Genome-wide association studies (case/control and family-based) Heather J. Cordell, Institute of Genetic Medicine Newcastle University, UK

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1 Genome-wide association studies (case/control and family-based) Heather J. Cordell, Institute of Genetic Medicine Newcastle University, UK GWAS For the last 8 years, genome-wide association studies (GWAS) have been the method of choice for detection of genetic effects in complex diseases Starting to be superceded by whole-exome/whole-genome sequencing studies? Still too expensive for routine use GWAS have been enabled by advances in high-throughput genotyping technologies E.g. microarray technologies that allow us to genotype invididuals at 100s of 1000s of known polymorphic sites across the genome Scan through genome looking for genetic variants (usually SNPs) that correlate with phenotype (e.g. disease status) GWAS Mostly (not exclusively) based on a case/control design Greater sample size and thus greater power achievable However family-based collections can also be used Represent an arguably more natural data set for exploring genetic causes of disease Family data often available from previous linkage studies Potentially allows you to investigate alternative mechanisms e.g. maternal effects, imprinting

2 Case/control design Collect sample of affected individuals (cases) and unaffected individuals (controls) Or use population-based controls, assuming disease reasonably rare Examine association (correlation) between alleles present at a genetic locus and presence/absence of disease Each person can have one of 3 possible genotypes at a diallelic genetic locus 1 1, 1 2 = 2 1, 2 2 Statistical analysis Genotype Cases Controls (= a) 20 (= b) (= c) 82 (= d) (= e) 98 (= f ) Total Standard χ 2 test for independence on 2 df (tests genotype effects, allowing for dominance) Two odds ratios can be estimated OR (2 2 :1 1) = af be OR (1 2 :1 1) = cf de Odds ratios Odds of disease are defined as P(diseased)/P(not diseased) Odds ratio OR (2 2 :1 1) repesents the factor by which your odds of disease must be multiplied, if you have genotype 2 2 as opposed to 1 1 i.e. the effect of genotype 2 2 Similarly, we can define the OR for 1 2 vs1 1 As the factor by which your odds of disease must be multiplied, if you have genotype 1 2 as opposed to 1 1 If your genotype has no effect on your probability (and therefore your odds) of disease, then the ORs=1.

3 Genotype relative risks If a disease is reasonably rare, the odds ratio approximates the genotype relative risk (GRR, RR) i.e. the factor by which your probability of disease must be multiplied, if you have genotype 2 2 (or 1 2) as opposed to 1 1 Genotype Penetrance GRR Odds OR 1/ /0.99 = / /0.98 = / /0.95 = If your genotype has no effect on your probability (and therefore your RR) of disease, then the GRRs=1. χ 2 tests Genotype Cases Controls Total Total Work out row and column totals (margins), overall total N Expected value in each cell = (row total col total)/n χ 2 test statistic on 2 df = i (O i E i ) 2 /E i where O i and E i are the observed and expected values in cell i. Can rearrange table to assume dominant/recessive effects: Dominant/recessive effects Dominant: Recessive: Genotype Cases Controls Total 2 2 and Total Genotype Cases Controls Total and Total Can also rearrange table to examine effects of alleles (1 df tests):

4 Counting alleles Counts in Allele Cases Controls (=a) 122 (=b) (=c) 278 (=d) Total Allelic OR = ad/bc χ 2 test statistic on 1 df = i (O i E i ) 2 /E i where O i and E i are the observed and expected values in cell i. Assumes HWE under null and multiplicative allelic effects under alternative: considers chromosomes as independent units Better approach: use counts in previous genotype table to perform a Cochran-Armitage trend test More sophisticated approach Association test in case/control studies can be formulated as logistic regression Standard linear regression: model outcome y as function of predictor variable x * * * y * * * y = mx + c vs y * * * * * * * y = c x x Logistic regression Used in case/control studies Outcome is affected or unaffected Model as function of variable x coding for genotype Model probability (and thus odds) of disease p as function of variable x coding for genotype: ln p 1 p = β 0 + β 1 x c + mx Use observed genotypes in cases and controls to estimate the values of regression coefficients β 0 and β 1 And to test whether β 1 = 0 Standard method used in standard epidemiological studies e.g. of risk factors such as smoking in lung cancer

