[The affected sib-set method: revision based on the mixed model using a conditional probability approach].

Abstract

One of the implicit assumptions of the single locus model, having been used so far in the analysis of linkage between the genetic marker locus and the disease predisposition locus, is the requirement of independent--from the rest of genotype--action of genotypes of the disease predisposition locus considered. In this communication, it is emphasized that the lack of this requirement makes problematical the theoretical substantiation of the affected sib-pair method in the linkage analysis. To remove this obstacle, explicit pointing out of independence of the action of the single locus genotypes on the rest of the genotype is necessary in formulating of the single locus model which, with due regard for this assumption, represents a special, perhaps, unique case of the gene action characterized by incomplete differential penetrances of the genotypes under conditions, when the genes of the rest of genotype involved to the disease, are fixed. In this connection, the mixed model of inheritance with the "major gene", proposed by Morton and MacLean (1974), is considered, on the basis of which the theoretical expectations of the proportions of the affected sib pairs, sharing the x = 2, 1, 0 haplotypes, identical by descent (IBD) in phenotypic matings with the h = 2, 1, 0 affected parents are derived. Based on the combinatorial analysis of IBD relationships in sib pairs and of the distribution of sibships of any size s greater than or equal to 2 by the numbers L = 2, 3, 4 haplotypes, inherited by s siblings, the empirical assessment of data on sibships of any size with r greater than or equal to 2 affected siblings is considered, which makes it possible to reduce the data observed on distribution of the numbers L in sibships, to that of the IBD relationships in the affected sib pairs. It is also pointed out that conditional probability approach, proposed by the author earlier, allows at the same time to obtain the empirical estimates of the recurrence risks, conditional both on phenotypes of siblings (r affected; s-r normal siblings), and on the number of L haplotypes inherited by sibships.