ANNEX B
UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER
I. INTRODUCTION
1. Cancer risks* of exposure to ionizing radiation are much better known than those of most other carcinogens. The Committee has previously summarized the results of numerous epidemiological studies of populations exposed to moderate to high doses of radiation exposure [U11, U12]. However, as discussed in annex A, at lower doses (generally below an absorbed dose* of about 100 mGy from low-LET* radiation), the uncertainties* associated with epidemiological studies become increasingly large and tend to mask any possible effect. The estimation of risk from such exposures requires judgements against a backdrop of different sources of uncertainty and ongoing scientific debate. The uncertainties involved in these judgements and hence the estimation of risk need to be properly addressed and communicated in order to improve understanding by decision-makers and others.
2. In order to support its findings and provide a more rational basis for discussions of the risk from radiation exposure, the Committee has prepared this scientific annex on the uncertainties in estimates of risk following exposure to ionizing radiation. Many epidemiological studies of the health effects* of radiation exposure derive risk estimates with confidence intervals* that express only the impact of statistical fluctuations of the data in the frame of the risk model* chosen. Other specific sources of uncertainty, such as those due to incomplete knowledge of exposures, or factors and mechanisms influencing the development of the disease, must also be addressed in order to more realistically describe the current state of knowledge. A main purpose of this annex then is to describe the current state of knowledge on (a) the various factors influencing estimates of risk from radiation exposure; and (b). the methodologies to integrate information on different sources of uncertainties so as to describe uncertainties on estimates of risk from radiation exposure more comprehensively than have previous reports of the Committee.
3. This scientific annex includes: (a) an evaluation of current knowledge on the impact of various sources of uncertainty on estimates of risk from radiation exposure and how they may be treated; (b). a comparison of frequentistic and Bayesian interpretations of uncertainty and probability for deriving information from new data; (c) a discussion of uncertainties in transferring risk estimates derived from a study to another population or a situation of interest; and (d) three examples of evaluations of cancer risk to demonstrate the structure and analysis of uncertainty. The main text of the annex is supported by four detailed technical appendices that provide more extensive discussion. A glossary supports the interpretation of terms for both this annex and annex A.
4. Uncertainty analyses in the field of risk estimation for radiation exposure have up to now focussed mainly on the risk of cancer. Consequently, much of the material summarized in this annex relates to radiation-induced cancer. The methods outlined, however, are equally well applicable to the analysis of other radiation-induced health effects.
5. The estimation of risks to human health from exposure to ionizing radiation is mainly based on epidemiological studies either of large exposed populations (cohort studies) or of the exposure distribution of persons with and without the disease of interest (caseâcontrol studies). There are also many radiobiological studies, including animal experiments, related to the effects of exposure to ionizing radiation [U11, U12]. These studies provide some insight into the mechanisms and processes that are involved in carcinogenesis after exposure to ionizing radiation. However, the studies cannot yet be used to improve quantitative estimation of the risks for humans of radiation exposure.
6. Risk estimates are derived generally for a group of people, defined by sex, birth year, ethnicity, occupation, smoking behaviour or other characteristics, and to specified exposure conditions. However, whether or not an individual will be affected depends on further, unknown factors, such as genetic or familial predisposition, pre-existing illnesses or pre-cancerous lesions, repair capacity, or immunological characteristics. At present, the possibilities for determining individual sensitivity are still limited and there is insufficient understanding of its interaction* with radiation exposure. Therefore this report does not treat the assessment of individual sensitivity to radiation exposure.
II. FUNDAMENTAL CONCEPTS
7. This chapter recapitulates some fundamental statistical concepts, including types of error* and uncertainty, and statistical inference,* as well as key concepts and terminology of epidemiology. Appendix A provides more detailed explanatory material on these concepts and on methods for quantifying and analysing uncertainties.
A. Statistical concepts of uncertainty
8. The difference between an estimate of a quantity of interest* (e.g. a dose or the excess relative risk* per unit dose in some exposed population) and the true but unknown value of that quantity is called the âerrorâ, which itself cannot be observed or quantified. âUncertaintyâ refers to the probability distribution of the possible errors and âuncertainty analysisâ to the characterization of the error distribution taking account of all known sources of uncertainty.
9. Uncertainty in estimation of cancer risk from radiation exposure comes from several sources, including the inherently random nature of processes that lead to cancer, limitations in data, and the use of idealized models to describe the nature of the risks in both an exposed and a non-exposed population.
