort is an important addition to existing radio-epidemiological cohorts, given the moderate-to-high doses received fractionated over several years, the type of irradiation (external irradiation only), radiation type (X rays only), a balanced combination of both genders and inclusion of people of all ages.

The Methodology Used to Assess Doses from the First Nuclear Weapons Test (Trinity) to the Populations of New Mexico.

Trinity was the first test of a nuclear fission device. The test took place in south-central New Mexico at the Alamogordo Bombing and Gunnery Range at 05:29 AM on 16 July 1945. This article provides detailed information on the methods that were used in this work to estimate the radiation doses that were received by the population that resided in New Mexico in 1945. The 721 voting precincts of New Mexico were classified according to ecozone (plains, mountains, or mixture of plains and mountains), and size of resident population (urban or rural). Methods were developed to prepare estimates of absorbed doses from a range of 63 radionuclides to five organs or tissues (thyroid, active marrow, stomach, colon, and lung) for representative individuals of each voting precinct selected according to ethnicity (Hispanic, White, Native American, and African American) and age group in 1945 (in utero, newborn, 1-2 y, 3-7 y, 8-12 y, 13-17 y, and adult). Three pathways of human exposure were included: (1) external irradiation from the radionuclides deposited on the ground; (2) inhalation of radionuclide-contaminated air during the passage of the radioactive cloud and, thereafter, of radionuclides transferred (resuspended) from soil to air; and (3) ingestion of contaminated water and foodstuffs. Within the ingestion pathway, 13 types of foods and sources of water were considered. Well established models were used for estimation of doses resulting from the three pathways using parameter values developed from extensive literature review. Because previous experience and calculations have shown that the annual dose delivered during the year following a nuclear test is much greater than the doses received in the years after that first year, the time period that was considered is limited to the first year following the day of the test (16 July 1945). Numerical estimates of absorbed doses, based on the methods described in this article, are presented in a separate article in this issue.

NCRP Report 181, Evaluation of the Relative Effectiveness of Low-energy Photons and Electrons in Inducing Cancer in Humans: A Critique and Alternative Analysis.

A recent report from the National Council on Radiation Protection and Measurements presents an evaluation of the effectiveness of low-energy photons and electrons, relative to higher-energy photons, in inducing cancer in humans. The objective of that evaluation was to develop subjective probability distributions of an uncertain quantity, denoted by ρ, to represent ranges of credible values of the effectiveness of five groups of low-energy radiations (L): photons at about 1.5 keV; 15 to 30 keV photons; 40 to 60 keV photons; >60 to 150 keV photons; and electrons from beta decay of tritium (H). Probability distributions of ρL for all low-energy groups were derived based on an evaluation of uncertainties in data on biological effectiveness from five areas of research and use of an elicitation process and decomposition method to combine probability distributions to represent those uncertainties. In this paper, we argue that uncertainties in ρLs for all low-energy groups are too small compared with uncertainties in biological effectiveness from the different areas of research, especially that upper confidence limits of all ρLs are too low. These deflations of uncertainty in all ρLs apparently are due, at least in part, to an invalid assumption in the decomposition method that probability distributions of biological effectiveness from the different areas of research are representations of random uncertainty that arises from repeated measurements of the same quantity under the same conditions using well-calibrated instruments. However, those distributions essentially are representations of systematic uncertainty in different estimates of biological effectiveness from each area of research, which means that a deflation of uncertainty in ρLs is not a credible result. We then use the same probability distributions of biological effectiveness from the different areas of research in an alternative analysis to derive wider probability distributions of ρL that we believe provide a better representation of the state of knowledge of the effectiveness of low-energy photons and electrons in inducing cancer in humans. Our analysis is based on the notion that each probability distribution of biological effectiveness from an area of research represents a distinctly different model of a ρL and use of the concept of model averaging to combine those distributions.