Figure 1.

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.