Group sampling. A cohort of 
cases is shown on the left, where the cases outlined in red—
, 
, 
, and 
—harbor an interacting pair of recessive variables. In other words, more cases carry the recessive–recessive combination than
would be expected by chance, given the marginal frequencies of each recessive allele. By repeatedly drawing random groups
of 
cases (here 
), we are guaranteed to have drawn at least one group of individuals that carries both the variables in 
attempts with probability 
. These variables (and others) are quickly determined by a bitwise-AND operation between the group of cases. Then, all pairs
of cocarried variables are enumerated and tested against the stage 1 null hypothesis (case-only analysis). Rejected combinations
are shortlisted and followed up in stage 2 (case vs. control analysis), where an interaction is identified.
