Genome Scanning by Composite Likelihood Prof. Andrew Collins

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1 Andrew Collins and Newton Morton University of Southampton Frequency by effect Frequency Effect 2 Classes of causal alleles Allelic Usual Penetrance Linkage Association class frequency analysis Maj or gene Rare High Oligogene Common Low + ++ Polygene Common Very low Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 1

2 Fifty years of genetic epidemiology Double helix First steps Segregation and linkage Major loci, cytogenetics DNA markers Where are the causal genes? Complex inheritance Human genome Genome analyses, association mapping 4 Occurs during meiosis Recombination Essential for chromosome segregation Breaks haplotypes: increases haplotype diversity Breakage -> mapping disease-related loci Recombination not random hot-spots Recombination frequencies from linkage in families (polymorphic markers) Linkage map -> recombination structure 5 Linkage mapping of disease genes M D M D M D 6 Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 2

3 Linkage disequilibrium LD - linked alleles inherited together more often than expected under random segregation Reflects inheritance of ancestral haplotypes (chromosome segments) transmitted un-recombined across many generations Disease polymorphism located using LD (association) between marker allele and disease status (-> case-control study) 7 Mapping disease genes by linkage disequilibrium M D After n generations D M D M M D D M D M D D 8 Not all allelic association is due to LD Direct causation: having allele M causes disease D Natural selection: having allele M is protective if you have disease D Population stratification - population subgroups with M and D more frequent in one subgroup Statistical artifact inadequate correction for number of tests Linkage disequilibrium - close linkage produces association with M if D chromosomes descended from a few ancestral chromosomes 9 Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 3

4 Single nucleotide polymorphisms (SNPs) Single-base changes usually two allelic forms Very abundant in the genome (~15 million) A tiny proportion influence disease directly but most are markers for association with disease Ideal for automated chip genotyping technologies 500,000 SNP chips becoming cost effective 10 Association between pairs of SNPs SNP Marker Causal SNP B R b 1-R Total A Q Observed Expected AB n11 p 11 = QR + D Ab n12 p 12 = Q(1-R) - D Q a 1-Q Observed Expected ab n21 p 21 = R(1-Q) - D ab n22 p 22 = (1-R)(1-Q) + D 1-Q Total R 1-R 1 11 Association (ρ) Covariance D between pairs SNPs efficiently estimated for haplotypes and diplotypes Hill (1974 heredity, 33, )-> obtain D iteratively (EM) 3 x 3 genotype table reduces to haplotype frequencies: π11 π12 π21 π22 Allele frequencies: Q = π11 + π12 R = π11 + π21 ρ requires Q < R, Q<1-R, π11 π22 > π12 π21 D = π11 π22 π12 π21 ρ = D / Q (1- R) 12 Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 4

5 Linkage disequilibrium (LD) by distance The Malecot model ρ = (1 - L) Me -εd + L 13 Linkage disequilibrium unit (LDU) maps and the LDMAP program What is an LD map? A map expressed in LD units (LDU) with additive distances discriminating blocks of conserved LD with distances and locations analogous to genetic linkage maps A linkage disequilibrium map is needed to: Facilitate gene mapping by association Enhance the resolution of the linkage map Compare populations Detect selective sweeps and other evolutionary events 15 Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 5

6 Constructing linkage disequilibrium maps Linkage disequilibrium unit (LDU) SNP 2 ρ = (1 L) Me -εd + L SNP 3 SNP 4 SNP 5 Recombination hotspot SNP Physical Dist. (Kb) ρ ρ ρ ρ LDU Map SNP LDU = SNP 2, 3 SNP 4, 5 LDU = 0.5 LDU = 0.0 LDU = 0.0 LDU = ε X d Kb Kb Kb Kb 16 The graph of LD map, 216-Kb segment of class II region of MHC? Recombination hot spots from Jeffreys et al. (2001): 216-Kb 17 LD maps for isolated populations 11 population isolates + 1 outbred sample of Caucasians 200 unrelated individuals each Chromosome 22, ~ 2486 SNPs, ~ 13.8 Kb marker spacing Only 3.5% of gaps > 50 Kb Large sample, many populations, very uniform comparisons Service et al., Nat Genet 38, 2006, Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 6

7 Demographic history of population isolates Population Years since founding Founding group Pop. size Antioquia, Colombia (ANT) s 1000 s 4 million Ashkenazi (ASH) s 10.5 million Azores (AZO) 650 large 250,000 Costa Rican Central Valley (CR) million SW Netherlands (ERF) <400 <400 20,000 Early Settlement Fin (FIC) s 1000 s 130,000 Late Settlement Fin Kuusamo (FIK) ,000 Finland Nationwide (FIP) s 1000 s 5.2 million Newfoundland (NFL) 400 6,000 10, ,000 Afrikaner (SAF) million Sardinia (SAR) > , Isolates LD pattern conserved across populations Differences in extent of LD (20-45% shorter map for isolates compared to CAU) Kuusamo recent founding, famine bottleneck, few founders far more extensive LD Extensive LD: recently founded (CR, ANT); older but recent bottleneck (ASH, early settlement Finland) followed by rapid expansion Some isolates look like general populations (AZO, NFL): many founders, limited expansion (persons separated by more meiotic steps) Afrikaner population is a puzzle (less LD than expected) 21 Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 7

