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

A generalisation of the method of regression calibration and comparison with Bayesian and frequentist model averaging methods

For many cancer sites low-dose risks are not known and must be extrapolated from those observed in groups exposed at much higher levels of dose. Measurement error can substantially alter the dose-response shape and hence the extrapolated risk. Even in studies with direct measurement of low-dose exposures measurement error could be substantial in relation to the size of the dose estimates and thereby distort population risk estimates. Recently, there has been considerable attention paid to methods of dealing with shared errors, which are common in many datasets, and particularly important in occupational and environmental settings. In this paper we test Bayesian model averaging (BMA) and frequentist model averaging (FMA) methods, the first of these similar to the so-called Bayesian two-dimensional Monte Carlo (2DMC) method, and both fairly recently proposed, against a very newly proposed modification of the regression calibration method, the extended regression calibration (ERC) method, which is particularly suited to studies in which there is a substantial amount of shared error, and in which there may also be curvature in the true dose response. The quasi-2DMC with BMA method performs well when a linear model is assumed, but very poorly when a linear-quadratic model is assumed, with coverage probabilities both for the linear and quadratic dose coefficients that are under 5% when the magnitude of shared Berkson error is large (50%). For the linear model the bias is generally under 10%. However, using a linear-quadratic model it produces substantially biased (by a factor of 10) estimates of both the linear and quadratic coefficients, with the linear coefficient overestimated and the quadratic coefficient underestimated. FMA performs as well as quasi-2DMC with BMA when a linear model is assumed, and generally much better with a linear-quadratic model, although the coverage probability for the quadratic coefficient is uniformly too high. However both linear and quadratic coefficients have pronounced upward bias, particularly when Berkson error is large. By comparison ERC yields coverage probabilities that are too low when shared and unshared Berkson errors are both large (50%), although otherwise it performs well, and coverage is generally better than the quasi-2DMC with BMA or FMA methods, particularly for the linear-quadratic model. The bias of the predicted relative risk at a variety of doses is generally smallest for ERC, and largest for the quasi-2DMC with BMA and FMA methods (apart from unadjusted regression), with standard regression calibration and Monte Carlo maximum likelihood exhibiting bias in predicted relative risk generally somewhat intermediate between ERC and the other two methods. In general ERC performs best in the scenarios presented, and should be the method of choice in situations where there may be substantial shared error, or suspected curvature in the dose response.

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.

A generalisation of the method of regression calibration and comparison with the Bayesian 2-dimensional Monte Carlo method

For many cancer sites it is necessary to assess risks from low-dose exposures via extrapolation from groups exposed at moderate and high levels of dose. Measurement error can substantially alter the shape of this relationship and hence the derived population risk estimates. Even in studies with direct measurement of low-dose exposures measurement error could be substantial in relation to the size of the dose estimates and thereby distort population risk estimates. Recently, much attention has been devoted to the issue of shared errors, common in many datasets, and particularly important in occupational settings. In this paper we test a Bayesian model averaging method, the so-called Bayesian two-dimensional Monte Carlo (2DMC) method, that has been fairly recently proposed against a very newly proposed modification of the regression calibration method, which is particularly suited to studies in which there is a substantial amount of shared error, and in which there may also be curvature in the true dose response. We also compared both methods against standard regression calibration and Monte Carlo maximum likelihood. The Bayesian 2DMC method performs poorly, with coverage probabilities both for the linear and quadratic dose coefficients that are under 5%, particularly when the magnitudes of classical and Berkson error are both moderate to large (20%-50%). The method also produces substantially biased (by a factor of 10) estimates of both the linear and quadratic coefficients, with the linear coefficient overestimated and the quadratic coefficient underestimated. By comparison the extended regression calibration method yields coverage probabilities that are too low when shared and unshared Berkson errors are both large (50%), although otherwise it performs well, and coverage is generally better than the Bayesian 2DMC and all other methods. The bias of the predicted relative risk at a variety of doses is generally smallest for extended regression calibration, and largest for the Bayesian 2DMC method (apart from unadjusted regression), with standard regression calibration and Monte Carlo maximum likelihood exhibiting bias in predicted relative risk generally somewhat intermediate between the other two methods.

A generalisation of the method of regression calibration

There is direct evidence of risks at moderate and high levels of radiation dose for highly radiogenic cancers such as leukaemia and thyroid cancer. For many cancer sites, however, it is necessary to assess risks via extrapolation from groups exposed at moderate and high levels of dose, about which there are substantial uncertainties. Crucial to the resolution of this area of uncertainty is the modelling of the dose-response relationship and the importance of both systematic and random dosimetric errors for analyses in the various exposed groups. It is well recognised that measurement error can alter substantially the shape of this relationship and hence the derived population risk estimates. Particular attention has been devoted to the issue of shared errors, common in many datasets, and particularly important in occupational settings. We propose a modification of the regression calibration method which is particularly suited to studies in which there is a substantial amount of shared error, and in which there may also be curvature in the true dose response. This method can be used in settings where there is a mixture of Berkson and classical error. In fits to synthetic datasets in which there is substantial upward curvature in the true dose response, and varying (and sometimes substantial) amounts of classical and Berkson error, we show that the coverage probabilities of all methods for the linear coefficient [Formula: see text] are near the desired level, irrespective of the magnitudes of assumed Berkson and classical error, whether shared or unshared. However, the coverage probabilities for the quadratic coefficient [Formula: see text] are generally too low for the unadjusted and regression calibration methods, particularly for larger magnitudes of the Berkson error, whether this is shared or unshared. In contrast Monte Carlo maximum likelihood yields coverage probabilities for [Formula: see text] that are uniformly too high. The extended regression calibration method yields coverage probabilities that are too low when shared and unshared Berkson errors are both large, although otherwise it performs well, and coverage is generally better than these other three methods. A notable feature is that for all methods apart from extended regression calibration the estimates of the quadratic coefficient [Formula: see text] are substantially upwardly biased.

