Quantifying disease genotype enrichment under multiple causative loci
F. Takeuchi, R. McGinnis
Wellcome Trust Sanger Institute, Cambridge, UK

Enrichment of disease-causing genotypes in affecteds versus
unaffecteds plays a key role in detectability of disease loci by
linkage or association. Designate a polymorphism being tested for
linkage or association as "foreground" and other disease loci as
"background". In unrelated affecteds, mean foreground genotype
frequency is unchanged by background loci but in related affecteds the
enrichment of foreground susceptibility genotypes can be attenuated by
background loci. However, understanding of this phenomenon rests on
simulated results [Howson et al. Genet Epidemiol 2005. 29:51-67].

We quantify enrichment of foreground genotypes by assigning a "risk"
to each background and foreground genotype such that the penetrance of
each multilocus genotype is determined by combining these risks either
multiplicatively or additively. For comparison purposes, we also
consider a single locus model with no background loci.

As previously shown [ibid], foreground genotype frequencies for
multiplicative models are identical to those of a corresponding single
locus model. By contrast, the frequency of disease-predisposing
foreground genotypes in additive models varies between the highly
enriched frequency of the single locus model and unenriched frequency
in the general population. For related affecteds, the degree of
enrichment in this range is the ratio of recurrence risks for the
single locus and corresponding multilocus models.

Our quantification of this phenomenon and of an analogous one
impinging on allele sharing in affected sib pairs enables better
evaluation of association and linkage studies of diseases caused by
multiple loci.