Efficient identification of identical-by-descent status in pedigrees with many untyped individuals

Motivation: Inference of identical-by-descent (IBD) probabilities is the key in family-based linkage analysis. Using high-density single nucleotide polymorphism (SNP) markers, one can almost always infer haplotype configurations of each member in a family given all individuals being typed. Consequently, the IBD status can be obtained directly from haplotype configurations. However, in reality, many family members are not typed due to practical reasons. The problem of IBD/haplotype inference is much harder when treating untyped individuals as missing. Results: We present a novel hidden Markov model (HMM) approach to infer the IBD status in a pedigree with many untyped members using high-density SNP markers. We introduce the concept of inheritance-generating function, defined for any pair of alleles in a descent graph based on a pedigree structure. We derive a recursive formula for efficient calculation of the inheritance-generating function. By aggregating all possible inheritance patterns via an explicit representation of the number and lengths of all possible paths between two alleles, the inheritance-generating function provides a convenient way to theoretically derive the transition probabilities of the HMM. We further extend the basic HMM to incorporate population linkage disequilibrium (LD). Pedigree-wise IBD sharing can be constructed based on pair-wise IBD relationships. Compared with traditional approaches for linkage analysis, our new model can efficiently infer IBD status without enumerating all possible genotypes and transmission patterns of untyped members in a family. Our approach can be reliably applied on large pedigrees with many untyped members, and the inferred IBD status can be used for non-parametric genome-wide linkage analysis.