Introduc)on to Sta)s)cal Gene)cs: emphasis on Gene)c Associa)on Studies

Transcription

1 Introduc)on to Sta)s)cal Gene)cs: emphasis on Gene)c Associa)on Studies Lisa J. Strug, PhD Guest Lecturer Biosta)s)cs Laboratory Course (CHL5207/8) March 5, 2015

2 Gene Mapping in the News Study Finds Gene Associated With Prostate Cancer North American Group IDs Loci Influencing Cystic Fibrosis Lung Disease Severity May 23, 2011 Study identifies second gene associated with specific congenital heart defects Unique Study Identifies Gene Associated With Anxiety Phenotypes! Discovery of a gene associated with a leukemia mostly affecting children

3 A, C, T, G A, C, T, G

4 SNP haplotype M1 M2 Diseasecausing variant

5 Gene)c Associa)on Studies Aim to detect associa)on between one or more gene)c polymorphisms and a trait A trait may be some quan)ta)ve characteris)c, a discrete apribute or disease In case- control studies for gene)c associa)on we ascertain unrelated cases on the basis of a discrete, dichotomous trait, and unrelated controls without the trait who are ascertained from the same popula)on as the cases to avoid poten)al confounders (e.g. ethnicity)

6 Measures of Associa)on In epidemiology, associa)on between disease and ae)ological factors are usually expressed in terms of rela%ve risk measures i.e. Disease risk/odds in exposed subjects Disease risk/odds in unexposed subjects In gene)c epidemiology, rela)ve risks/ors can be defined for Alleles Genotypes Haplotypes

7 Mul)plica)ve Model for Risk Allelic rela)ve risks ϕ A ϕ a are defined by the mul%plica%ve model: θ i/j =ϕ i ϕ j where one allele is taken as reference. In the diallelic case using a as reference so that ϕ a =1: θ A/A =(ϕ A ) 2, θ A/a =(ϕ A )(1) where θ A/A is the genotypic relative risk i.e. θ A/A =risk for A/A genotype risk for a/a genotype

8 Hardy- Weinberg Equilibrium If the rela)ve frequency of alleles i, j are f i, f j, the rela)ve frequency of genotype i/j under H- W equilibrium is 2f i f j if i j and (f i ) 2 if i=j The HWE assump)on implies that each subject s two chromosomes are sampled independently from the popula)on A sample of N independent subjects can be viewed as a sample of 2N independent chromosomes Example: SNP marker with alleles A, a. Allele frequency of A=0.3. What are the three possible genotypes at this locus and their frequencies under HWE?

9 HWE Example Example: SNP marker with alleles A, a. Allele frequency of A is p A =0.3. What are the three possible genotypes at this locus and their frequencies under HWE? Genotypes: freq(a)=p A, freq(a)=p a =1- p A

10 Allele Coun)ng and the 2x2 table Assuming the mul)plica)ve risk model, HWE in the popula)on, and a rare disease, we can count alleles in cases and controls to assess associa)on For a diallelic locus: Allele Cases Controls A D A H A a D a H a Test for associa)on using conven)onal Χ 2 test, 1 df The allelic rela)ve risk (A vs. a) is es)mated by the odds ra)o D A /D a H A /H a = D AH a D a H A

11 Example: the Pro871Leu SNP in BrCa1 Subjects Genotype Cases Controls Leu/Leu Leu/Pro Pro/Pro Total Assume HWE in the popula)on under study (and hence in the controls) and that the mul)plica)ve risk model holds, then can treat chromosomes as independent Therefore the es)mated allelic OR is ˆ φ LEU = Chromosomes Allele Cases Controls Leu Pro Total =1.122 And the mul)plica)ve model implies an es)mated OR for Leu/Leu is ˆ θ LEU / LEU = ( ˆ φ LEU ) 2 = (1.122) 2 =1.259

12 Instead of a Mul)plica)ve model of risk: Genotype Cases Controls Leu/Leu Leu/Pro Pro/Pro Total Dominant Genotype Cases Controls Leu/* Pro/Pro Total Recessive Genotype Cases Controls Leu/Leu Pro/* Total Such tests are more reasonable for a func%onal variant Associa)ons with non- causal linked markers tend to give alterna)ves in which heterozygotes have intermediate risk; so mul)plica)ve models might be preferable

13 Mul)plica)ve model at the subject level Also called the addi%ve model 1- df test where the A/a risk is intermediate between A/A and a/ a risks Can be fit using logis)c regression with log odds(case)= α+xβ, where the risk factor x= number of (minor) alleles = 0,1,2 Genotype x Log Odds(case) =α+βx a/a 0 α A/a 1 α+β A/A 2 α+2β Log OR A/a = β => OR A/a =e β = ϕ Log OR A/A = 2β => OR A/A =e 2β = ϕ 2

14 Mul)plica)ve model, cont d In logis)c regression, the score test for β=0 is the Cochran- Armitage test for trend in propor)ons This test is preferable to allele coun)ng since it avoids the need to assume HW equilibrium

15 Genotypic Tests: 3x2 Table (2 df) Genotype Cases Controls Leu/Leu Leu/Pro Pro/Pro Total Taking the Pro/Pro as a reference group, calculate O ˆ R Leu / Leu,O ˆ R Leu / Pr o Compare these es)mates to those predicted by the mul)plica)ve model fit to the alleles table

