Mapping a disease locus by allelic association

Abstract

Allelic association provides a means to map disease genes that, in a dense map of polymorphic markers, has considerably higher resolution than linkage methods. We describe here a composite likelihood estimate of location for a disease gene against a high-resolution marker map by using allele frequencies at linked loci. Data may be family-based, as in the transmission disequilibrium test, or from a case-control study. chi2 tests, logarithm of odds, standard errors, and information weights are provided. The method is illustrated by analysis of published cystic fibrosis haplotypes, in which DeltaF508 is more accurately localized than by other association studies. This differs from current approaches by adopting a more general Malecot model for isolation by distance, where distance here is between marker and disease locus, allowance for errors in the map and model, and freedom from assumptions about demography, systematic pressures, and the ratio of physical to genetic distance. When these assumptions are introduced the number of generations since the original mutation may be estimated, but this is not required to determine location and its standard error, so that evidence from allelic association may be efficiently combined with linkage evidence to identify a region for positional cloning of a disease gene.

Figure 1

Association is described as a function of distance from disease to marker locus in megabases and parameters, with ɛ reflecting the number of generations since the original mutation, M reflecting mono- or polyphyletic origin of the mutation, and L representing bias introduced by assuming at least one associated allele per marker. Curves illustrate the decline of association with distance for a range of values of ɛ assuming M = 0.75 and L = 0.1.