This paper provides an efficient algorithm to generate exact distribut
ions for the bivariate logistic model with common and sub-unit-specifi
c covariates. The algorithm can be used to analyze correlated paired b
inary response data from studies lacking a large sample size. Possible
applications include a clinical trial with two distinct binary outcom
es, a binary outcome cross-over or two-time point cohort study, and a
pair-matched prospective study with binary outcome. Analysis of data f
rom an ophthalmologic study is provided to illustrate the method. Exte
nsion to three or more correlated binary responses is also outlined.