Flexible dose-response models for Japanese atomic bomb survivor data: Bayesian estimation and prediction of cancer risk

A Historical Survey of Key Epidemiological Studies of Ionizing Radiation Exposure

In this article we review the history of key epidemiological studies of populations exposed to ionizing radiation. We highlight historical and recent findings regarding radiation-associated risks for incidence and mortality of cancer and non-cancer outcomes with emphasis on study design and methods of exposure assessment and dose estimation along with brief consideration of sources of bias for a few of the more important studies. We examine the findings from the epidemiological studies of the Japanese atomic bomb survivors, persons exposed to radiation for diagnostic or therapeutic purposes, those exposed to environmental sources including Chornobyl and other reactor accidents, and occupationally exposed cohorts. We also summarize results of pooled studies. These summaries are necessarily brief, but we provide references to more detailed information. We discuss possible future directions of study, to include assessment of susceptible populations, and possible new populations, data sources, study designs and methods of analysis.

Recommendations on statistical approaches to account for dose uncertainties in radiation epidemiologic risk models

PURPOSE

Epidemiological studies of stochastic radiation health effects such as cancer, meant to estimate risks of the adverse effects as a function of radiation dose, depend largely on estimates of the radiation doses received by the exposed group under study. Those estimates are based on dosimetry that always has uncertainty, which often can be quite substantial. Studies that do not incorporate statistical methods to correct for dosimetric uncertainty may produce biased estimates of risk and incorrect confidence bounds on those estimates. This paper reviews commonly used statistical methods to correct radiation risk regressions for dosimetric uncertainty, with emphasis on some newer methods. We begin by describing the types of dose uncertainty that may occur, including those in which an uncertain value is shared by part or all of a cohort, and then demonstrate how these sources of uncertainty arise in radiation dosimetry. We briefly describe the effects of different types of dosimetric uncertainty on risk estimates, followed by a description of each method of adjusting for the uncertainty.

CONCLUSIONS

Each of the method has strengths and weaknesses, and some methods have limited applicability. We describe the types of uncertainty to which each method can be applied and its pros and cons. Finally, we provide summary recommendations and touch briefly on suggestions for further research.

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.

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.

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.

Lifetime Mortality Risk from Cancer and Circulatory Disease Predicted from the Japanese Atomic Bomb Survivor Life Span Study Data Taking Account of Dose Measurement Error

Dosimetric measurement error is known to potentially bias the magnitude of the dose response, and can also affect the shape of dose response. In this report, generalized relative and absolute rate models are fitted to the latest Japanese atomic bomb survivor solid cancer, leukemia and circulatory disease mortality data (followed from 1950 through 2003), with the latest (DS02R1) dosimetry, using Bayesian techniques to adjust for errors in dose estimates and assessing other model uncertainties. Linear-quadratic models are fitted and used to assess lifetime mortality risks for contemporary UK, USA, French, Russian, Japanese and Chinese populations. For a test dose of 0.1 Gy absorbed dose weighted by neutron relative biological effectiveness, solid cancer, leukemia and circulatory disease mortality risks for a UK population using a generalized linear-quadratic relative rate model were estimated to be 3.88% Gy-1 [95% Bayesian credible interval (BCI): 1.17, 6.97], 0.35% Gy-1 (95% BCI: -0.03, 0.78) and 2.24% Gy-1 (95% BCI: -0.17, 13.76), respectively. Using a generalized absolute rate linear-quadratic model at 0.1 Gy, the lifetime risks for these three end points were estimated to be 3.56% Gy-1 (95% BCI: 0.54, 6.78), 0.41% Gy-1 (95% BCI: 0.01, 0.86) and 1.56% Gy-1 (95% BCI: -1.10, 7.21), respectively. There was substantial evidence of curvature for solid cancer (in particular, the group of solid cancers excluding lung, breast and stomach cancers) and leukemia, so that for solid cancer and leukemia, estimates of excess risk per unit dose were nearly doubled by increasing the dose from 0.01 to 1.0 Gy, with most of the increase occurring in the interval from 0.1 to 1.0 Gy. For circulatory disease, the dose-response curvature was inverse, so that risk per unit dose was nearly halved by going from 0.01 t o 1.0 Gy weighted absorbed dose, although there were substantial uncertainties. In general, there were higher radiation risks for females compared to males. This was true for solid cancer and circulatory disease overall, as well as for lung, breast, stomach and the group of other solid cancers, and was the case whether relative or absolute rate projection models were employed; however, for leukemia this pattern was reversed. Risk estimates varied somewhat between populations, with lower cancer risks in aggregate for China and Russia, but higher circulatory disease risks for Russia, particularly using the relative rate model. There was more pronounced variation for certain cancer sites and certain types of projection models, so that breast cancer risk was markedly lower in China and Japan using a relative rate model, but the opposite was the case for stomach cancer. There was less variation between countries using the absolute rate models for stomach cancer and breast cancer, but this was not the case for lung cancer and the group of other solid cancers, or for circulatory disease.

