Biostatistics-Lecture 19 Linkage Disequilibrium and SNP detection Ruibin Xi Peking University School of Mathematical Sciences

Haplotype Freqeuncies

Linkage Equilibrium

Linkage Disequilibrium

Disequilibrium Coefficient DAB

DAB is hard to interpret Sign is arbitrary … A common convention is to set A, B to be the common allele and a, b to be the rare allele Range depends on allele Frequencies Hard to compare between markers

r2 (also called Δ2) Ranges between 0 and 1 1 when the two markers provide identical information 0 when they are in perfect equilibrium

Raw r2 data from chr22

Comparing Populations CEPH: Utah residents with ancestry from northern and western Europe (CEU)

Use LD for SNP imputation and detection fastPhase

Use LD for SNP imputation and detection fastPhase

Model for haplotypes Observed n haplotypes Each with M markers bij = 0, 1 Assume each haplotye originates from one of K clusters zi: unknown cluster of origin of bi Since clusters of origin are unknown

Local clustering of haplotype Assume zi = (zi1,…, ziM) forms a Markov chain on {1,…,K} zim denote the cluster origin for bim Initial probabilities Transition probabilities Conditional on the cluster of origin Marginal

Local clustering of genotype data We have genotype data gim: genotype at marker m of individual i Take values 0, 1, 2 Initial probabilities ( unordered cluster of origins) Transition probabilities

Local clustering of genotype data Genotype probabilities conditional on cluster of origins Joint likelihood

Algorithms for genotype imputation fastPhase BEAGLE IMPUTE PLINK MaCH

Algorithms for genotype imputation fastPhase BEAGLE IMPUTE PLINK MaCH Picture taken from IMPUTE v2

SNP detection with LD information MaCH: (G: genotye, S: cluster)

SNP detection with LD information For sequencing data G is not observed Coverage of base A, B are observed, we have the HMM

SNP detection with LD information Nielsen et al. 2011 Nature Review Genetics