5 Test of association Association test in case/control studies can be formulated as logistic regression Advantage is can include more than one predictor in regression equation ln p 1 p = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3 where x 1, x 2, x 3 code for genotypes at 3 loci Can also include covariates (e.g. age, sex, smoking etc), interactions between loci etc. etc. Details of regression We have an outcome variable y = 1 or 0 (= case/control) and potentially predictive variables x 1, x 2, x 3 etc. E.g. x 1 = genotype at diallelelic locus: Genotype x 1 1/1 0 1/2 1 2/2 2 We model probability of disease p in terms of log odds: ln p 1 p = β 0 + β 1 x 1 Details (cont) Our coding scheme assumes two copies of allele 2 has twice the effect of a single copy on log odds scale Genotype x 1 log odds Odds OR 1/1 0 β 0 e β /2 1 β 0 + β 1 e β 0+β 1 e β 1 2/2 2 β 0 + 2β 1 e β 0+2β 1 [e β 1] 2 Corresponds to additive allelic effects on log odds scale, or multiplicative allelic effects on odds scale If genotype has no effect on the odds of disease, then β 1 = 0 and all ORs=1

6 Details (cont) Could assume dominant or recessive models on log odds scale by using other codings Dominant model Genotype x 1 log odds 1/1 0 β 0 1/2 1 β 0 + β 1 2/2 1 β 0 + β 1 Recessive model Genotype x 1 log odds 1/1 0 β 0 1/2 0 β 0 2/2 1 β 0 + β 1 In all cases, if genotype has no effect on the odds of disease, then β 1 = 0 To model effect of genotype on a quantitative trait, simply use linear regression rather than logistic regression Early GWAS Ozaki et al. (2002) Nat Genet 32: Genotyped 92,788 gene-based SNPs In 94 Japanese individuals with myocardial infarction Compared to 658 Japanese controls Found a SNP in intron 1 of LTA that was weakly associated with disease status Increased in significance (p= ) when they increased the sample size (1133 cases, 1006 controls) Genotyped 26 other SNPs in region (LD block): Two showed even stronger effects (p= ) Functional assays suggested a possible relationship between SNP genotype and expression of LTA Complement Factor H in AMD First real GWAS (?) was that of Klein et al. (2005) Science 308: Typed 116,204 SNPs in 96 cases (with age-related macular degeneration, AMD) and 50 controls Very small sample size they were very lucky to find anything! Luck was due to the fact the polymorphism has a very large effect (recessive OR=7.4) Klein et al. followed up on two SNPs passing threshold (p < ) Plus a third SNP that just failed to pass significance threshold, but lay in same region as first SNP

7 Klein et al. (2005) Of the 3 SNPs followed up: One appeared to be due to genotyping errors: significance disappeared on filling in some missing genotypes First and third SNP lie in intron of Complement Factor H (CFH) gene Lies in region previously implicated by family-based linkage studies Resequencing of region identified a polymorphism of plausible functional effect Immunofluorescence experiments in the eyes of AMD patients supported the involvement of CFH in disease pathogenesis. WTCCC 2007/2008 saw a slew of high-profile GWAS publications Breast cancer (Easton et al. 2007) Rheumatoid Arthritis (Plenge et al. 2007) Type 1 and Type 2 diabetes (Todd et al. 2007; Zeggini et al. 2008) Arguably the most influential was the UK-based Wellcome Trust Case Control Consortium (WTCCC) study of 7 different diseases (using a common control panel) Nature 447: (2007) WTCCC Considered 2000 cases for each of the following diseases: Bipolar disorder, coronary artery disease, Crohn s disease, hypertension, rheumatoid arthritis, type 1 diabetes, type 2 diabetes Compared each disease cohort to common control panel 3000 population-based controls 1958 birth cohort (58BC) and National Blood Service (NBS) Highly successful WTCCC found 24 independent association signals in 6 out of the 7 diseases studied Has been expanded into WTCCC2 and WTCCC3 studies Involving 5200 common controls (2600 each from 58BC and NBS) typed on both Illumina 1.2M and Affymetrix 6.0 chips

8 WTCCC3 PBC (Mells et al. 2011) Genome-wide association studies Typically use rather standard statistical/epidemiological methods (χ 2 tests, t tests, logistic regression etc.) Success largely due to An appreciation of the importance of large sample size (> 2000 cases, similar or greater number of controls) Stringent quality control procedures for discarding low-quality SNPs and/or samples Stringent significance thresholds (p = ) to account for multiple testing and/or low prior prob of true effect Importance of replication in an independent data set Quality control (QC) Stringent QC checks required for GWAS Discard samples (people) deemed unreliable Low call rates, excess heterozygosity etc. X chromosomal markers useful for checking gender Males should appear homozygous at all X markers Genome-wide SNP data useful for checking relationships and ethnicity Discard data from SNPs deemed unreliable On basis of call rates, Mendelian misinheritances, Hardy-Weinberg disequilibrium (?) Exclude SNPs with low minor allele frequency

