Analysis of complex human genetic traits: an ordered-notation method and new tests for mode of inheritance

A novel ordered notation is introduced that allows description and calculation of the probability of any nuclear-pedigree configuration of disease status and marker-allele information. Algorithms are given that allow for complex models of disease predisposition, a highly polymorphic or less polymorphic marker locus, gametic disequilibrium between the marker and disease loci (marker association with disease), recombination between the marker and disease loci, and different ascertainment schemes. The theoretical foundation is presented for a series of new tests to identify modes of inheritance and genetic heterogeneity. These use marker-locus data in nuclear families from four ascertainment schemes: simplex (S), multiplex parent-child (MPC), multiplex sibs (MS), and multiplex parent-sibs (MPS). The tests are (1) extension of the antigen-geno-type-frequencies-among-patients method to MPC, MS, and MPS pedigrees; (2) determination of the expected rates of transmission, or not, of marker alleles from parents to an affected child, for all pedigree types; (3) determination of expected identity by descent (IBD) values for affected sib pairs when a parent is affected (MPS pedigrees); and (4) determination of the expected marker-allele frequencies in affected-sib-pair IBD categories (MS and MPS pedigrees). A sampling strategy that includes the four pedigree types S, MPC, MS, and MPS is recommended for complex diseases once linkage and/or association of a marker with disease has been established. The full array of new and old tests that can be applied to these pedigrees provides a complementary suite of methods that can facilitate the mapping and characterization of complex human genetic traits.