The Euclidean distance between individuals in the eigenmap are representative of their ancestral differences. Either the fullmatch or the pairmatch algorithm [31] can be used to find genetically homogeneous strata. For the case–control design, the fullmatch algorithm minimizes distances between individuals within strata with the constraint that each stratum consists of either a single case matched to one or more controls, or a single control matched to one or more cases within. Alternatively, the pairmatch algorithm minimizes the distances between cases and controls in strata with the constraint that each case is matched with a single control. The contribution to the likelihood for the kth matched stratum, including 1 case (i =0) and m controls (i =1, ...,m), follows the conditional logistic form, ex0β∕∑i=0mexiβ.