10. Uncertainties are composed of mixtures of systematic and random errors.* The nature of the different types of error contributing to the uncertainty is important. Errors that are statistically independent between individuals are called âunshared errorsâ,* while correlated ones are called âshared errorsâ.*
11. There are two types of unshared errors:
(a). âMeasurement errorâ* is independent of the true value, and typically arises when using an imprecise (but unbiased) measuring device. The main determinants of the measurement error are characteristics of the measurement device, the study protocol and skill of the measuring personnel. In the case of measurement error, the variance of the observed values* exceeds that of the true values by the variance of the measurement error. It is known that the regression coefficients in a doseâresponse analysis will be biased towards zero depending on the importance of measurement errors in the dose estimates. Measurement errors are also called âclassical errorsâ.
(b). âAssignment errorâ* arises when individuals are assigned representative values, often as a result of grouping, and is independent of the assigned value. Assignment errors describe random inter-individual variability* of true values about a single value assigned to every individual belonging to a distinct group. The variance of the assigned values will be less than that of the true variance by the variance of the individual peculiarity in the values about a given assigned value. When dose values are assigned in a doseâresponse analysis, the regression coefficients tend to be unbiased. Assignment errors are also called âBerkson errorsâ.*
12. Shared errors include shared measurement errors (such as the use of an improperly calibrated measuring device) and shared assignment errors (such as mis-specification of values for parameters used in computation of observed values). Shared errors almost inevitably lead to biased estimates of the quantity of interest, and failure to account for them can lead to overconfidence in deriving risk estimates.
13. Statistical inference is critical in characterizing and quantifying uncertainty in both estimation of risk from radiation exposure for specific studies and in projection of risk to other populations and exposure scenarios. Statistical inference is based on data (observations) and models used to analyse the data. The probability density function* for the data given a model, , its parameters, β, and the values . When viewed as a function of the parameters given the data, the model and the values of the explanatory variables, the probability density function is called the likelihood* function (L), which plays a central role in statistical inference. A hypothetical and unrealistic example would be the likelihood of a set of breast cancer incidence data being observed in a cohort of women given a model of the incidence rate* that, say, were:
I = β1 a (1 + β2 d)
Here, the age, a, and the dose, d, would be explanatory variables, and best estimates of the parameters β1 and β2 would be determined, e.g. by identifying the maximum of the likelihood function of the observed data.
14. There are two main approaches of statistical inference:
(a). âFrequentistâ inference* uses observed data and aims at establishing the probability of the truth of statements about quantities of interest given the data and the model used to analyse the data. Frequentist probability can be interpreted as the relative frequency* in a hypothetical set of realizations given the true parameter values of the assumed model;
(b). âBayesianâ inference interprets probability as a measure of the degree of belief or state of knowledge concerning the true values of the quantities of interest. With this interpretation, oneâs âpriorâ state of knowledge about the quantity of interest can be explicitly updated with new information to make Bayesian probability statements about oneâs âposteriorâ state of knowledge. From this probability density function of possibly true values, a central value (usually the arithmetic mean, median or mode) and a 90% or 95% credible interval* can be obtained. A review of the application of Bayesian methods in epidemiology can be found in [G17].
15. Although the two concepts are fundamentally different, they often lead to similar conclusions, especially when their implementation is well-informed by the scientific context or when the data are strong enough to make the choice of the prior distribution less relevant.
16. Frequentist methods for quantification and assessment of uncertainties have generally served well in the estimation of risk in specific exposed populations, such as the survivors of the atomic bombings in Japan. However, Bayesian methods become more appropriate with increasing complexity, such as when estimating uncertainties in deriving cancer-specific risks from limited data or in doses calculated using complex Monte Carlo dosimetric modelling systems. They also become more important in making informed but qualified judgements about risk estimates so that they may be applied appropriately to address important societal questions.
17. Depending on the objective of an assessment, it may be necessary to distinguish variability from uncertainty. Variability describes the variation of values between individuals, while uncertainty refers to the variation in values due to unexplained stochastic processes or the state of knowledge about imperfectly known fixed quantities.
18. The Committee recommends that uncertainty in the measurements, variables, and models used to estimate exposures, doses and risksâboth for specific individuals and for groupsâbe defined as probability density functions, representing the analystâs state of kn...