Analysis of Cataract in Relationship to Occupational Radiation Dose Accounting for Dosimetric Uncertainties in a Cohort of U.S. Radiologic Technologists

Cataract is one of the major morbidities in the U.S. population and it has long been appreciated that high and acutely delivered radiation doses of 1 Gy or more can induce cataract. Some more recent studies, in particular those of the U.S. Radiologic Technologists, have suggested that cataract may be induced by much lower, chronically delivered doses of ionizing radiation. It is well recognized that dosimetric measurement error can substantially alter the shape of the radiation dose-response relationship and thus, the derived study risk estimates, and can also inflate the variance of the estimates. In the current study, we evaluate the impact of uncertainties in eye-lens absorbed doses on the estimated risk of cataract in the U.S. Radiologic Technologists' Monte Carlo Dosimetry System, using both absolute and relative risk models. Among 11,345 cases we show that the inflation in the standard error for the excess relative risk (ERR) is generally modest, at most approximately 20% of the unadjusted standard error, depending on the model used for the baseline risk. The largest adjustment results from use of relative risk models, so that the ERR/Gy and its 95% confidence intervals change from 1.085 (0.645, 1.525) to 1.085 (0.558, 1.612) after adjustment. However, the inflation in the standard error of the excess absolute risk (EAR) coefficient is generally minimal, at most approximately 0.04% of the standard error.

Dynamical modeling approach to risk assessment for radiogenic leukemia among astronauts engaged in interplanetary space missions

A recently developed biologically motivated dynamical model of the assessment of the excess relative risk (ERR) for radiogenic leukemia among acutely/continuously irradiated humans (Smirnova, 2015, 2017) is applied to estimate the ERR for radiogenic leukemia among astronauts engaged in long-term interplanetary space missions. Numerous scenarios of space radiation exposure during space missions are used in the modeling studies. The dependence of the ERR for leukemia among astronauts on several mission parameters including the dose equivalent rates of galactic cosmic rays (GCR) and large solar particle events (SPEs), the number of large SPEs, the time interval between SPEs, mission duration, the degree of astronaut's additional shielding during SPEs, the degree of their additional 12-hour's daily shielding, as well as the total mission dose equivalent, is examined. The results of the estimation of ERR for radiogenic leukemia among astronauts, which are obtained in the framework of the developed dynamical model for various scenarios of space radiation exposure, are compared with the corresponding results, computed by the commonly used linear model. It is revealed that the developed dynamical model along with the linear model can be applied to estimate ERR for radiogenic leukemia among astronauts engaged in long-term interplanetary space missions in the range of applicability of the latter. In turn, the developed dynamical model is capable of predicting the ERR for leukemia among astronauts for the irradiation regimes beyond the applicability range of the linear model in emergency cases. As a supplement to the estimations of cancer incidence and death (REIC and REID) (Cucinotta et al., 2013, 2017), the developed dynamical model for the assessment of the ERR for leukemia can be employed on the pre-mission design phase for, e.g., the optimization of the regimes of astronaut's additional shielding in the course of interplanetary space missions. The developed model can also be used on the phase of the real-time responses during the space mission to make the decisions on the operational application of appropriate countermeasures to minimize the risks of occurrences of leukemia, especially, for emergency cases.

