SNP Association Studies with Case-Parent Trios

Transcription

1 SNP Association Studies with Case-Parent Trios Department of Biostatistics Johns Hopkins Bloomberg School of Public Health September 3, 2009 Population-based Association Studies Balding (2006). Nature Reviews Genetics 7(0): 78-9.

2 Case-control Design Balding (2006). Nature Review Genetics 7(0): Family-based Designs Laird and Lange (2006), Nature Reviews Genetics 7,

3 Linkage From Goncalo Abecasis Linkage versus Association From Goncalo Abecasis

4 Family-based Designs Benyamin, Visscher, and McRae (2009), Pharmacogenomics 0(2), Parent-of-Origin Sull et al (2008), Genetic Epidemiology 32:

5 De-novo Deletion Homozygous and Hemizygous Deletions GF GM M A B S Grandfather Grandmother Mother Aunt Brother Sister AB 0.0 BB 0.05 AB -0. AB AB 0.06 BB AA 0.27 NC AA AA AB 0.2 BB AB 0.5 NC AA AA AB BB AB NC AA AA AA 0.30 AA BB 0.20 NC NC BB BB 0.22 BB AB 0.03 NC -6.4 BB BB AB 0.09 AA AB NC BB -0.7 BB AB AA -.06 BB 0.0 NC BB 0.04 BB BB 0.4 NC AB 0.7 NC AA AA AA AA AB 0.0 NC AA AA AA 0.6 AA AB -0.0 NC BB BB AB 0.3 AA AB 0.0 NC BB -0.7 BB -0.5 AB -0.5 AA BB 0.6 NC BB BB BB 0.0 BB AB 0.06 NC AA AA AB 0.07 BB AA 0.7 NC AA AA AB BB BB 0.02 NC BB BB AB 0.3 AA AA 0.2 NC -6.0 AA AA AB 0.20 BB BB 0.05 BB 0. BB 0.5 BB 0.29 AB 0.3 AB -0.0

6 Family-based Designs - Advantages Robust to possible effects of population stratification and genetic heterogeneity. Parent-of-origin effects (imprinting) can be assessed. Data quality control is usually more thorough (e. g. genotyping errors and sample swaps are easier to catch). Distinction between de-novo and inherited events (copy number changes) is possible. Logistically easier for childhood diseases. In case-parent data, low minor allele frequencies are of less worry (genotyping errors are still possible). Case-parent designs do not require phenotyping parents. Linkage information from previous family studies can be employed in association studies. Family-based Designs - Disdvantages Typically less power per SNP typed than case-control studies. Pedigrees maybe hard to get except for childhood diseases, and may not be feasible for late-onset diseases. Can be a lot more expensive. Highly sensitive to genotyping errors. Might be computationally more demanding, especially for studies with large pedigrees. Software may be an issue.

7 Summary Pearson and Manolio (2008). JAMA. 299(): Family versus Case-control IGES 2009 (Hawaii) Monday, October 9 - Kuilima Ballroom Session 3: Family Studies & Family Data :30 2:30 Family Studies: Are they still relevant? Pro vs Con Discussion Nan Laird (Pro) & David Balding (Con)

8 TDT - Allelic The transmission disequilibrium test measures the over-transmission of an allele from parents to affected offsprings. For a set of n parents with alleles and 2 at a genetic locus, each parent can be summarized by the transmitted and the non-transmitted allele: Non-TA P 2 a b a + b TA 2 c d c + d P a + c b + d 2n Only the heterozygous parents contribute information! Under the null of no association, Even better, use binom.test() in R. (b c)2 b + c χ 2 TDT - Genotypic Assume that at a certain locus the father has alleles and the mother has alleles 2. The four Mendelian children thus have alleles, 2,, and 2. Assume the affected proband has genotype. The three Pseudo controls then have the genotypes, 2, and 2. Y X Affected proband Pseudo control # 0 Pseudo control #2 0 2 Pseudo control #3 0 2 We can use conditional logistic regression to analyze the data.

