Abecasis, Cookson, and Cardon (2000) define a pair of orthogonal allelic transmission scores,
and
, the expected genotype and deviate, respectively, for each individual at each marker. To create these scores, the genotype in terms of allele
must first be defined as
for individual
, where
represents the number of
alleles that the genotype comprises. For any founder
, an individual whose parents are not observed, in the sample, these scores are defined as
and
. Otherwise, let
and
be the respective indices of the mother and father of individual
. Then for any nonfounder, assuming scores for an individual’s ancestors are calculated before his or her own,
where
, and then
. These scores are calculated for all alleles at the markers specified in the VAR statement and are included in the OUTQ= data set.