Levels of naturally occurring gamma radiation measured in British homes and their prediction in particular residences

Gamma radiation from natural sources (including directly ionising cosmic rays) is an important component of background radiation. In the present paper, indoor measurements of naturally occurring gamma rays that were undertaken as part of the UK Childhood Cancer Study are summarised, and it is shown that these are broadly compatible with an earlier UK National Survey. The distribution of indoor gamma-ray dose rates in Great Britain is approximately normal with mean 96 nGy/h and standard deviation 23 nGy/h. Directly ionising cosmic rays contribute about one-third of the total. The expanded dataset allows a more detailed description than previously of indoor gamma-ray exposures and in particular their geographical variation. Various strategies for predicting indoor natural background gamma-ray dose rates were explored. In the first of these, a geostatistical model was fitted, which assumes an underlying geologically determined spatial variation, superimposed on which is a Gaussian stochastic process with Matérn correlation structure that models the observed tendency of dose rates in neighbouring houses to correlate. In the second approach, a number of dose-rate interpolation measures were first derived, based on averages over geologically or administratively defined areas or using distance-weighted averages of measurements at nearest-neighbour points. Linear regression was then used to derive an optimal linear combination of these interpolation measures. The predictive performances of the two models were compared via cross-validation, using a randomly selected 70 % of the data to fit the models and the remaining 30 % to test them. The mean square error (MSE) of the linear-regression model was lower than that of the Gaussian-Matérn model (MSE 378 and 411, respectively). The predictive performance of the two candidate models was also evaluated via simulation; the OLS model performs significantly better than the Gaussian-Matérn model.

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.

Myeloid leukemia risk assessment and dynamics of the granulocytopoietic system in acutely and continuously irradiated humans: modeling approach

A dynamic modeling approach to the risk assessment of radiogenic myeloid leukemia is proposed. A basic tool of this approach is a biologically motivated mathematical model of the granulocytopoietic system, which is capable of predicting the dynamics of blood granulocytes and bone marrow granulocytopoietic cells in acutely and chronically irradiated humans. The performed modeling studies revealed that the dose dependence of the scaled maximal concentration of bone marrow granulocytopoietic cells with radiation-induced changes, which make a cell premalignant, and the dose dependence of the scaled integral of the concentration of these cells over the period of the response of the granulocytopoietic system to acute irradiation conform to the dose dependence of excess relative risk for myeloid leukemia among atomic bomb survivors in a wide range of doses and in a range of comparatively low doses, respectively. Additionally, the dose dependence of the scaled integral of the concentration of these cells over the period of the response of the granulocytopoietic system to continuous irradiation with the dose rate and durations, which were used in brachytherapy, conforms to the dose dependence of excess relative risk for leukemia among the respective groups of exposed patients. These modeling findings demonstrate the potential to use the proposed modeling approach for predicting the excess relative risk for myeloid leukemia among humans exposed to various radiation regimes. Obviously, this is especially important in the assessment of the risks for radiogenic myeloid leukemia among people residing in contaminated areas after an accident or explosion of a radiological device, among astronauts on long-term space missions, as well as among patients treated with radiotherapy.

Minimizing second cancer risk following radiotherapy: current perspectives

Secondary cancer risk following radiotherapy is an increasingly important topic in clinical oncology with impact on treatment decision making and on patient management. Much of the evidence that underlies our understanding of secondary cancer risks and our risk estimates are derived from large epidemiologic studies and predictive models of earlier decades with large uncertainties. The modern era is characterized by more conformal radiotherapy technologies, molecular and genetic marker approaches, genome-wide studies and risk stratifications, and sophisticated biologically based predictive models of the carcinogenesis process. Four key areas that have strong evidence toward affecting secondary cancer risks are 1) the patient age at time of radiation treatment, 2) genetic risk factors, 3) the organ and tissue site receiving radiation, and 4) the dose and volume of tissue being irradiated by a particular radiation technology. This review attempts to summarize our current understanding on the impact on secondary cancer risks for each of these known risk factors. We review the recent advances in genetic studies and carcinogenesis models that are providing insight into the biologic processes that occur from tissue irradiation to the development of a secondary malignancy. Finally, we discuss current approaches toward minimizing the risk of radiation-associated secondary malignancies, an important goal of clinical radiation oncology.

Association of chromosome translocation rate with low dose occupational radiation exposures in U.S. radiologic technologists

