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 taui>0, then the probability that a parent with heterozygous genotype i/j transmits allele i is Pr(i/j-->)=tau(i)/(tau(i) + tau(j). 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 likelihood-ratio test under the constraint that one tau(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 tau(i)=exp(beta(t)x(k)), where beta is a parameter vector and xk 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.