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Regression Diagnostics For The Exponential Relative Risk Function For All Cancer

In previous reports and in the screening procedure used in this report the exponential relative risk function, , was used to describe the effect of cumulative radiation dose on cancer risk. One way to check this is to plot estimates of the relative risk versus the average dose in each of the dose categories (e.g. see Figure 2A). Another approach is to use regression diagnostic techniques that describe the influence of individual data points on parameter estimates [5,1]. The diagonal term from the hat matrix provides a measure of the influence of each cell in the ADS. The left hand panel of Fig. AII ( see below ) shows the values ---scaled so that average(h) = 2--- plotted against the dose value for each of 4160 cells that were used in the example. This plot indicates that there are a small number of cells with high relative influence in the highest dose group. To directly evaluate the influence of each cell in the ADS on the dose response coefficient , Eq. 3 was fit to each table obtained by deleting the cell to obtain . The relative percent change (RCB) due to the cell is then

The right hand panel of Fig. AII ( see below ) shows the RCB values plotted versus dose for this example. This plot shows that there are a small number of cells with high leverage values for the linear exponential dose-response coefficient. This suggests that this dose-response relation may not be appropriate for these data. In the Results Section we provide a more detailed evaluation of alternative dose-response functions, and visual summaries which further demonstrate this point.


Fig. AII