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

Abstract

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.Availability: The algorithm is implemented in Matlab and is freely available upon request.Contact: jingli@cwru.eduSupplementary information: Supplementary data are available on Bioinformatics online.

Haplotype Reconstruction in Large Pedigrees with Untyped Individuals through IBD Inference

“…This method is introduced in Li et al (2010). We briefly reiterate its essential elements here for the completeness of the article.…”

“…In the second part of this subsection, we will present an alternative backup approach for inconsistent data by utilizing posterior decoding. To construct the global IBD in a family, a simple approach is to enumerate all possible inheritance patterns and check their consistency with pairwise IBD, which was implemented in Li et al (2010). However, this algorithm is not efficient.…”

“…We have recently developed an algorithm to efficiently infer identical-by-descent (IBD) status among family members (Li et al, 2010). The approach overcomes these computational challenges by first constructing hidden Markov models (HMMs) for all relative pairs with genotypes, and then constructing the global (pedigree-wise) IBD relationship from the inferred pairwise IBD relationships from these HMMs.…”

IPED: Inheritance Path-based Pedigree Reconstruction Algorithm Using Genotype Data

“…nferring genetic relationships from genotype data is a fundamental problem in genetics and has a long history (Elston and Stewart, 1971;Lander and Green, 1987;Abecasis et al, 2002;Fishelson et al, 2005;Li et al, 2010;Sobel and Lange, 1996). Pedigree reconstruction is a hard problem and even constructing sibling relationships is known to be NP-hard (Kirkpatrick et al, 2011).…”

“…Every individual in the graph is associated with a generation g. All the extant individuals are associated with g = 1, and their direct parents are associated with generation g = 2. The height of a pedigree is the biggest g. We define an inheritance path between a child and his ancestor the same as it is defined in Li et al (2010), namely as a path between the two corresponding nodes in the pedigree graph. For example, the inheritance path between 1 and 15 consists of nodes 1-6-11-15.…”