Bithell's method hinges on Relative Risk and how it changes over distance from a focus. The Relative Risk Function (RRF) describes this change in mathematical terms.
In the null hypothesis for Bithell's method, relative risk is the same regardless of location and equal to 1. In the alternative spatial model, risk depends on distance from the case location to the focus (d), the rate of decay of cases with distance from the source (phi or 
) and the ratio of risk at the focus over that infinitely far from the focus ( the parameter 1 + 
(beta)). It can be represented by a number of different models. The models available in ClusterSeer are similar to those described in Bithell (1995), with the difference that the scale parameter is not included.
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Model 1:
This model has a serious potential problem: it is infinite at the origin (the focus). This model is appropriate if disease risk increases towards certainty towards the focus. Thus, the figure displays the inverse of the additive model: as this surface tends towards zero at the center, the RR is tending towards infinity. |
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Model 2: This model comes to a sharp point at the origin (focus): risk increases more rapidly the closer the subject is to the focus.
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Much smoother than the other similar models, 2 and 4. |
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Very similar to Model 2. |
Model 3:
Model 4: