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.
