Efficient methods for computing linkage likelihoods of recessive diseases in inbred pedigrees

Traditional methods for computing linkage likelihoods can be infeasible for data that involve considerable inbreeding and missing information, characteristics of large pedigrees affected by rare recessive diseases. For this type of data, we propose alternative procedures that can efficiently provide good approximates of linkage likelihoods. These approximation procedures are constructed based on a new mathematical representation of the multiloci inheritance model. Instead of representing each person by a single variable, the genotype, the disease gene alleles, and the marker alleles are taken as separate variables. This allows us to break down the computations into manageable pieces. This new representation is also potentially useful for multipoint mapping.