8 Haplotype Map (HapMap) Project $100 million public-priv ate effort Objectiv e: To develop a genome-wide haplotype map for identifying haplotype blocks and the common haplotypes in Yoruban, CEPH, Japanese and Chinese samples ->millions of genotypes in two phases from the four populations 22 and genome-wide LD maps Caucasian (CEU), Chinese (CHB), Japanese (JPT), Yoruban (YRI) Phase I Phase II Number of SNPs 0.67~0.78 million 1.88~2.34 million SNP density 1 SNP per 3.75 ~4.40 Kb 1 SNP per 1.26~1.56 Kb Intervals 74% intervals <5 Kb 91% intervals <8 Kb 81% intervals <2 Kb 93% intervals <4 Kb Build 34 July 03 Build 35 May Phase I and phase II maps Linkage Disequilibrium Units (LDUs) CEU population Physical distance (Kb) 24 Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 8

9 HapMap chromosome 19 LD and linkage maps 25 Phase II data for chromosome 22 Linkage Disequilibrium Units (LDUs) Kilo bases 26 Relationship between LDU (phase II) and linkage map 27 Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 9

10 Association mapping by linkage disequilibrium and the CHROMSCAN program 28 HFE region of chromosome 6 29 Association mapping (CHROMSCAN) z = (ad-bc)/(a+b)(b+d) for SNP allele count x affection Z = (1-L)Me -ε (Sk-S) + L Model A (M = 0, L = Lp), model D (M, S, L estimated) compute difference (X) in Λ = ΣK z (z Z) 2 for models A and D Compute error variance (V) free of autocorrelation: ij denotes replicates (i) in region (j) Replicates (H 0):(-> rank of X) P ij X ij /χ 2 ij V ij For H 1 V j and hence P j estimated from replicates, location standard error (SE) from the information (K) about S 30 Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 10

11 Composite likelihood and meta-analysis Disadvantage: Autocorrelation requires simulation by shuffling to obtain standard error (SE) of estimated location S Advantages: Information for meta-analysis is K = (1/SE) 2 Mean S = S ik i/ K i Does not assume causal SNP in sample Extracts appropriate LD information from regional LD map 31 LD mapping identifies 390 Kb region associated with CYP2D6 poor drug metabolizing activity CYP2D6 metabolises 20% of marketed drugs Poor metaboliser (PM) phenotype has frequency 5-10% in Caucasians Five mutations contribute to PM phenotype (> 99% of cases in Caucasians) 1018 Caucasians genotyped for 27 CYP2D6 polymorphisms, 41 individuals with predicted PM phenotype (Hosking et al., 2002, Pharmacogenomics J. 2(3): ) 32 Meng et al., (2003) Am J Hum Genet 73: Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 11

12 Comparison of kilobase and LDU maps Map Chi - square Location (Kb) Error (Kb) 95% CI Kb LDU (177) Kb (83) LDU HapMap and CYP LDU maps for the CYP2D6 region CYP HapMap Kb CYP2D6 35 Comparison of alternative LDU maps Map Scale Chisquare Location (Kb) Error (Kb) 95% CI CYP2D6 LDU (177) HapMap LDU (198) 36 Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 12

13 Localization of CYP2D6 Authors Interv al (Kb) Error (Kb) Hosking et al. 390? Morris AP (2005) 185 >30 * (Genetic Epidemiol 29(2): ) This study * Estimated from graph 37 CFH gene identified from 96 cases + 50 controls (116,204 SNPs typed) Gene located on chromosome 1 in region implicated in linkage studies Nominal p-value = CHROMSCAN analysis of chromosome 1 yields 202 regions Permutation p-value for region 154 (A-D model) = , Chi-square (3df) = 27.6 Klein et al. (2005), Complement factor H polymorphism in age-related macular degeneration; Science 308, Chromosome 1 - AMD 39 Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 13

14 mssnps Chi-squares for association between phenotype and individual SNPs commonly examined Most significant ms SNP used to guide further genotyping on more samples Potentially misleading: only small fraction of total SNPs tested, significance levels hugely distorted, information from LD structure and neighbouring SNPs ignored therefore power is low 40 mssnp Chi-squares (201 regions, chromosome 1) 6 Permutation-based (mean ~1) Uncorrected (mean ~4.7) 41 P value distribution for 201 regions on chromosome 1 (CFH data) 42 Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 14

15 Genome-wide association: conclusions Modelling association between multiple SNPs and disease maximises power (using LD map) Robustly determined p-values require permutation-based test Parallel computing analyses regions efficiently on distributed cluster (e.g., Beowulf) First stage identifies small number of regions for follow up Further sample(s) to confirm interesting regions Simple meta-analysis can be applied given locations and standard errors from independent samples/studies Ultimately functional tests are required for putatively causal variants 43 Publications Maniatis et al., 2002; The first Linkage Disequilibrium (LD) maps: PNAS, USA; 99(4): Morton, N., Maniatis, N., Zhang, W., Ennis, S., Collins, A. Genome scanning by composite likelihood; Am J Hum Genet 80 (1), 2007, Software LDMAP - LD map construction CHROMSCAN - Disease mapping by association in LD maps 44 Acknowledgements Nik Maniatis Sarah Ennis Jane Gibson Will Tapper Winston Lau Tai-Yue Kuo Weihua Zhang Josephine Hoh (Yale) GlaxoSmithKline Funding sources: NIH, BBSRC 45 Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 15

16 46 Linkage DisequilibriumThe screen versions of these slides have full details of copyright and acknowledgements 16