DETECTING LINKAGE FOR GENETICALLY HETEROGENEOUS DISEASES AND DETECTING HETEROGENEITY WITH LINKAGE DATA

  • 1 May 1986
    • journal article
    • research article
    • Vol. 38  (5) , 599-616
Abstract
Interest in searching for genetic linkage between diseases and marker loci has been greatly increased by the recent introduction of DNA polymorphisms. However, even for the most well-behaved Mendelian disorders, those with clear-cut mode of inheritance, complete penetrance, and no phenocopies, genetic heterogeneity may exist; that is, in the population there may be more than one locus that can determine the disease, and these loci may not be linked. In such cases, two questions arise: (1) What sample size is necessary to detect linkage for a genetically heterogeneous disease? (2) What sample size is necessary to detect heterogeneity given linkage between a disease and marker locus? We have answered these questions for the most important types of matings under specified conditions: linkage phase known or unknown, number of alleles involved in the cross at the marker locus, and different numbers of affected and unaffected children. In general, the presence of heterogeneity increases the recombination value at which lod scores peak, by an amount that increases with the degree of heterogeneity. There is a corresponding increase in the number of families necessary to establish linkage. For the specific case of backcrosses between disease and marker loci with two alleles, linkage can be detected at recombination fractions up to 20% with reasonable numbers of families, even if only half the families carry the disease locus linked to the marker. The task is easier if more than two informative children are available or if phase is known. For recessive diseases, highly polymorphic markers with four different alleles in the parents greatly reduce the number of families required. It is possible to detect heterogeneity by comparing the maximum likelihood value obtained as a function of both recombination and heterogeneity with the likelihood value obtained on the assumption of no heterogeneity. The numbers of families necessary to establish heterogeneity are minimal near 50% heterogeneity. For recessive diseases with phase unknown, backcrosses for the disease and marker loci do not allow separate estimation of linkage and heterogeneity and, therefore, preclude testing heterogeneity, unless the number of affected children per family is at least four, an inevitably rare situation. This impasse is overcome if phase is known (a rare event for rare recessive diseases) or if a highly polymorphic marker is available, yielding A1A2 .times. A3A4 parental genotypes. For rare dominant diseases, for which most matings are backcrosses involving only one informative parent, heterogeneity can be detected only if phase is known or if at least four children per family are available. Linkage can be tested in the presence of undetected heterogeneity, but if heterogeneity exists, the estimated recombination value for linkage will be too high.