Analysis question involving logistic regression

[David Parkhurst <parkhurs@imap.iu.edu>]

A colleague has data of the following general structure:

Treatment T
Year    Site
1    T1 T2 T3 T4
2    T1 T2 T3 T4
(Same sites both years)

Control C
Year    Site
1    C1 C2 C3 C4
2    C1 C2 C3 C4
(Same sites both years)

For each site and year, n organisms are found, and k of those respond in 
a certain way. (n varies from 3--36 over the 16 site-year combinations).
We are interested in whether and how much the change in ps=k/n, the 
probability of success, from year 1 to year 2 differs between the 
treatment and control.
Question:  Is there a way to use logistic regression here that
would account for the pairing of sites across years, and would
allow for a test of whether
[ps(control,year2)/ps(control,year1)]/[ps(treatment,year2)/ps(treatment,year1)]
is detectably greater than unity?

Thanks for any advice.