Chromosome translocations are a well-recognized biological marker of radiation exposure and cancer risk. However, there is uncertainty about the lowest dose at which excess translocations can be detected, and whether there is temporal decay of induced translocations in radiation-exposed populations. Dosimetric uncertainties can substantially alter the shape of dose-response relationships; although regression-calibration methods have been used in some datasets, these have not been applied in radio-occupational studies, where there are also complex patterns of shared and unshared errors that these methods do not account for. In this article we evaluated the relationship between estimated occupational ionizing radiation doses and chromosome translocation rates using fluorescent in situ hybridization in 238 U.S. radiologic technologists selected from a large cohort. Estimated cumulative red bone marrow doses (mean 29.3 mGy, range 0-135.7 mGy) were based on available badge-dose measurement data and on questionnaire-reported work history factors. Dosimetric assessment uncertainties were evaluated using regression calibration, Bayesian and Monte Carlo maximum likelihood methods, taking account of shared and unshared error and adjusted for overdispersion. There was a significant dose response for estimated occupational radiation exposure, adjusted for questionnaire-based personal diagnostic radiation, age, sex and study group (5.7 translocations per 100 whole genome cell equivalents per Gy, 95% CI 0.2, 11.3, P = 0.0440). A significant increasing trend with dose continued to be observed for individuals with estimated doses <100 mGy. For combined estimated occupational and personal-diagnostic-medical radiation exposures, there was a borderline-significant modifying effect of age (P = 0.0704), but little evidence (P > 0.5) of temporal decay of induced translocations. The three methods of analysis to adjust for dose uncertainty gave similar results. In summary, chromosome translocation dose-response slopes were detectable down to <100 mGy and were compatible with those observed in other radiation-exposed populations. However, there are substantial uncertainties in both occupational and other (personal-diagnostic-medical) doses that may be imperfectly taken into account in our analysis.

Impact of uncertainties in exposure assessment on estimates of thyroid cancer risk among Ukrainian children and adolescents exposed from the Chernobyl accident

The 1986 accident at the Chernobyl nuclear power plant remains the most serious nuclear accident in history, and excess thyroid cancers, particularly among those exposed to releases of iodine-131 remain the best-documented sequelae. Failure to take dose-measurement error into account can lead to bias in assessments of dose-response slope. Although risks in the Ukrainian-US thyroid screening study have been previously evaluated, errors in dose assessments have not been addressed hitherto. Dose-response patterns were examined in a thyroid screening prevalence cohort of 13,127 persons aged <18 at the time of the accident who were resident in the most radioactively contaminated regions of Ukraine. We extended earlier analyses in this cohort by adjusting for dose error in the recently developed TD-10 dosimetry. Three methods of statistical correction, via two types of regression calibration, and Monte Carlo maximum-likelihood, were applied to the doses that can be derived from the ratio of thyroid activity to thyroid mass. The two components that make up this ratio have different types of error, Berkson error for thyroid mass and classical error for thyroid activity. The first regression-calibration method yielded estimates of excess odds ratio of 5.78 Gy⁻¹ (95% CI 1.92, 27.04), about 7% higher than estimates unadjusted for dose error. The second regression-calibration method gave an excess odds ratio of 4.78 Gy⁻¹ (95% CI 1.64, 19.69), about 11% lower than unadjusted analysis. The Monte Carlo maximum-likelihood method produced an excess odds ratio of 4.93 Gy⁻¹ (95% CI 1.67, 19.90), about 8% lower than unadjusted analysis. There are borderline-significant (p = 0.101–0.112) indications of downward curvature in the dose response, allowing for which nearly doubled the low-dose linear coefficient. In conclusion, dose-error adjustment has comparatively modest effects on regression parameters, a consequence of the relatively small errors, of a mixture of Berkson and classical form, associated with thyroid dose assessment.

Potential impacts of radon, terrestrial gamma and cosmic rays on childhood leukemia in France: a quantitative risk assessment

Previous epidemiological studies and quantitative risk assessments (QRA) have suggested that natural background radiation may be a cause of childhood leukemia. The present work uses a QRA approach to predict the excess risk of childhood leukemia in France related to three components of natural radiation: radon, cosmic rays and terrestrial gamma rays, using excess relative and absolute risk models proposed by the United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR). Both models were developed from the Life Span Study (LSS) of Japanese A-bomb survivors. Previous risk assessments were extended by considering uncertainties in radiation-related leukemia risk model parameters as part of this process, within a Bayesian framework. Estimated red bone marrow doses cumulated during childhood by the average French child due to radon, terrestrial gamma and cosmic rays are 4.4, 7.5 and 4.3 mSv, respectively. The excess fractions of cases (expressed as percentages) associated with these sources of natural radiation are 20 % [95 % credible interval (CI) 0-68 %] and 4 % (95 % CI 0-11 %) under the excess relative and excess absolute risk models, respectively. The large CIs, as well as the different point estimates obtained under these two models, highlight the uncertainties in predictions of radiation-related childhood leukemia risks. These results are only valid provided that models developed from the LSS can be transferred to the population of French children and to chronic natural radiation exposures, and must be considered in view of the currently limited knowledge concerning other potential risk factors for childhood leukemia. Last, they emphasize the need for further epidemiological investigations of the effects of natural radiation on childhood leukemia to reduce uncertainties and help refine radiation protection standards.

