More on Bithell's test

At the heart of the method is the concept of Relative Risk (RR). If you are twice as likely as I am to get a disease, then your relative risk is 2, using mine as a reference. My RR would be .5 using yours as a reference. There is always some referent group in the background. Imagine, therefore, that we take a national average as a background RR for a test.

Bithell's test requires an understanding of the relative risk as a function of space. Suppose that the only cause of a cancer were factor X, and exposure to factor X were a function of distance. Then, given the distribution of factor X, we could create an exposure function, through which people would pass as they live their lives, accumulating exposure.

In the immediate vicinity of a heap of factor X, the exposure would be (locally) some decreasing function of distance from the heap. The RR would peak at the focus (as a result of increased exposure).

Bithell's test requires that we construct a relative risk function (a function of distance from the focus), and we then compare known rates for the subregions around the focus with the expected rates given the disease background, to check whether our model of relative risk is reasonable. It could fail to be reasonable for a variety of reasons:

Locations (e.g. home addresses) might not reflect actual exposure, as individuals do not stay at home.
If the latency period of a disease is long, and a neighborhood in the vicinity of a heap of factor X is recent, then the disease rates will not yet have caught up to the population.
The model form may be inappropriate (i.e. the functional form assumed for the RR is incorrect).

Website maintained by Andy Long. Comments appreciated.

longa@nku.edu