Gamete-competition models

The gamete-competition model is an application of the Bradley-Terry model for ranking of sports teams. If allele i of a marker locus is assigned parameter τ(i) > 0, then the probability that a parent with heterozygous genotype i/j transmits allele i is Pr (i/j→i) = τ(i)/(τ(i) + τ(i)). Mendelian segregation corresponds to the choice τ(i) = 1 for all i. To test whether Mendelian segregation is true, one can estimate the τ(i) from pedigree data and perform a likelihood-ratio test under the constraint that one τ(i) equals 1. Although this procedure generates an interesting method for performance of segregation analysis with a marker locus, its real promise lies in generalization of the transmission/disequilibrium test. Quantitative as well as qualitative outcomes can be considered. The gamete-competition model uses full pedigree data and gives an estimate of the strength of transmission distortion to affected children for each allele. Covariates are incorporated by rewriting of τ(i) = exp (β(t)x(k)), where β is a parameter vector and x(k) is a covariate vector for the kth transmitted gamete. Examples of covariates include disease-severity indicators for the child, sex of the child, or repeat number for tandem-repeat alleles.