Impact of parental relationships in maximum lod score affected sib-pair method

Many studies are done in small isolated populations and populations where marriages between relatives are encouraged. In this paper, we point out some problems with applying the maximum lod score (MLS) method (Risch, [1990] Am. J. Hum. Genet. 46:242-253) in these populations where relationships exist between the two parents of the affected sib-pairs. Characterizing the parental relationships by the kinship coefficient between the parents (f), the maternal inbreeding coefficient (alpha(m), and the paternal inbreeding coefficient (alpha(p)), we explored the relationship between the identity by descent (IBD) vector expected under the null hypothesis of no linkage and these quantities. We find that the expected IBD vector is no longer (0.25, 0.5, 0.25) when f, alpha(m), and alpha(p) differ from zero. In addition, the expected IBD vector does not always follow the triangle constraints recommended by Holmans ([1993] Am. J. Hum. Genet. 52:362-374). So the classically used MLS statistic needs to be adapted to the presence of parental relationships. We modified the software GENEHUNTER (Kruglyak et al. [1996] Am. J. Hum. Genet. 58: 1347-1363) to do so. Indeed, the current version of the software does not compute the likelihood properly under the null hypothesis. We studied the adapted statistic by simulating data on three different family structures: (1) parents are double first cousins (f=0.125, alpha(m)=alpha(p)=0), (2) each parent is the offspring of first cousins (f=0, alpha(m)=alpha(p)=0.0625), and (3) parents are related as in the pedigree from Goddard et al. ([1996] Am. J. Hum. Genet. 58:1286-1302) (f=0.109, alpha(m)=alpha(p)=0.0625). The appropriate threshold needs to be derived for each case in order to get the correct type I error. And using the classical statistic in the presence of both parental kinship and parental inbreeding almost always leads to false conclusions.