A generalisation of the method of regression calibration

There is direct evidence of risks at moderate and high levels of radiation dose for highly radiogenic cancers such as leukaemia and thyroid cancer. For many cancer sites, however, it is necessary to assess risks via extrapolation from groups exposed at moderate and high levels of dose, about which there are substantial uncertainties. Crucial to the resolution of this area of uncertainty is the modelling of the dose-response relationship and the importance of both systematic and random dosimetric errors for analyses in the various exposed groups. It is well recognised that measurement error can alter substantially the shape of this relationship and hence the derived population risk estimates. Particular attention has been devoted to the issue of shared errors, common in many datasets, and particularly important in occupational settings. We propose a modification of the regression calibration method which is particularly suited to studies in which there is a substantial amount of shared error, and in which there may also be curvature in the true dose response. This method can be used in settings where there is a mixture of Berkson and classical error. In fits to synthetic datasets in which there is substantial upward curvature in the true dose response, and varying (and sometimes substantial) amounts of classical and Berkson error, we show that the coverage probabilities of all methods for the linear coefficient \(\alpha\) are near the desired level, irrespective of the magnitudes of assumed Berkson and classical error, whether shared or unshared. However, the coverage probabilities for the quadratic coefficient \(\beta\) are generally too low for the unadjusted and regression calibration methods, particularly for larger magnitudes of the Berkson error, whether this is shared or unshared. In contrast Monte Carlo maximum likelihood yields coverage probabilities for \(\beta\) that are uniformly too high. The extended regression calibration method yields coverage probabilities that are too low when shared and unshared Berkson errors are both large, although otherwise it performs well, and coverage is generally better than these other three methods. A notable feature is that for all methods apart from extended regression calibration the estimates of the quadratic coefficient \(\beta\) are substantially upwardly biased.

Dose estimates and their uncertainties for use in epidemiological studies of radiation-exposed populations in the Russian Southern Urals

Many residents of the Russian Southern Urals were exposed to radioactive environmental pollution created by the operations of the Mayak Production Association in the mid- 20th century. There were two major releases: the discharge of about 1x1017 Bq of liquid waste into the Techa River between 1949 and 1959; and the atmospheric release of 7.4 * 1016 Bq as a result an explosion in the radioactive waste-storage facility in 1957. The releases into the Techa River resulted in the exposure of more than 30,000 people who lived in riverside villages between 1950 and 1961. The 1957 accident contaminated a larger area with the highest exposure levels in an area that is called the East Urals Radioactive Trace (EURT). Current epidemiologic studies of the exposed populations are based on dose estimates obtained using a Monte-Carlo dosimetry system (TRDS-2016MC) that provides multiple realizations of the annual doses for each cohort member. These dose realizations provide a central estimate of the individual dose and information on the uncertainty of these dose estimates. In addition, the correlation of individual annual doses over realizations provides important information on shared uncertainties that can be used to assess the impact of shared dose uncertainties on risk estimate uncertainty.This paper considers dose uncertainties in the TRDS-2016MC. Individual doses from external and internal radiation sources were reconstructed for 48,036 people based on environmental contamination patterns, residential histories, individual 90Sr body-burden measurements and dietary intakes. Dietary intake of 90Sr resulted in doses accumulated in active bone marrow (or simply, marrow) that were an order of magnitude greater than those in soft tissues. About 84% of the marrow dose and 50% of the stomach dose was associated with internal exposures. The lognormal distribution is well-fitted to the individual dose realizations, which, therefore, could be expressed and easily operated in terms of geometric mean (GM) and geometric standard deviation (GSD). Cohort average GM for marrow and stomach cumulative doses are 0.21 and 0.03 Gy, respectively. Cohort average dose uncertainties in terms of GSD are as follows: for marrow it is 2.93 (90%CI: 2.02-4.34); for stomach and the other non-calcified tissues it is 2.32 (90% CI: 1.78-2.9).

Impact of delineation errors on the estimated organ at risk dose and of dose errors on the normal tissue complication probability model

BACKGROUND

Normal tissue complication probability (NTCP) models are often based on doses retrieved from delineated volumes. For retrospective dose-response studies focusing on organs that have not been delineated historically, automatic segmentation might be considered. However, automatic segmentation risks generating considerable delineation errors and knowledge regarding how these errors impact the estimated organ dose is important. Furthermore, organ-at-risk (OAR) dose uncertainties cannot be eliminated and might affect the resulting NTCP model. Therefore, it is also of interest to study how OAR dose errors impact the NTCP modeling results.