16 Reasons for Gene)c Associa)on 1. The locus/polymorphism is a func%onal variant. That is, the associa)on is causal: Func%onal variant è Disease 2. The locus is in linkage disequilibrium with a func)onal variant; that is the polymorphism has no causal role but is associated with a nearby causal variant marker locus è Func%onal variant è Disease 3. The associa%on is due to confounding by popula%on stra%fica%on; ie some underlying stra)fica)on or admixture in the popula)on Popula)on stra)fica)on - > can result in spurious associa)on results as a result of a systema)c difference in allele and disease frequencies between sub- popula)ons in a popula)on, possible due to ancestry

17 Direct Associa)on Studies of direct associa)on target polymorphisms which are puta)ve causal variants eg. a muta)on leading to an amino acid change However, many causal variants will likely be non- coding and affect things such as gene regula)on, expression or differen)al splicing >70% of variants iden)fied as associated in GWAS are intergenic

18 Indirect Associa)on The polymorphism is a surrogate for the causal locus, allowing us to search for causal genes in indirect way However, indirect associa)ons are even weaker than direct associa)ons, and typing many surrounding markers are required to detect the associa)on Cannot be a defini)ve nega)ve result, in contrast with direct associa)on studies (ie. hard to rule out a gene) This approach used for candidate gene studies and for genome- wide associa)on studies

19 Confounded Associa)on Associa)on due to confounding by stra)fica)on and admixture within the popula)on Can result in spurious findings (posi)ve confounding) or obscure true associa)ons (nega)ve confounding) Gene)c epidemiology offers possibili)es to overcome this problem e.g. adjustment for popula)on stra)fica)on using principal component analysis or other methods

20 Linkage Disequilibrium and Indirect Associa)ons mapping genes indirectly depends on the existence of associa)on at the popula)on level (or linkage disequilibrium), between causal variants and nearby markers Consider 2 loci Locus 1 has alleles A, a with frequencies p A and p a, and locus 2 has alleles B, b with frequencies p B and p b in the popula)on How many possible haplotypes are there for the 2 loci?

21 Linkage Disequilibrium (LD) Two loci are said to be in LD if their respec)ve alleles do not associate independently Suppose that the frequency of our 4 haplotypes p AB, p Ab, p ab, p ab in the popula)on are 0.4, 0.1, 0.2 and 0.3, where p A = 0.8, p B = 0.4, are A and B in LE? If not, which alleles on the two loci occur together on haplotypes more onen than would be expected under LE?

22 Measures of LD One measure of LD for our two biallelic loci is D AB =p AB - p A p B Similarly, D Ab =- D AB and D ab = D AB LD is a property of 2 loci, not their alleles Thus the magnitude of D is important not the sign The magnitude of D does not depend on the choice of alleles The range of values that D can take on varies with allele frequency but max( p A p B, p a p b ) D AB min(p a p B, p A p b )

23 Example What is the theore)cal range of D AB when p A =1/2 and p B = 1/3? Reminder: max( p A p B, p a p b ) D AB min(p a p B, p A p b )

24 Normalized D or D The possible values of D depend on allele frequencies, making D difficult to interpret For repor)ng purposes, the normalized D is onen used ' D AB = # D AB max( p A p B, p a p b ),D ' AB < 0 % % $ ( D AB min(p a p B, p A p b ),D > 0 AB &% )% D can then be es)mated from the sample frequencies

25 Measuring LD with r 2 r AB = D AB p A p a p B p b Which is the correlation between 2 random variables It is usually more common to consider r AB squared r 2 AB = D 2 AB p A p a p B p b r 2 has the same value regardless of how the alleles are labeled

26 D and r 2 When D =1, referred to as Complete LD In this case there are at most 3 of the 4 possible haplotypes present in the popula)on The intui)on here is that the 2 loci are not being separated by a recombina)on in this popula)on When r 2 =1, referred to as Perfect LD occurs when there are exactly 2 of the 4 possible haplotypes present in the popula)on, and as a result the two loci have the same allele frequencies Loci that are in perfect LD are necessarily in complete LD

27 D and r 2 It is possible for D to be 1 and for r 2 to be small r 2 =1 implies that the two loci carry the same informa)on whereas D is derived from popula)on gene)cs considera)on For this and other reasons, it is onen useful to report both D and r 2

28 LD and Haplotype Blocks The genome falls into LD blocks, with liple haplotype diversity within blocks and liple disequilibrium between blocks Mean block size appears to be about 14kb in Caucasians, 8kb in Africans (but this is variable with blocks up to 200kb in size) A consequence of the lack of haplotype diversity in regions of strong LD is that there is considerable redundancy that is, most polymorphisms and haplotypes in a given block can be predicted from a smaller set Johnson et al. (Nature Gene)cs 2001) referred to this smaller set as haplotype tagging SNPs The concept of haplotype tagging SNPs is used to create genome- wide SNP chips to be used for Genome- wide associa)on studies (GWAS)

29 GWAS >1M haplotype tagging SNPs spanning the genome Substan)al quality control of the genotype data is required! Test for associa)on between disease/con)nuous trait/etc. and each SNP; >1M tests (more if imputa)on is used)! Requires strict significance criteria; onen p< 10^- 8 to reach genome- wide significance for a given SNP test

30 Manhattan Plot Sample GWAS QQ Plot 2.09E E-08

31 Gene Mapping in the News Study Finds Gene Associated With Prostate Cancer North American Group IDs Loci Influencing Cystic Fibrosis Lung Disease Severity May 23, 2011 Study identifies second gene associated with specific congenital heart defects Unique Study Identifies Gene Associated With Anxiety Phenotypes! Discovery of a gene associated with a leukemia mostly affecting children