Comparison of parametric and nonparametric methods to map oligogenes by linkage

A sample of 95 sib pairs affected with insulin-dependent diabetes and typed with their normal parents for 28 markers on chromosome 6 has been analyzed by several methods. When appropriate parameters are efficiently estimated, a parametric model is equivalent to the β model, which is superior to nonparametric alternatives both in single point tests (as found previously) and in multipoint tests. Theory is given for meta-analysis combined with allelic association, and problems that may be associated with errors of map location and/or marker typing are identified. Reducing by multipoint analysis the number of association tests in a dense map can give a 3-fold reduction in the critical lod, and therefore in the cost of positional cloning.

Trials of the beta model for complex inheritance.

Theoretical advantages of nonparametric logarithm of odds to map polygenic diseases are supported by tests of the beta model that depends on a single logistic parameter and is the only model under which paternal and maternal transmissions to sibs of specified phenotypes are independent. Although it does not precisely describe recurrence risks in monozygous twins, the beta model has greater power to detect family resemblance or linkage than the more general delta model which describes the probability of 0, 1, or 2 alleles identical by descent (ibd) with two parameters. Available data on ibd in sibs are consistent with the beta model, but not with the equally parsimonious but less powerful gamma model that assumes a fixed probability of 1/2 for 1 allele ibd. Additivity of loci on the liability scale is not disproven. A simple equivalence extends the beta model to multipoint analysis.