PURPOSE

To investigate how random delineation errors of the proximal bronchial tree, heart, and esophagus impact the estimated OAR dose, and to investigate how random errors in the doses used for dose-response modeling affect the estimated NTCPs.

METHODS

We investigated the impact of random delineation errors on the estimated OAR dose using the treatment plans of 39 patients treated with conventionally fractionated radiation therapy of non-small-cell lung cancer. Study-specific reference structures were defined by manually contouring the proximal bronchial tree, heart and esophagus. For each patient and organ, 120 reshaped structures were created by introducing random shifts and margins to the entire reference structure. The mean and near-maximum dose to the reference and reshaped structures were compared. In a separate investigation, the impact of random dose errors on the NTCP model was studied performing dose-response modeling with study sets containing treatment outcomes and OAR doses with and without introduced errors. Universal patient populations with defined population risks, dose-response relationships and distributions of OAR doses were used as ground truth. From such a universal population, we randomly sampled data sets consisting of OAR dose and treatment outcome into reference populations. Study sets of different sizes were created by repeatedly introducing errors to the OAR doses of each reference population. The NTCP models generated with dose errors were compared to the reference NTCP model of the corresponding reference population.

RESULTS

A total of 14 040 reshaped structures with random delineation errors were created. The delineation errors resulted in systematic mean dose errors of less than 1% of the prescribed dose (PD). Mean dose differences above 15% of PD and near-maximum doses differences above 25% of PD were observed for 211 and 457 reshaped structures, respectively. Introducing random errors to OAR doses used for dose-response modeling resulted in systematic underestimations of the median NTCP. For all investigated scenarios, the median differences in NTCP were within 0.1 percentage points (p.p.) when comparing different study sizes.

CONCLUSIONS

Introducing random delineation errors to the proximal bronchial tree, heart and esophagus resulted in mean dose and near-maximum dose differences above 15% and 25% of PD, respectively. We did not observe an association between the dose level and the magnitude of the dose errors. For the scenarios investigated in this study, introducing random errors to OAR doses used for dose-response modeling resulted in systematic underestimations of the median NTCP for reference risks higher than the universal population risk. The median NTCP underestimation was similar for different study sizes, all within 0.1 p.p.

Impact of uncertainties in exposure assessment on thyroid cancer risk among cleanup workers in Ukraine exposed due to the Chornobyl accident

A large excess risk of thyroid cancer was observed among Belarusian/Russian/Baltic Chornobyl cleanup workers. A more recent study of Ukraine cleanup workers found more modest excess risks of thyroid cancer. Dose errors in this data are substantial, associated with model uncertainties and questionnaire response. Regression calibration is often used for dose-error adjustment, but may not adequately account for the full error distribution. We aimed to examine the impact of exposure-assessment uncertainties on thyroid cancer among Ukrainian cleanup workers using Monte Carlo maximum likelihood, and compare with results derived using regression calibration. Analyses assessed the sensitivity of results to various components of internal and external dose. Regression calibration yielded an excess odds ratio per Gy (EOR/Gy) of 0.437 (95% CI - 0.042, 1.577, p = 0.100), compared with the EOR/Gy using Monte Carlo maximum likelihood of 0.517 (95% CI - 0.039, 2.035, p = 0.093). Trend risk estimates for follicular morphology tumors exhibited much more extreme effects of full-likelihood adjustment, the EOR/Gy using regression calibration of 3.224 (95% CI - 0.082, 30.615, p = 0.068) becoming ~ 50% larger, 4.708 (95% CI - 0.075, 85.143, p = 0.066) when using Monte Carlo maximum likelihood. Results were sensitive to omission of external components of dose. In summary, use of Monte Carlo maximum likelihood adjustment for dose error led to increases in trend risks, particularly for follicular morphology thyroid cancers, where risks increased by ~ 50%, and were borderline significant. The unexpected finding for follicular tumors needs to be replicated in other exposed groups.

Lung Cancer in the Mayak Workers Cohort: Risk Estimation and Uncertainty Analysis

