Estimated Doses

The standard theory and methods of risk modeling and estimation are appropriate under the assumption that dose is measured accurately. Estimated radiation dose is a common characteristic of human epidemiologic data, and questions naturally arise regarding the adequacy of dose estimates for the estimation of risk parameters and the calculation of risk estimates. These are different problems and are discussed separately.

First, consider the problem of calculating risk estimates from a given risk equation. Suppose that the risk equation has been estimated without bias and with sufficient precision to justify its use in the calculation of risks. Assume also that risk increases with dose: that is, the risk equation yields higher risks for higher doses. Suppose that an estimate of lifetime risk is desired for an individual whose dose is estimated to be d. If d overestimates the individual’s true dose, the lifetime risk will be overestimated; if d underestimates the true dose, the risk will be underestimated. This is intuitive and is a consequence of the fact that risk is an increasing function of dose.

The problem of estimating risk equation parameters from data with estimated doses is a little more complicated. Errors in estimated doses can arise in a number of different ways, not all of which have the same impact on risk parameter estimation. For example, flaws in a dosimetry system have the potential to affect all (or many) dose estimates in the same manner, leading to systematic errors for which all (or many) dose estimates are too high or too low. Errors or incomplete records in data from which dose estimates are constructed (e.g., badge data from nuclear industry workers) are likely to result in more or less random errors in dose estimates (i.e., some individuals will have dose estimates that are too high and others will have estimates that are too low). Systematic errors can result in biased estimates of risk equation parameters. The type of bias depends on the nature of the systematic error. For example, risk equations derived from data with doses that are overestimated by a constant factor (>1) will result in an underestimation of risk at a particular given dose d; doses that are underestimated by a constant factor (<1) will result in an overestimation of risk. Random errors in dose estimates also have the potential to bias estimated risk equations. Random error-induced bias generally results in the underestimation of risk. That is, random errors tend to have the same qualitative effect as systematic overestimation of doses.

The estimation of risk models from atomic bomb survivors has been carried out with a statistical technique that accounts for the random uncertainties in nominal doses (Pierce and others 1990). To the extent that it is based on correct assumptions about the forms and sizes of dose uncertainties, it removes the bias due to random dose measurement errors.

Data from Select Populations

Ideally, risk models would be developed from data gathered on individuals selected at random from the population for which risk estimates are desired. For example, in estimating risks for medical workers exposed to radiation on the job, the ideal data set would consist of exposure and health information from a random sample of the population of such workers. However, data on specific populations of interest are generally not available in sufficient quantity or with exposures over a wide enough range to support meaningful statistical modeling. Radiation epidemiology is by necessity opportunistic with regard to the availability of data capable of supporting risk modeling, as indicated by the intense study of A-bomb survivors and victims of the Chernobyl accident.

A consequence of much significance and concern is the fact that risk models are often estimated using data from one population (often not even a random sample) for the purpose of estimating risks in some other population(s). Cross-population extrapolation of this type is referred to as “transporting” the model from one population to another. The potential problem it creates is the obvious one—namely, that a risk equation valid for one population need not be appropriate for another. Just as there are differences in the risk of cancer among males and females and among different age groups, there are differences in cancer risks among different populations. For example, the disparity between baseline rates for certain cancers (e.g., stomach cancer) in Japanese and U.S. populations suggests the possibility of differences in the risks due to radiation exposure.

Transporting models is generally regarded as a necessity, and much thought and effort are expended to ensure that problems of model transportation are minimized. The decision to use EAR models or ERR models is sometimes influenced by concerns of model transport. Problems of transporting models from one population to another can never be eliminated completely. However, to avoid doing so would mean that risk estimates would have to be based on data so sparse as to render estimated risks statistically unreliable.

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