Linkage studies utilizing sib pairs usually assume all of them are full sibs. Some
of these pairs, however, may be half sibs. When the true status of these pairs is
known, a combined test for accommodating half sib pairs in the extremely discordant
(ED) sib pair design is proposed. Although investigators often genotype
additional markers to identify half sibs, recent concerns with the loss of privacy
as well as identity theft suggest that many people will not be willing to have so
many loci being genotyped once they become aware of this extra genotyping. In
order to assess the potential effect of a small fraction of unknown half sib pairs
in the data on the analysis, the sensitivity of the Risch and Zhang ED statistic
is examined. It turns out that the type I error or the probability of a false positive
linkage results is roughly doubled when undetected half sib pairs form 5%
of the data. A similar analysis for extremely concordant (EC) pairs shows that
undetected half sibs reduce the power of the usual tests based on them.