The workers at the Mayak nuclear facility near Ozyorsk, Russia are a primary source of information about exposure to radiation at low-dose rates, since they were subject to protracted exposures to external gamma rays and to internal exposures from plutonium inhalation. Here we re-examine lung cancer mortality rates and assess the effects of external gamma and internal plutonium exposures using recently developed Monte Carlo dosimetry systems. Using individual lagged mean annual lung doses computed from the dose realizations, we fit excess relative risk (ERR) models to the lung cancer mortality data for the Mayak Workers Cohort using risk-modeling software. We then used the corrected-information matrix (CIM) approach to widen the confidence intervals of ERR by taking into account the uncertainty in doses represented by multiple realizations from the Monte Carlo dosimetry systems. Findings of this work revealed that there were 930 lung cancer deaths during follow-up. Plutonium lung doses (but not gamma doses) were generally higher in the new dosimetry systems than those used in the previous analysis. This led to a reduction in the risk per unit dose compared to prior estimates. The estimated ERR/Gy for external gamma-ray exposure was 0.19 (95% CI: 0.07 to 0.31) for both sexes combined, while the ERR/Gy for internal exposures based on mean plutonium doses were 3.5 (95% CI: 2.3 to 4.6) and 8.9 (95% CI: 3.4 to 14) for males and females at attained age 60. Accounting for uncertainty in dose had little effect on the confidence intervals for the ERR associated with gamma-ray exposure, but had a marked impact on confidence intervals, particularly the upper bounds, for the effect of plutonium exposure [adjusted 95% CIs: 1.5 to 8.9 for males and 2.7 to 28 for females]. In conclusion, lung cancer rates increased significantly with both external gamma-ray and internal plutonium exposures. Accounting for the effects of dose uncertainty markedly increased the width of the confidence intervals for the plutonium dose response but had little impact on the external gamma dose effect estimate. Adjusting risk estimate confidence intervals using CIM provides a solution to the important problem of dose uncertainty. This work demonstrates, for the first time, that it is possible and practical to use our recently developed CIM method to make such adjustments in a large cohort study.

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.

Radiation-induced lens opacities: Epidemiological, clinical and experimental evidence, methodological issues, research gaps and strategy

In 2011, the International Commission on Radiological Protection (ICRP) recommended reducing the occupational equivalent dose limit for the lens of the eye from 150 mSv/year to 20 mSv/year, averaged over five years, with no single year exceeding 50 mSv. With this recommendation, several important assumptions were made, such as lack of dose rate effect, classification of cataracts as a tissue reaction with a dose threshold at 0.5 Gy, and progression of minor opacities into vision-impairing cataracts. However, although new dose thresholds and occupational dose limits have been set for radiation-induced cataract, ICRP clearly states that the recommendations are chiefly based on epidemiological evidence because there are a very small number of studies that provide explicit biological and mechanistic evidence at doses under 2 Gy. Since the release of the 2011 ICRP statement, the Multidisciplinary European Low Dose Initiative (MELODI) supported in April 2019 a scientific workshop that aimed to review epidemiological, clinical and biological evidence for radiation-induced cataracts. The purpose of this article is to present and discuss recent related epidemiological and clinical studies, ophthalmic examination techniques, biological and mechanistic knowledge, and to identify research gaps, towards the implementation of a research strategy for future studies on radiation-induced lens opacities. The authors recommend particularly to study the effect of ionizing radiation on the lens in the context of the wider, systemic effects, including in the retina, brain and other organs, and as such cataract is recommended to be studied as part of larger scale programs focused on multiple radiation health effects.

Organ Doses from Chest Radiographs in Tuberculosis Patients in Canada and Their Uncertainties in Periods from 1930 to 1969

This paper describes a study to estimate absorbed doses to various organs from film-based chest radiographs and their uncertainties in the periods 1930 to 1948, 1949 to 1955, and 1956 to 1969. Estimated organ doses will be used in new analyses of risks of cancer and other diseases in tuberculosis patients in Canada who had chest fluoroscopic and radiographic examinations in those periods. In this paper, doses to lungs, female breast, active bone marrow, and heart from a single chest radiograph in adults and children of ages 1, 5, 10, and 15 y in the Canadian cohort and their uncertainties are estimated using (1) data on the tube voltage (kV), total filtration (mm Al), tube-current exposure-time product (mA s), and tube output (mR [mA s]) in each period; (2) assumptions about patient orientation, distance from the source to the skin of a patient, and film size; and (3) new calculations of sex- and age-specific organ dose conversion coefficients (organ doses per dose in air at skin entrance). Variations in estimated doses to each organ across the three periods are less than 20% in adults and up to about 30% at younger ages. Uncertainties in estimated organ doses are about a factor of 2 to 3 in adults and up to a factor of 4 at younger ages and are due mainly to uncertainties in the tube voltage and tube-current exposure-time product.

Uncertainties in Radiation Doses for a Case-control Study of Thyroid Cancer among Persons Exposed in Childhood to 131 I from Chernobyl Fallout

Uncertainties in thyroid doses due to I intake were evaluated for 2,239 subjects in a case-control study of thyroid cancer following exposure to Chernobyl fallout during childhood and adolescence carried out in contaminated regions of Belarus and Russia. Using new methodological developments that became available recently, a Monte Carlo simulation procedure was applied to calculate 1,000 alternative vectors of thyroid doses due to I intake for the study population of 2,239 subjects accounting for sources of shared and unshared errors. An overall arithmetic mean of the stochastic thyroid doses in the study was estimated to be 0.43 Gy and median dose of 0.16 Gy. The arithmetic mean and median of deterministic doses estimated previously for 1,615 of 2,239 study subjects were 0.48 Gy and 0.20 Gy, respectively. The geometric standard deviation of individual stochastic doses varied from 1.59 to 3.61 with an arithmetic mean of 1.94 and a geometric mean of 1.89 over all subjects of the study. These multiple sets of thyroid doses were used to update radiation-related thyroid cancer risks in the study population exposed to I after the Chernobyl accident.

