When conducting genetic studies for complex traits, large samples are commonly required to detect any of the number of genes with relatively low effect thought to underly such traits. This is because, in contrast to monogenic diseases, complex traits typically result from a number of different genetic pathways (genetic heterogeneity) and any sample is likely to contain a considerable fraction of sporadic cases (phenocopies). Such samples are time-consuming and costly to recruit and analyse. Methods which might be used to decrease sample size include attempting to select families, with the aim of reducing genetic heterogeneity or phenocopy rate within the sample. Selecting cases with positive family history of disease should reduce the phenocopy rate, and this strategy has been employed in linkage studies of complex disease, although evaluations of such a strategy have been equivocal.
This paper shows how identity by descent (IBD) distributions may be calculated for affected relative pairs recruited conditional on the affection status of a third relative. These distributions are then used to calculate expected power in affected sib and half-sib linkage studies when recruitment is conditional on family history of disease. We consider the proxy conditions of recruitment conditional on disease in an affected parent or third sibling with single-locus and additive multilocus genetic models. We show that while such selection strategies can reduce power if disease risk alleles are common and environmental heterogeneity low, under models more likely to underly common complex diseases power will generally be increased, and that this effect is greater as more loci are involved. Though the proxy cases studied are more extreme than a general strategy of asking potential recruits whether they have any family history of disease, these results suggest that conditional recruitment is more generally useful than previous studies have suggested.