The performance of functional methods for correcting non-Gaussian measurement error within Poisson regression: corrected excess risk of lung cancer mortality in relation to radon exposure among French uranium miners

A broad variety of methods for measurement error (ME) correction have been developed, but these methods have rarely been applied possibly because their ability to correct ME is poorly understood. We carried out a simulation study to assess the performance of three error-correction methods: two variants of regression calibration (the substitution method and the estimation calibration method) and the simulation extrapolation (SIMEX) method. Features of the simulated cohorts were borrowed from the French Uranium Miners' Cohort in which exposure to radon had been documented from 1946 to 1999. In the absence of ME correction, we observed a severe attenuation of the true effect of radon exposure, with a negative relative bias of the order of 60% on the excess relative risk of lung cancer death. In the main scenario considered, that is, when ME characteristics previously determined as most plausible from the French Uranium Miners' Cohort were used both to generate exposure data and to correct for ME at the analysis stage, all three error-correction methods showed a noticeable but partial reduction of the attenuation bias, with a slight advantage for the SIMEX method. However, the performance of the three correction methods highly depended on the accurate determination of the characteristics of ME. In particular, we encountered severe overestimation in some scenarios with the SIMEX method, and we observed lack of correction with the three methods in some other scenarios. For illustration, we also applied and compared the proposed methods on the real data set from the French Uranium Miners' Cohort study.

Impact of measurement error in radon exposure on the estimated excess relative risk of lung cancer death in a simulated study based on the French Uranium Miners' Cohort

Measurement error (ME) can lead to bias in the analysis of epidemiologic studies. Here a simulation study is described that is based on data from the French Uranium Miners' Cohort and that was conducted to assess the effect of ME on the estimated excess relative risk (ERR) of lung cancer death associated with radon exposure. Starting from a scenario without any ME, data were generated containing successively Berkson or classical ME depending on time periods, to reflect changes in the measurement of exposure to radon ((222)Rn) and its decay products over time in this cohort. Results indicate that ME attenuated the level of association with radon exposure, with a negative bias percentage on the order of 60% on the ERR estimate. Sensitivity analyses showed the consequences of specific ME characteristics (type, size, structure, and distribution) on the ERR estimates. In the future, it appears important to correct for ME upon analyzing cohorts such as this one to decrease bias in estimates of the ERR of adverse events associated with exposure to ionizing radiation.

Density-dependent mortality of the human host in onchocerciasis: relationships between microfilarial load and excess mortality

Background

The parasite Onchocerca volvulus has, until recently, been regarded as the cause of a chronic yet non-fatal condition. Recent analyses, however, have indicated that in addition to blindness, the parasite can also be directly associated with human mortality. Such analyses also suggested that the relationship between microfilarial load and excess mortality might be non-linear. Determining the functional form of such relationship would contribute to quantify the population impact of mass microfilaricidal treatment.

Methodology/Principal Findings

Data from the Onchocerciasis Control Programme in West Africa (OCP) collected from 1974 through 2001 were used to determine functional relationships between microfilarial load and excess mortality of the human host. The goodness-of-fit of three candidate functional forms (a (log-) linear model and two saturating functions) were explored and a saturating (log-) sigmoid function was deemed to be statistically the best fit. The excess mortality associated with microfilarial load was also found to be greater in younger hosts. The attributable mortality risk due to onchocerciasis was estimated to be 5.9%.

Conclusions/Significance

Incorporation of this non-linear functional relationship between microfilarial load and excess mortality into mathematical models for the transmission and control of onchocerciasis will have important implications for our understanding of the population biology of O. volvulus, its impact on human populations, the global burden of disease due to onchocerciasis, and the projected benefits of control programmes in both human and economic terms.