Issues in Interpreting Epidemiologic Studies of Populations Exposed to Low-Dose, High-Energy Photon Radiation

This article addresses issues relevant to interpreting findings from 26 epidemiologic studies of persons exposed to low-dose radiation. We review the extensive data from both epidemiologic studies of persons exposed at moderate or high doses and from radiobiology that together have firmly established radiation as carcinogenic. We then discuss the use of the linear relative risk model that has been used to describe data from both low- and moderate- or high-dose studies. We consider the effects of dose measurement errors; these can reduce statistical power and lead to underestimation of risks but are very unlikely to bring about a spurious dose response. We estimate statistical power for the low-dose studies under the assumption that true risks of radiation-related cancers are those expected from studies of Japanese atomic bomb survivors. Finally, we discuss the interpretation of confidence intervals and statistical tests and the applicability of the Bradford Hill principles for a causal relationship.

Dose-response Analysis in the Presence of Shared and Unshared Uncertainties of the Dose Values

The dose values used in dose-response analyses are often the result of a computer model. Epistemic uncertainties of the model application make it necessary to perform an uncertainty analysis. Such uncertainties are model parameters, model formulations, and input data subject to either classical or Berkson additive or multiplicative measurement error. Epistemic uncertainties are often shared among the computed dose values of all individuals in a cohort or among groups thereof. The effect of these uncertainties on the estimate of the dose-response parameter in least-squares linear regression is difficult to judge. Additive classical error is known to bias the estimate towards lower values (attenuation). The method suggested in this paper is applicable in situations where any combination of uncertainties mentioned above is involved. All it requires is a random sample of dose vectors taken from their joint subjective probability distribution. Such a sample is the output of a Monte Carlo uncertainty analysis of the model application. The covariance matrix of the vectors is used in the computation of correction factors that are possibly true, given the dose vector used in the estimation of the dose-response parameter. The efficiency of the method is demonstrated with five cases. They differ by the combination of uncertainties involved in the uncertainty analysis of a small illustrative dose reconstruction model.

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.

Recent Epidemiologic Studies and the Linear No-Threshold Model For Radiation Protection-Considerations Regarding NCRP Commentary 27

National Council on Radiation Protection and Measurements Commentary 27 examines recent epidemiologic data primarily from low-dose or low dose-rate studies of low linear-energy-transfer radiation and cancer to assess whether they support the linear no-threshold model as used in radiation protection. The commentary provides a critical review of low-dose or low dose-rate studies, most published within the last 10 y, that are applicable to current occupational, environmental, and medical radiation exposures. The strengths and weaknesses of the epidemiologic methods, dosimetry assessments, and statistical modeling of 29 epidemiologic studies of total solid cancer, leukemia, breast cancer, and thyroid cancer, as well as heritable effects and a few nonmalignant conditions, were evaluated. An appraisal of the degree to which the low-dose or low dose-rate studies supported a linear no-threshold model for radiation protection or on the contrary, demonstrated sufficient evidence that the linear no-threshold model is inappropriate for the purposes of radiation protection was also included. The review found that many, though not all, studies of solid cancer supported the continued use of the linear no-threshold model in radiation protection. Evaluations of the principal studies of leukemia and low-dose or low dose-rate radiation exposure also lent support for the linear no-threshold model as used in protection. Ischemic heart disease, a major type of cardiovascular disease, was examined briefly, but the results of recent studies were considered too weak or inconsistent to allow firm conclusions regarding support of the linear no-threshold model. It is acknowledged that the possible risks from very low doses of low linear-energy-transfer radiation are small and uncertain and that it may never be possible to prove or disprove the validity of the linear no-threshold assumption by epidemiologic means. Nonetheless, the preponderance of recent epidemiologic data on solid cancer is supportive of the continued use of the linear no-threshold model for the purposes of radiation protection. This conclusion is in accord with judgments by other national and international scientific committees, based on somewhat older data. Currently, no alternative dose-response relationship appears more pragmatic or prudent for radiation protection purposes than the linear no-threshold model.

Implications of recent epidemiologic studies for the linear nonthreshold model and radiation protection

