Excess relative risk model

Whatever mathematical model is assumed for the dose-incidence relationship, it is noteworthy that susceptibility can vary markedly with age, so that the radiation-induced cancer excess at various times after irradiation may more nearly approximate a constant percentage of the natural age-specific incidence than a constant number of additional cases, depending on the neoplasm in question. For some individual neoplasms, but not the leukemias, the data do in fact suggest that the "relative risk model is more appropriate than the absolute risk model (see Section 6.1.7). For all neoplasms combined, also, the excess of radiation-induced cases at different times after irradiation approximates more nearly a constant percentage of the age-specific incidence. 

Two types of models are often used for conducting statistical analysis of cancer risks (1) absolute-risk models and (2) relative-risk models. With absolute-risk models, the excess risk due to exposure to radiation does not depend on the normal risk that would arise when there is no radiation exposure. With relative-risk models, the relative risk is a multiple of the normal risk. Unlike absolute risk, which is measured on a scale that starts at 0 and goes to 1, relative risk values begin at 1 and go to infinity (i.e., very large numbers). A value of 1 for the relative risk means that there is no excess risk. 

Analyses of radio-epidemiological data, e.g., the A-bomb survivors data, can be based on the assumption of an excess relative risk (ERR) model or an excess absolute risk (EAR) model. The ERR model assumes that the excess risk is proportional to the baseline (or spontaneous) risk, the cancer risk for a person to be diseased with a specific cancer in the absence of radiation. The EAR model expresses the risk as difference in the total risk and the basehne risk. The choice whether the ERR or the EAR model is taken to estimate radiation risks can be a crucial point due to the fact that risk estimates based on an ERR or an EAR model can vary considerably when individual tumor sites are considered. This issue is also called transport (or transfer) of risks from the exposed population to the target population (e.g., from a Japanese to a European population) and corresponds to the question whether the ERR or the EAR is taken to be the same in the exposed population and in the reference population (see below). Section 3.3 elaborates on the issue of radiation risk transfer, and Fig. 7.3 gives an illustration. 

Fig. 7.3. Transfer of risk in a population with low to a population with high cancer rates leftpanel) and transfer of risk in a population with high to a population with low cancer rates right panel). The broken lines in the upper panels are the increased cancer rates representing a relative excess of 50%. The transfer of the excess relative rate of 0.5 ( multiplicative model ) to a population with diverging cancer rates solid lines below) results in the dotted lines in the lower panels. A transfer of the excess absolute rate ( additive model ), Le., the difference between the solid and the broken lines in the upper panelsy results in the dashed lines in lower panels...

Selecting a model to define the POD involves several factors, most importantly the nature of the available data, the desired risk metric, and the size and statistical power of the study. Depending on whether the data is quantal (based on incidence data) or continuous (based on a continuous biological parameter), as well the nature or severity of the adverse outcome, different modeling decisions may be appropriate. For quantal data, excess risk is usually examined, while for continuous data, several other metrics may be more useful (e.g., metrics that measure relative and absolute differences in mean responses, changes in mean relative to the standard deviation of controls, changes above specified value, etc.). Using information on cancer... 

---