Human onchocerciasis (River Blindness) is a parasitic disease leading to visual impairment including blindness. Blindness may lead to premature death, but infection with the parasite itself (Onchocerca volvulus) may also cause excess mortality in sighted individuals. The excess risk of mortality may not be directly (linearly) proportional to the intensity of infection (a measure of how many parasites an individual harbours). We analyze cohort data from the Onchocerciasis Control Programme in West Africa, collected between 1974 and 2001, by fitting a suite of quantitative models (including a ‘null’ model of no relationship between infection intensity and mortality, a (log-) linear function, and two plateauing curves), and choosing the one that is the most statistically adequate. The risk of human mortality initially increases with parasite density but saturates at high densities (following an S-shape curve), and such risk is greater in younger individuals for a given infection intensity. Our results have important repercussions for programmes aiming to control onchocerciasis (in terms of how the benefits of the programme are calculated), for measuring the burden of disease and mortality caused by the infection, and for a better understanding of the processes that govern the density of parasite populations among human hosts.

Radiation dosimetry and safety issues in the investigation of pulmonary embolism

When considering the investigation of the patient with possible pulmonary embolism, one needs to balance the likelihood of disease and the diagnostic utility of the test against the risks associated with the investigation. Both computed tomography pulmonary angiography (CTPA) and the ventilation/perfusion (V/Q) scan involve exposure to ionizing radiation. The effect of low-level ionizing radiation remains an issue of some controversy. CTPA delivers a greater effective dose and, in particular, greater doses to breast tissue, than the V/Q scan (typically 10-70 mGy for CTPA vs <1.5 mGy for V/Q to breast). Since breast tissue is particularly radiosensitive in younger women, the V/Q study has an advantage over CTPA in this group. In the pregnant patient, fetal exposure has been raised as a concern. In fact, there is typically only low fetal exposure from either study (<1 mGy). The CTPA does deliver less fetal exposure, particularly in the first trimester, but the difference between CTPA and V/Q scan is small when compared with the difference in dose to maternal breast from the 2 investigations. The "as low as reasonably achievable" (ie, ALARA) principle favors the use of V/Q scans in young women, assuming the diagnostic power of the 2 tests is comparable. CTPA requires a contrast injection that can cause adverse reactions in a small number of patients. No significant risk, however, has been demonstrated with the radiopharmaceuticals involved in V/Q scans.

Use of the individual data of the A-bomb survivors for biologically based cancer models

All recent analyses of the data on solid cancer incidence of the atomic bomb survivors are corrected for migration and random dose errors. In the usual treatment with grouped data and regression calibration, the calibration of doses depends on the used dose response. For solid cancers, it usually is linear. Here, an individual likelihood is presented which works without further adjustment for all dose responses. When the same assumptions are made as in the usual Poisson regression, equivalent results are obtained. But, the individual likelihood has the potential to use more detailed models for dose errors and to estimate non-linear dose responses without recalibration. As an example for the potential of the individual data set for the analysis of risk at low doses, signals for a saturating bystander effect are investigated.

A new view of radiation-induced cancer: integrating short- and long-term processes. Part II: second cancer risk estimation

As the number of cancer survivors grows, prediction of radiotherapy-induced second cancer risks becomes increasingly important. Because the latency period for solid tumors is long, the risks of recently introduced radiotherapy protocols are not yet directly measurable. In the accompanying article, we presented a new biologically based mathematical model, which, in principle, can estimate second cancer risks for any protocol. The novelty of the model is that it integrates, into a single formalism, mechanistic analyses of pre-malignant cell dynamics on two different time scales: short-term during radiotherapy and recovery; long-term during the entire life span. Here, we apply the model to nine solid cancer types (stomach, lung, colon, rectal, pancreatic, bladder, breast, central nervous system, and thyroid) using data on radiotherapy-induced second malignancies, on Japanese atomic bomb survivors, and on background US cancer incidence. Potentially, the model can be incorporated into radiotherapy treatment planning algorithms, adding second cancer risk as an optimization criterion.

Predicting future excess events in risk assessment

Risk characterization in a study population relies on cases of disease or death that are causally related to the exposure under study. The number of such cases, so-called "excess" cases, is not just an indicator of the impact of the risk factor in the study population, but also an important determinant of statistical power for assessing aspects of risk such as age-time trends and susceptible subgroups. In determining how large a population to study and/or how long to follow a study population to accumulate sufficient excess cases, it is necessary to predict future risk. In this study, focusing on models involving excess risk with possible effect modification, we describe a method for predicting the expected magnitude of numbers of excess cases and assess the uncertainty in those predictions. We do this by extending Bayesian APC models for rate projection to include exposure-related excess risk with possible effect modification by, e.g., age at exposure and attained age. The method is illustrated using the follow-up study of Japanese Atomic-Bomb Survivors, one of the primary bases for determining long-term health effects of radiation exposure and assessment of risk for radiation protection purposes. Using models selected by a predictive-performance measure obtained on test data reserved for cross-validation, we project excess counts due to radiation exposure and lifetime risk measures (risk of exposure-induced deaths (REID) and loss of life expectancy (LLE)) associated with cancer and noncancer disease deaths in the A-Bomb survivor cohort.

