Some adjustments to the fullmatch algorithm are necessary in practice. There is a computational advantage to limiting each stratum to include only one case. Specifically, for computational reasons, the conditional logit algorithm works best for 1 : m or m : 1 matching. In the general case of n : m matching the contribution of the k-th stratum to the conditional likelihood is lk(β)=∏i=1mexiβ∑j=1ck∏ij=1mexjijβ, where ck =(n+m)!/m!n!. One can see that by adding multiple cases to a stratum we are increasing the number of terms in the denominator. For instance, if m =20 and n 1, 20 terms are in the denominator, whereas at n 2 it is 190 terms, and at n =3 it is 1140 terms. By design there are multiple pseudo-controls per case. Therefore, we maintain the 1 : m structure by matching additional controls to the case, if the ancestral match is suitable. Moreover, to be useful in the association analysis, every unrelated case must be matched to an unrelated control. Thus we first match unrelated cases to one or more unrelated controls. These individuals are