9 Call rates and heterozygosity heterozygosity callrate < call rate 61 exclusions (low call-rate); 23 exclusions (heterozygosity) Ethnicity tests PC CEU JPT_CHB YRI PC1 Multidimensional scaling (with 210 HapMap individuals) identifies 33 samples with non-caucasian ancestry Pedigree QC Can use Mendelian inheritance error checks to exclude/adjust Pairs of samples showing high missinheritance rates SNPs showing high missinheritance rates With genome-wide data, can infer relationships based on average identity by descent (IBD) or identity by state (IBS) Using thinned subset of markers with high minor allele frequency (MAF) and in approximate linkage equilibrium Simple relationships (PO, FS, MZ/duplicates) can identified with only a few hundred markers More complicated relationships require 10,000-50,000 SNPs

10 Expected IBD sharing Assuming no inbreeding, the IBD state probabilities are: Number of alleles shared IBD Relationship MZ twins Parent Offspring Full siblings 1/4 1/2 1/4 Half siblings 0 1/2 1/2 Grandchild grandparent 0 1/2 1/2 Uncle/aunt nephew/niece 0 1/2 1/2 First cousins 0 1/4 3/4 Second cousins 0 1/16 15/16 Double 1st cousins 1/16 6/16 9/16 A useful visualisation tool is to plot SE(IBD) vs mean(ibd) Full/half sibs FS HS seibd seibd meanibd meanibd Parents/offspring and Unrelateds PO UNsmall seibd seibd meanibd meanibd

11 Resolving families Many full sib/half sib discrepencies easy to resolve Usually in light of parent/offspring discrepencies e.g. mispaternities Some duplicates may be known MZ twins Some discrepencies require shifting whole branches of a family Using expected structure as starting point And considering posterior (0, 1, 2) IBD sharing probabilities In some cases we reconstruct whole family from scratch May also join together several families Full/half sibs seibd seibd meanibd meanibd Parent/offspring and Unrelateds seibd seibd meanibd meanibd

12 SNP QC and genotype calling SNP genotypes called on the basis of intensity measurements Cluster plots show the intensities of alleles A and B (say) at each SNP, as measured in a large number of people B B A A CHD GWAS results (low QC) CHD GWAS results (better QC)

13 CHD GWAS results (final QC) Q-Q Plots (good) Plot ordered test statistics (y axis) against their expected values (x axis) Observed ordered test statistics Observed ordered test statistics Expected ordered test statistics Expected ordered test statistics Q-Q Plots (bad) Observed ordered test statistics Observed ordered test statistics Expected ordered test statistics Expected ordered test statistics

14 Population stratification A QQ plot showing constant inflation (straight line with slope >1) can indicate population stratification (= population substructure) Population sampled actually consists of several sub-populations that do not really intermix Can lead to spurious false positives (type 1 errors) in case/control studies Simple solution: Genomic Control (Devlin and Roeder 1999) Use your observed test statistics to estimate the slope (=inflation factor λ) Divide each test statistic by λ to get an adjusted (deflated) test statistic More complicated solutions Principal components analysis (PCA) or multidimensional scaling (MDS) Compute the eigenvectors and eigenvalues of matrix of correlations between individuals Based on genome-wide IBS or IBD sharing (from thinned subset of markers, not in LD with one another) Include principal component scores from top 10 (say) eigenvectors as covariates in a logistic regresssion analysis Linear mixed models Estimate kinship matrix (IBD sharing) between pairs of individuals using genome-wide genotype data Use this to model their (extra) correlation, in a linear regression type analysis PCA or MDS Can use this approach to detect gross ethnic outliers Or to adjust for subtle differences in ancestry (e.g. UK versus Slovenian) 2nd principal component st principal component

15 Variance components (mixed) models Recently, an alternative approach based on variance components (mixed) models has been proposed Kang et al. (2010) Nat Genet 42: Zhang et al. (2010) Nat Genet 42: Based on methods designed to test for genotype associations with quantitative traits: linear regression y is the trait value y = μ + βx + ɛ x is a variable coding for genotype (e.g. 0, 1, 2 for genotypes 1/1, 1/2, 2/2) Residual error ɛ N(0, σ 2 ) Linear mixed models Linear mixed models allow this idea to be applied to related individuals ɛ MVN(0, V) where variance/covariance matrix V follows standard variance components model, accounting for known kinship V ij = σg 2 + σe 2 (i = j) V ij = 2Φ ij σ 2 g (i = j) σg, 2 σe 2 represent the additive polygenic variance (due to all loci) and the environmental (=error) variance, respectively Φ ij is half the expected IBD sharing between individuals i and j (= their kinship coefficient) μ, β, σg, 2 σe 2 estimated by maximum likelihood Closely related to QTDT (Abecasis et al. 2000a;b) which implements a slightly more general/complex model Linear mixed models LMMs have been used in plant and animal breeding literature for many years Difference here is we apply them to apparently unrelated individuals Estimate kinship matrix (IBD sharing) from genome-wide genotype data rather than assuming known relationships And apply case/control data (dichotomous traits) rather than quantitative traits Kang et al. (2010) argue that you can simply code data as 0/1 quantitative response, and still get valid inference (test statistics and confidence intervals) Many software packages now available (GenABEL [FASTA, GRAMMAR-γ], EMMAX, FaST-LMM, GEMMA, MMM, Mendel)

