The FAMILY Procedure
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,
![\[ b_{jv} = \left\{ \begin{array}{ll} (b_{M_ j v} + b_{F_ j v})/2 , & b_{M_ j v} \mbox{ and } b_{F_ j v} \mbox{ are nonmissing} \\ \sum _{k\in S_ j} g_{kv}/|S_ j|, & \mbox{otherwise} \end{array} \right. \]](images/geneug_family0073.png){kind=small}
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.