New models for evaluation of radiation-induced lifetime cancer risk and its uncertainty employed in the UNSCEAR 2006 report

Generalized relative and absolute risk models are fitted to the latest Japanese atomic bomb survivor solid cancer and leukemia mortality data (through 2000), with the latest (DS02) dosimetry, by classical (regression calibration) and Bayesian techniques, taking account of errors in dose estimates and other uncertainties. Linear-quadratic and linear-quadratic-exponential models are fitted and used to assess risks for contemporary populations of China, Japan, Puerto Rico, the U.S. and the UK. Many of these models are the same as or very similar to models used in the UNSCEAR 2006 report. For a test dose of 0.1 Sv, the solid cancer mortality for a UK population using the generalized linear-quadratic relative risk model is estimated as 5.4% Sv(-1) [90% Bayesian credible interval (BCI) 3.1, 8.0]. At 0.1 Sv, leukemia mortality for a UK population using the generalized linear-quadratic relative risk model is estimated as 0.50% Sv(-1) (90% BCI 0.11, 0.97). Risk estimates varied little between populations; at 0.1 Sv the central estimates ranged from 3.7 to 5.4% Sv(-1) for solid cancers and from 0.4 to 0.6% Sv(-1) for leukemia. Analyses using regression calibration techniques yield central estimates of risk very similar to those for the Bayesian approach. The central estimates of population risk were similar for the generalized absolute risk model and the relative risk model. Linear-quadratic-exponential models predict lower risks (at least at low test doses) and appear to fit as well, although for other (theoretical) reasons we favor the simpler linear-quadratic models.

Second cancers after fractionated radiotherapy: stochastic population dynamics effects

When ionizing radiation is used in cancer therapy it can induce second cancers in nearby organs. Mainly due to longer patient survival times, these second cancers have become of increasing concern. Estimating the risk of solid second cancers involves modeling: because of long latency times, available data is usually for older, obsolescent treatment regimens. Moreover, modeling second cancers gives unique insights into human carcinogenesis, since the therapy involves administering well-characterized doses of a well-studied carcinogen, followed by long-term monitoring. In addition to putative radiation initiation that produces pre-malignant cells, inactivation (i.e. cell killing), and subsequent cell repopulation by proliferation, can be important at the doses relevant to second cancer situations. A recent initiation/inactivation/proliferation (IIP) model characterized quantitatively the observed occurrence of second breast and lung cancers, using a deterministic cell population dynamics approach. To analyze if radiation-initiated pre-malignant clones become extinct before full repopulation can occur, we here give a stochastic version of this IIP model. Combining Monte-Carlo simulations with standard solutions for time-inhomogeneous birth-death equations, we show that repeated cycles of inactivation and repopulation, as occur during fractionated radiation therapy, can lead to distributions of pre-malignant cells per patient with variance>>mean, even when pre-malignant clones are Poisson-distributed. Thus fewer patients would be affected, but with a higher probability, than a deterministic model, tracking average pre-malignant cell numbers, would predict. Our results are applied to data on breast cancers after radiotherapy for Hodgkin disease. The stochastic IIP analysis, unlike the deterministic one, indicates: (a) initiated, pre-malignant cells can have a growth advantage during repopulation, not just during the longer tumor latency period that follows; (b) weekend treatment gaps during radiotherapy, apart from decreasing the probability of eradicating the primary cancer, substantially increase the risk of later second cancers.