The recently published NCRP Commentary No. 27 evaluated the new information from epidemiologic studies as to their degree of support for applying the linear nonthreshold (LNT) model of carcinogenic effects for radiation protection purposes (NCRP 2018 Implications of Recent Epidemiologic Studies for the Linear Nonthreshold Model and Radiation Protection, Commentary No. 27 (Bethesda, MD: National Council on Radiation Protection and Measurements)). The aim was to determine whether recent epidemiologic studies of low-LET radiation, particularly those at low doses and/or low dose rates (LD/LDR), broadly support the LNT model of carcinogenic risk or, on the contrary, demonstrate sufficient evidence that the LNT model is inappropriate for the purposes of radiation protection. An updated review was needed because a considerable number of reports of radiation epidemiologic studies based on new or updated data have been published since other major reviews were conducted by national and international scientific committees. The Commentary provides a critical review of the LD/LDR studies that are most directly applicable to current occupational, environmental and medical radiation exposure circumstances. This Memorandum summarises several of the more important LD/LDR studies that incorporate radiation dose responses for solid cancer and leukemia that were reviewed in Commentary No. 27. In addition, an overview is provided of radiation studies of breast and thyroid cancers, and cancer after childhood exposures. Non-cancers are briefly touched upon such as ischemic heart disease, cataracts, and heritable genetic effects. To assess the applicability and utility of the LNT model for radiation protection, the Commentary evaluated 29 epidemiologic studies or groups of studies, primarily of total solid cancer, in terms of strengths and weaknesses in their epidemiologic methods, dosimetry approaches, and statistical modelling, and the degree to which they supported a LNT model for continued use in radiation protection. Recommendations for how to make epidemiologic radiation studies more informative are outlined. The NCRP Committee recognises that the risks from LD/LDR exposures are small and uncertain. The Committee judged that the available epidemiologic data were broadly supportive of the LNT model and that at this time no alternative dose-response relationship appears more pragmatic or prudent for radiation protection purposes.

A cautionary comment on the generation of Berkson error in epidemiological studies

Exposure measurement error can be seen as one of the most important sources of uncertainty in studies in epidemiology. When the aim is to assess the effects of measurement error on statistical inference or to compare the performance of several methods for measurement error correction, it is indispensable to be able to generate different types of measurement error. This paper compares two approaches for the generation of Berkson error, which have recently been applied in radiation epidemiology, in their ability to generate exposure data that satisfy the properties of the Berkson model. In particular, it is shown that the use of one of the methods produces results that are not in accordance with two important properties of Berkson error.

Shared and unshared exposure measurement error in occupational cohort studies and their effects on statistical inference in proportional hazards models

Exposure measurement error represents one of the most important sources of uncertainty in epidemiology. When exposure uncertainty is not or only poorly accounted for, it can lead to biased risk estimates and a distortion of the shape of the exposure-response relationship. In occupational cohort studies, the time-dependent nature of exposure and changes in the method of exposure assessment may create complex error structures. When a method of group-level exposure assessment is used, individual worker practices and the imprecision of the instrument used to measure the average exposure for a group of workers may give rise to errors that are shared between workers, within workers or both. In contrast to unshared measurement error, the effects of shared errors remain largely unknown. Moreover, exposure uncertainty and magnitude of exposure are typically highest for the earliest years of exposure. We conduct a simulation study based on exposure data of the French cohort of uranium miners to compare the effects of shared and unshared exposure uncertainty on risk estimation and on the shape of the exposure-response curve in proportional hazards models. Our results indicate that uncertainty components shared within workers cause more bias in risk estimation and a more severe attenuation of the exposure-response relationship than unshared exposure uncertainty or exposure uncertainty shared between individuals. These findings underline the importance of careful characterisation and modeling of exposure uncertainty in observational studies.

The Mayak Worker Dosimetry System (MWDS-2013): How to Reduce Hyper-Realisations to Realisations

Two important aspects in which the MWDS-2013 output (absorbed dose to organs calculated in each calendar year) differs from previous data bases (MWDS-2008 and DOSES-2005) are that they have been designed to (a) deal explicitly with uncertainties in model parameters, and (b) differentiate parameters that are considered to be shared (unknown, but having the same value for all workers) and unshared (unknown, but having different values between workers). A multiple-realisation approach is used to preserve information on the effects of shared and unshared parameters both for internal and external doses. Previously, a single realisation (a set of organ doses: one for each worker in the cohort) was calculated using the best estimates of parameter values only. In MWDS-2013, a set of 1000 realisations is produced, to reflect the uncertainty in assumed model parameters: each realisation using a different set of parameter values. Within each realisation, shared parameter values are fixed throughout the cohort, while unshared parameters are allowed to vary between workers. One problem is that because the calculation of organ dose is Bayesian, the estimate for each organ dose is not just a single value, but is itself a distribution (hyper-dose). Technically, it is the probability density of dose given the sampled set of parameter values and given the data for that worker. Thus, in our case, the realisations consist not of single doses, but distributions of doses. The term hyper-realisation is used to differentiate this from the more conventional realisation. Although the multiple hyper-realisation in principle contains all of the necessary information on parameter uncertainty, including shared and unshared parameters, in order to make preliminary epidemiological analyses tractable, and also for consistency with the external doses, it was required to convert the hyper-realisations to realisations. The aim of this paper is to discuss the different approaches that were considered to do this, and to define the method that was eventually chosen. Single spot (point) estimates of dose (for each worker) were also calculated to support the epidemiological analysis. The different methods for obtaining these and the implications are also discussed.

