
Poisson Models 359
status indica tors, I
i
= 1 if y
i
is a case a nd I
i
= 0 if it is a control. Then, by the principle explained in
Section 9.10.2, the disease status indicators satisfy a binary regression
log
P {I
i
= 1}
P {I
i
= 0}
= log
p
i
1 − p
i
= logr(y
i
,θ).
If the risk function r(u , θ) is loglinear in θ, the relationship is a logistic regression. This is a
well-known principle in epidemiology. Digg le and Rowlingson [236] argue the advantages of this
approa c h in a spatial context, which include not having to estimate th e population density.
For the Chorley-Ribble dataset we can carry out such an analysis as fo llows:
> X <- split(chorley)$larynx
> D <- split ...