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 tau(i)> 0, then the probability that a parent with heterozygous genotype i/j transmits allele i is Pr(i/j --> i) = tau(i)/(tau(i) +/- tau(i)). Mendelian segregation corresponds to the choice tau(i)= 1 for all i. To test whether Mendelian segregation is true, one can estimate the tau(i) from pedigree data and perform a likelihaodratio test under the constraint that one tau(i) equals i. 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 tan 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 tau(i) exp (beta(t)x(k)), where beta 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.