Correction of confidence intervals in excess relative risk models using Monte Carlo dosimetry systems with shared errors

In epidemiological studies, exposures of interest are often measured with uncertainties, which may be independent or correlated. Independent errors can often be characterized relatively easily while correlated measurement errors have shared and hierarchical components that complicate the description of their structure. For some important studies, Monte Carlo dosimetry systems that provide multiple realizations of exposure estimates have been used to represent such complex error structures. While the effects of independent measurement errors on parameter estimation and methods to correct these effects have been studied comprehensively in the epidemiological literature, the literature on the effects of correlated errors, and associated correction methods is much more sparse. In this paper, we implement a novel method that calculates corrected confidence intervals based on the approximate asymptotic distribution of parameter estimates in linear excess relative risk (ERR) models. These models are widely used in survival analysis, particularly in radiation epidemiology. Specifically, for the dose effect estimate of interest (increase in relative risk per unit dose), a mixture distribution consisting of a normal and a lognormal component is applied. This choice of asymptotic approximation guarantees that corrected confidence intervals will always be bounded, a result which does not hold under a normal approximation. A simulation study was conducted to evaluate the proposed method in survival analysis using a realistic ERR model. We used both simulated Monte Carlo dosimetry systems (MCDS) and actual dose histories from the Mayak Worker Dosimetry System 2013, a MCDS for plutonium exposures in the Mayak Worker Cohort. Results show our proposed methods provide much improved coverage probabilities for the dose effect parameter, and noticeable improvements for other model parameters.

THE GROWTH OF BIOSTATISTICS AND ESTIMATION OF CANCER RISK ESTIMATES: PAST, CURRENT, AND FUTURE CHALLENGES

There has been a long process of growth and development of statistical approaches to the analysis of cancer incidence and mortality data obtained from the follow-up of radiation exposed populations. The challenges of radiation risk analysis provided impetus for innovative statistical methods, including, the inception and continued improvement of hazard rate regression methods. Key statistical contributions that improved cancer risk estimation include statistical advances pertaining to the measurement error problem. Current statistical problems involve extensions of the measurement error methods to account for shared non-independent uncertainties in dose estimation, 'transportability' of risk coefficients for radioprotection and risk estimation world-wide, and extrapolation from high dose rate to low-dose rate exposures or from low LET to high LET. Future problems include quantification of individual sensitivity to radiation-related diseases due to individual genetic differences (or other factors), and in understanding the synergy (additive, multiplicative, etc.) between underlying individual risk and radiation exposure.

Concerted Uranium Research in Europe (CURE): toward a collaborative project integrating dosimetry, epidemiology and radiobiology to study the effects of occupational uranium exposure

The potential health impacts of chronic exposures to uranium, as they occur in occupational settings, are not well characterized. Most epidemiological studies have been limited by small sample sizes, and a lack of harmonization of methods used to quantify radiation doses resulting from uranium exposure. Experimental studies have shown that uranium has biological effects, but their implications for human health are not clear. New studies that would combine the strengths of large, well-designed epidemiological datasets with those of state-of-the-art biological methods would help improve the characterization of the biological and health effects of occupational uranium exposure. The aim of the European Commission concerted action CURE (Concerted Uranium Research in Europe) was to develop protocols for such a future collaborative research project, in which dosimetry, epidemiology and biology would be integrated to better characterize the effects of occupational uranium exposure. These protocols were developed from existing European cohorts of workers exposed to uranium together with expertise in epidemiology, biology and dosimetry of CURE partner institutions. The preparatory work of CURE should allow a large scale collaborative project to be launched, in order to better characterize the effects of uranium exposure and more generally of alpha particles and low doses of ionizing radiation.

Impact of Uncertainties in Exposure Assessment on Thyroid Cancer Risk among Persons in Belarus Exposed as Children or Adolescents Due to the Chernobyl Accident

Background

The excess incidence of thyroid cancer in Ukraine and Belarus observed a few years after the Chernobyl accident is considered to be largely the result of ¹³¹I released from the reactor. Although the Belarus thyroid cancer prevalence data has been previously analyzed, no account was taken of dose measurement error.

Methods

We examined dose-response patterns in a thyroid screening prevalence cohort of 11,732 persons aged under 18 at the time of the accident, diagnosed during 1996–2004, who had direct thyroid ¹³¹I activity measurement, and were resident in the most radio-actively contaminated regions of Belarus. Three methods of dose-error correction (regression calibration, Monte Carlo maximum likelihood, Bayesian Markov Chain Monte Carlo) were applied.

Results

There was a statistically significant (p<0.001) increasing dose-response for prevalent thyroid cancer, irrespective of regression-adjustment method used. Without adjustment for dose errors the excess odds ratio was 1.51 Gy⁻ (95% CI 0.53, 3.86), which was reduced by 13% when regression-calibration adjustment was used, 1.31 Gy⁻ (95% CI 0.47, 3.31). A Monte Carlo maximum likelihood method yielded an excess odds ratio of 1.48 Gy⁻ (95% CI 0.53, 3.87), about 2% lower than the unadjusted analysis. The Bayesian method yielded a maximum posterior excess odds ratio of 1.16 Gy⁻ (95% BCI 0.20, 4.32), 23% lower than the unadjusted analysis. There were borderline significant (p = 0.053–0.078) indications of downward curvature in the dose response, depending on the adjustment methods used. There were also borderline significant (p = 0.102) modifying effects of gender on the radiation dose trend, but no significant modifying effects of age at time of accident, or age at screening as modifiers of dose response (p>0.2).

Conclusions

In summary, the relatively small contribution of unshared classical dose error in the current study results in comparatively modest effects on the regression parameters.