16 ROADTRIPS RObust Association-Detection Test for Related Individuals with Population Substructure Thornton and McPeek (2010) AJHG 86: Extension of Maximum Quasi-Likelihood Statistic (MQLS) Both methods construct adjusted version of case/control χ 2 (or Armitage Trend) test Using known pedigree relationships to correct for relatedness ROADTRIPS also uses covariance matrix based on kinship/ibd sharing (as estimated from genome-screen data) to correct for unknown relatedness/population stratification Traditional family-based tests Historically, family-based tests look at transmission within pedigrees In order to give robustness to population stratification Non-transmitted alleles (or all alleles that could have been transmitted) act as control for transmitted alleles e.g. Transmission/Disequilibrium Test (TDT) (Spielman et al. 1993) For a diallelic locus with alleles coded 1/2, consider transmissions of alleles from 1/2 heterozygous parents to affected offspring: Transmission/Disequilibrium Test Under null hypothesis of no association, expect 50:50 transmission by Mendelian laws Under the alternatve hypothesis, high-risk allele (e.g. 2) is more likely to have been transmitted Due to ascertainment through affected child So association is manifested as increased transmission of high-risk alleles in such families

17 Larger pedigrees Several related tests Tsp (=TDT for sib-pairs) Pedigree disequilibrium test (PDT) Family/pedigree-based association test (FBAT, PBAT) Similar principle to TDT: examine increased transmission of particular allele to set of affected individuals in pedigree Compared to that expected under null hypothesis FBAT statistic is S E(S) where S = ij T ij X ij Var(S) X ij is some genotype variable and T ij some trait variable for offspring i in family j FBAT Exact form of FBAT depends on genotype and trait coding used Genotype generally coded in allelic fashion (0, 1, 2) Trait T ij = Y ij μ ij where μ ij is an offset Can choose offset to consider transmissions to affected offspring only Or to contrast transmissions to affecteds with transmissions to unaffecteds Mean and variance calculated conditional on parental genotypes If parental genotypes not observed, FBAT conditions on sufficient statistics for offspring genotype FBAT (and related tests such as TDT) generally less powerful than ROADTRIPS or LMM approaches Owing to smaller effective sample size Disappointment In spite of the success of GWAS, we have the problem of missing heritability" SNPs identified through GWAS do not fully account for observed correlations in phenotype between close relatives Suggesting there are additional genetic factors to be found... In addition, SNPs identified through GWAS do not have strong predictive value (for predicting disease status) GWAS generally detect associations at SNPs with high minor allele frequencies ( ) and small effect sizes (OR<1.5) To detect associations at SNPs with lower MAFs and smaller ORs, we need to increase sample size

18 Meta-analysis Involves putting together data (or results) from a number of different studies Could analyse as one big study But preferable to analyse using meta-analytic techniques At each SNP construct an overall test based on the results (ORs and standard errors) from the individual studies See for example: Zeggini et al. (2008) Nat Genet 40: (Type 2 diabetes) Barrett et al. (2008) Nat Genet 40: (Crohn s disease) Barrett et al. (2009) Nat Genet 41: (Type 1 diabetes) Franke et al. (2010) Nat Genet 42: (Crohn s disease) Morris et al. (2012) Nat Genet 44: (Type 2 diabetes) Lambert et al. (2013) Nat Genet 45: (Alzheimer s) Imputation Meta-analysis is often made easier by using imputation Involves inferring (probabilistically) the genotypes at SNPs which have not actually been genotyped On the basis of their (expected) correlations with nearby SNPs that have been genotyped Using a reference panel of people (e.g. HapMap) who have been genotyped at all SNPs Can combine (meta-analyse) studies that have been genotyped on different genotyping platforms By imputing to generate data at a common set of SNPs Need to account for the imputation uncertainty in the downstream statistical analysis Utility of GWAS Some have expressed disappointment with the fact that we are detecting more and more significant SNPs with smaller and smaller effect sizes Yet we still don t know the functional (causal) polymorphism, in most cases The SNPs identified still don t explain the missing heritability Still not that useful for disease prediction Nevertheless, GWAS have been useful for generating new insight into mechanisms and pathways Through detection of SNPs, or combinations of SNPs, that implicate unexpected disease mechanisms See Visscher et al. (2012) AJHG 90:7-24