Incorporation of inter-individual heterogeneity into the multistage carcinogenesis model: approach to the analysis of cancer incidence data

We investigate a multistage carcinogenesis frailty model to incorporate inter-individual heterogeneity into carcinogenic response. Attention is focused on inference concerning the effects of different sources of population heterogeneity on cancer rates. The authors consider unobserved variability arising from either carcinogen exposure or background characteristics. Gamma and Inverse-Gaussian distributions are selected for frailty models, and the baseline hazard function is the generalized Armitage-Doll model (i.e. non-frailty model) in which exposure effects shift the age scale instead of acting multiplicatively on cancer rates. For illustration, we apply the method to solid cancer data from a cohort of atomic bomb survivors to examine some features of proposed models. The results show that the Gamma frailty model for the heterogeneity of baseline rates provides the best goodness-of-fit of the model and a non-zero frailty variance. Parameter estimates are, for the most part, comparable between the Gamma and Inverse-Gaussian frailty models. In a heterogeneous population the exposure effects on young adulthood cancer rates might be underestimated for the non-frailty model. Meaningful information regarding each source of heterogeneity has been provided by the proposed method. Therefore, the multistage carcinogenesis frailty model approach is useful for analyses of epidemiological cancer data to assess population heterogeneity and heterogeneity-influenced exposure effects.

Radiation-induced leukemia at doses relevant to radiation therapy: modeling mechanisms and estimating risks

BACKGROUND

Because many cancer patients are diagnosed earlier and live longer than in the past, second cancers induced by radiation therapy have become a clinically significant issue. An earlier biologically based model that was designed to estimate risks of high-dose radiation-induced solid cancers included initiation of stem cells to a premalignant state, inactivation of stem cells at high radiation doses, and proliferation of stem cells during cellular repopulation after inactivation. This earlier model predicted the risks of solid tumors induced by radiation therapy but overestimated the corresponding leukemia risks.

METHODS

To extend the model to radiation-induced leukemias, we analyzed--in addition to cellular initiation, inactivation, and proliferation--a repopulation mechanism specific to the hematopoietic system: long-range migration through the blood stream of hematopoietic stem cells (HSCs) from distant locations. Parameters for the model were derived from HSC biologic data in the literature and from leukemia risks among atomic bomb survivors who were subjected to much lower radiation doses.

RESULTS

Proliferating HSCs that migrate from sites distant from the high-dose region include few preleukemic HSCs, thus decreasing the high-dose leukemia risk. The extended model for leukemia provides risk estimates that are consistent with epidemiologic data for leukemia risk associated with radiation therapy over a wide dose range. For example, when applied to an earlier case-control study of 110,000 women undergoing radiotherapy for uterine cancer, the model predicted an excess relative risk (ERR) of 1.9 for leukemia among women who received a large inhomogeneous fractionated external beam dose to the bone marrow (mean = 14.9 Gy), consistent with the measured ERR (2.0, 95% confidence interval [CI] = 0.2 to 6.4; from 3.6 cases expected and 11 cases observed). As a corresponding example for brachytherapy, the predicted ERR of 0.80 among women who received an inhomogeneous low-dose-rate dose to the bone marrow (mean = 2.5 Gy) was consistent with the measured ERR (0.62, 95% CI = -0.2 to 1.9).

CONCLUSIONS

An extended, biologically based model for leukemia that includes HSC initiation, inactivation, proliferation, and, uniquely for leukemia, long-range HSC migration predicts, with reasonable accuracy, risks for radiation-induced leukemia associated with exposure to therapeutic doses of radiation.

Solid tumor risks after high doses of ionizing radiation

There is increasing concern regarding radiation-related second-cancer risks in long-term radiotherapy survivors and a corresponding need to be able to predict cancer risks at high radiation doses. Although cancer risks at moderately low radiation doses are reasonably understood from atomic bomb survivor studies, there is much more uncertainty at the high doses used in radiotherapy. It has generally been assumed that cancer induction decreases rapidly at high doses due to cell killing. However, recent studies of radiation-induced second cancers in the lung and breast, covering a very wide range of doses, contradict this assumption. A likely resolution of this disagreement comes from considering cellular repopulation during and after radiation exposure. Such repopulation tends to counteract cell killing and accounts for the large discrepancies between the current standard model for cancer induction at high doses and recent second-cancer data. We describe and apply a biologically based minimally parameterized model of dose-dependent cancer risks, incorporating carcinogenic effects, cell killing, and, additionally, proliferation/repopulation effects. Including stem-cell repopulation leads to risk estimates consistent with high-dose second-cancer data. A simplified version of the model provides a practical and parameter-free approach to predicting high-dose cancer risks, based only on data for atomic bomb survivors (who were exposed to lower total doses) and the demographic variables of the population of interest. Incorporating repopulation effects provides both a mechanistic understanding of cancer risks at high doses and a practical methodology for predicting cancer risks in organs exposed to high radiation doses, such as during radiotherapy.