Accounting for shared and unshared dosimetric uncertainties in the dose response for ultrasound-detected thyroid nodules after exposure to radioactive fallout

Dosimetic uncertainties, particularly those that are shared among subgroups of a study population, can bias, distort or reduce the slope or significance of a dose response. Exposure estimates in studies of health risks from environmental radiation exposures are generally highly uncertain and thus, susceptible to these methodological limitations. An analysis was published in 2008 concerning radiation-related thyroid nodule prevalence in a study population of 2,994 villagers under the age of 21 years old between August 1949 and September 1962 and who lived downwind from the Semipalatinsk Nuclear Test Site in Kazakhstan. This dose-response analysis identified a statistically significant association between thyroid nodule prevalence and reconstructed doses of fallout-related internal and external radiation to the thyroid gland; however, the effects of dosimetric uncertainty were not evaluated since the doses were simple point "best estimates". In this work, we revised the 2008 study by a comprehensive treatment of dosimetric uncertainties. Our present analysis improves upon the previous study, specifically by accounting for shared and unshared uncertainties in dose estimation and risk analysis, and differs from the 2008 analysis in the following ways: 1. The study population size was reduced from 2,994 to 2,376 subjects, removing 618 persons with uncertain residence histories; 2. Simulation of multiple population dose sets (vectors) was performed using a two-dimensional Monte Carlo dose estimation method; and 3. A Bayesian model averaging approach was employed for evaluating the dose response, explicitly accounting for large and complex uncertainty in dose estimation. The results were compared against conventional regression techniques. The Bayesian approach utilizes 5,000 independent realizations of population dose vectors, each of which corresponds to a set of conditional individual median internal and external doses for the 2,376 subjects. These 5,000 population dose vectors reflect uncertainties in dosimetric parameters, partly shared and partly independent, among individual members of the study population. Risk estimates for thyroid nodules from internal irradiation were higher than those published in 2008, which results, to the best of our knowledge, from explicitly accounting for dose uncertainty. In contrast to earlier findings, the use of Bayesian methods led to the conclusion that the biological effectiveness for internal and external dose was similar. Estimates of excess relative risk per unit dose (ERR/Gy) for males (177 thyroid nodule cases) were almost 30 times those for females (571 cases) and were similar to those reported for thyroid cancers related to childhood exposures to external and internal sources in other studies. For confirmed cases of papillary thyroid cancers (3 in males, 18 in females), the ERR/Gy was also comparable to risk estimates from other studies, but not significantly different from zero. These findings represent the first reported dose response for a radiation epidemiologic study considering all known sources of shared and unshared errors in dose estimation and using a Bayesian model averaging (BMA) method for analysis of the dose response.

The two-dimensional Monte Carlo: a new methodologic paradigm for dose reconstruction for epidemiological studies

Retrospective dose estimation, particularly dose reconstruction that supports epidemiological investigations of health risk, relies on various strategies that include models of physical processes and exposure conditions with detail ranging from simple to complex. Quantification of dose uncertainty is an essential component of assessments for health risk studies since, as is well understood, it is impossible to retrospectively determine the true dose for each person. To address uncertainty in dose estimation, numerical simulation tools have become commonplace and there is now an increased understanding about the needs and what is required for models used to estimate cohort doses (in the absence of direct measurement) to evaluate dose response. It now appears that for dose-response algorithms to derive the best, unbiased estimate of health risk, we need to understand the type, magnitude and interrelationships of the uncertainties of model assumptions, parameters and input data used in the associated dose estimation models. Heretofore, uncertainty analysis of dose estimates did not always properly distinguish between categories of errors, e.g., uncertainty that is specific to each subject (i.e., unshared error), and uncertainty of doses from a lack of understanding and knowledge about parameter values that are shared to varying degrees by numbers of subsets of the cohort. While mathematical propagation of errors by Monte Carlo simulation methods has been used for years to estimate the uncertainty of an individual subject's dose, it was almost always conducted without consideration of dependencies between subjects. In retrospect, these types of simple analyses are not suitable for studies with complex dose models, particularly when important input data are missing or otherwise not available. The dose estimation strategy presented here is a simulation method that corrects the previous deficiencies of analytical or simple Monte Carlo error propagation methods and is termed, due to its capability to maintain separation between shared and unshared errors, the two-dimensional Monte Carlo (2DMC) procedure. Simply put, the 2DMC method simulates alternative, possibly true, sets (or vectors) of doses for an entire cohort rather than a single set that emerges when each individual's dose is estimated independently from other subjects. Moreover, estimated doses within each simulated vector maintain proper inter-relationships such that the estimated doses for members of a cohort subgroup that share common lifestyle attributes and sources of uncertainty are properly correlated. The 2DMC procedure simulates inter-individual variability of possibly true doses within each dose vector and captures the influence of uncertainty in the values of dosimetric parameters across multiple realizations of possibly true vectors of cohort doses. The primary characteristic of the 2DMC approach, as well as its strength, are defined by the proper separation between uncertainties shared by members of the entire cohort or members of defined cohort subsets, and uncertainties that are individual-specific and therefore unshared.