ject forward in time and calculates the risk of developing a radiation-induced cancer at each age subsequent to age at exposure. This requires probabilities of survival to each subsequent age, which are obtained from life tables for the population of interest. ERR models are expressed in terms of a relative increase in the sex- and age-specific background rates for the cancer of interest; these rates are usually obtained from cancer mortality vital statistics for the population of interest (or incidence rates if cancer incidence is to be estimated).

An important issue in estimating lifetime risks is the extrapolation of risks beyond the period for which follow-up data are available. No population has been followed for more than 40 or 50 years; thus, it is not possible to model the EAR or ERR directly for the period after follow-up has ended, a limitation that is primarily important for those exposed early in life. Estimating lifetime risks for this group thus requires assumptions that are usually based on the observed pattern of risk over the period for which data are available. For example, if the ERR appears to be a constant function of time since exposure, it may be reasonable to assume that it remains constant. Alternatively, if the EAR or ERR has declined to nearly zero by the end of the follow-up period, it may be reasonable to assume that the risk remains at zero.

Another important issue is how to apply risks estimated from studying a particular exposed population to another population that may have different characteristics and different background risks. Specifically, the application of estimates based on Japanese atomic bomb survivors to a U.S. population is a concern, since background rates for some specific cancers (including stomach, colon, liver, lung, and breast) differ substantially between the two populations. The BEIR V (NRC 1990) committee calculations were based on the assumption that relative risks (ERR) were comparable for different populations; however, the BEIR III (NRC 1980) committee modified its ERR models based on the assumption that absolute risks were comparable. Some recent efforts have used intermediate approaches with allowance for considerable uncertainty (NIH 1985, 2003).

Estimating Probabilities of Causation

The probability of causation (PC; NIH 1985, 2003) is defined as the ratio of ERR to RR:

where for brevity the dependence of ERR on dose, time variables, and possibly other individual characteristics is suppressed. For the RR models described previously, ERR = fg, where f = f(d) and g = g(a, e, s), in which case

Thus, the ERR model provides immediate PC estimates.

Modeling Caveats

The theory of risk assessment, modeling, and estimation and the computational software for deriving statistically sound parameter estimates from data provide a powerful set of tools for calculating risk estimates. Risk models provide the general form of the dependence of risk on dose and risk-modifying factors. Specific risk estimates are obtained by fitting the models (estimating unknown parameters) to data. The role of data in the process of risk estimation cannot be overemphasized. Neither theory, models, nor model-fitting software can overcome limitations in the data from which risk estimates are derived. In human epidemiologic studies of radiation, both the quality and the quantity of the data available for risk modeling are limiting factors in the estimation of human cancer risks. The quality of data, or lack thereof, and its impact on risk modeling are discussed below under three broad headings. The primary consequence of less-than-ideal data is uncertainty in estimates derived from such data.

Incomplete Covariate Information

The specificity of risk models is limited by the information available in the data. Even the most extensive data sets contain, in addition to measurements of exposure, information on only a handful of predictor variables such as dose, age, age at exposure, and sex. Consequently, models fit to such data predict the same risk of cancer for individuals having the same values of these predictor variables, regardless of other differences between the two individuals. For example, two individuals who differ with respect to overall health status, family history of cancer (genetic disposition to cancer), exposure to other carcinogens, and so on, will be assigned the same estimated risk provided they were exposed to the same dose of radiation, are of the same age, and have the same age at exposure and the same gender.

Consequently, among a group of individuals having the same values of the predictor variables in the model, some will have a higher personal risk than that predicted by the model and some will have a lower personal risk. However, on average, the group risk will be predicted reasonably well by the model. The situation is similar to the assessment of insurance risk. Not all teenage males have the same personal risk of having an automobile accident (some are better drivers than others), yet as a group they are recognized as having a greater-than-average risk of accidents, and premiums are set accordingly. From the insurance company’s perspective, the premiums are set fairly in the sense that their risk models adequately predict the claims experience of the group.

Radiation risk models are similar in that they adequately predict the disease experience of a group of individuals sharing common values of predictor variables in the model. However, such estimated risks need not be representative of individual personal risks.

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