9 TDT Fallin MD et al (2006). Genetic Epidemiology 23:4586. International Cleft Consortium CL trios CLP trios CP trios Total Recruitment Site C NC C NC C NC C NC Utah 68 (6) 96 (20) 52 (2) 26 (48) Norway 06 (4) 74 (8) 07 (3) 387 (5) Korea 9 (0) 40 (2) 5 (0) 64 (2) Maryland 9 (2) 7 (42) 25 (8) 5 (72) Pittsburgh 26 (2) 70 (28) (4) 07 (34) Singapore 5 () 45 (7) 53 (4) 3 (2) Taiwan 42 (4) 76 () 74 (5) 292 (20) Iowa 6 (9) 29 () 24 (7) 69 (37) Denmark 6 (5) 5 (2) 5 (8) 26 (35) Philippines 0 (0) 94 (4) 0 (0) 94 (4) WuHan 39 (3) 36 (9) 42 (3) 29 (5)* Shandong Prov. 54 (2) 29 (70) 30 (8) 25 (0)* Western China 43 (3) 63 (3) 38 (2) 44 (8) Total 453 (90) 38 (227) 466 (84) 2060 (403)* *total includes probands of indeterminate cleft type: 2 in WuHan; 3 in Shandong Prov.

10 International Cleft Consortium International Cleft Consortium

11 Schizophrenia Study Case-parent trios of Ashkenazi Jewish descents. Diagnosis of SZ and SZA based on DSM IV. Dense coverage of 64 candidate genes. 375 SNPs on chromosomes genotyped for 32 trios. Original analysis through single marker TDT. Fallin MD et al (2005), Am J Hum Genet 77(6): Goal: Explore SNP-SNP interactions for association with SZ and SZA. Biological and Statistical Interactions BB Bb bb AA Aa aa (SNPA D SNPB R ) (SNPB D SNPA R ) Statistical interaction: Deviation from additivity in a linear statistical model. Epistasis: Masking of phenotype expressed by one gene by the effects of another gene. How can we detect models such as logit(p) =α + β Ind{(SNP24 D SNP80 R ) (SNP24 R SNP80 D )}...?

12 Logic Regression The predictors are the SNPs in dominant and recessive coding. SNP X X.R X.D AA 0 0 AT 0 TT Let X,...,X k be binary (0/) predictors, Y a response variable. Fit a model g(e(y)) = b 0 + t b j L j, j= where L j is a Boolean combination of the covariates, e.g. L j = (X X 2 ) X c 4. Determine the logic terms L j and estimate the b j simultaneously. Ruczinski et al (2003), Journal of Computational and Graphical Statistics 2(3): Trio Logic Regression The rough idea is as follows: Pseudo controls are generated from the trio data, taking the LD block structure into account. Missing data are handled using haplotype-based imputation. The conditional logistic likelihood is used in logic regression to assess differences in cases and pseudo controls.

13 Trio Logic Regression Trio Logic Regression The steps in more detail: Estimate the haplotype blocks and the haplotype frequencies using the parents genotypes. 2 For each block and each trio, sample haplotype pairs for the parents and the offspring consistent with the observed genotypes in the trio, allowing for missing data. 3 Generate the probands genotype data from the haplotypes that were passed from the parents. 4 For each block and each trio, generate genotypes for three pseudo-controls (PC, PC2, PC3) using the parents haplotypes that were not passed to the proband. The assignment to PC, PC2, and PC3 is random. 5 Assemble three pseudo-controls for each trio by augmenting the genotypes from the blocks. 6 For each locus, translate the genotype data into two binary variables in dominant and recessive coding.

14 Trio Logic Regression The conditional logistic likelihood is L(β) = ( ) N exp(x i0 β) i= exp(x i0 β)+σ 3 m= exp(x imβ) In this setting, i refers to a trio, X i0 refers to the exposure of the proband in trio i, and (X i, X i2, X i3 ) are the exposures of the 3 pseudo-controls in trio i. Does the likelihood always have a maximum? Trio Logic Regression Number of trios where k pseudo-controls match the proband k X i0 = 0 a 0 b 0 c 0 d 0 X i0 = a b c d Likelihood contributions for X i0 = 0 a 0 b 0 c 0 d 0 X i X i X i2 0 0 X i3 0 L i (β) +3 exp(β) 2+2 exp(β) 3+exp(β) 4 Likelihood contributions for X i0 = a b c d X i0 X i 0 X i2 0 0 X i L i (β) exp(β) exp(β)+3 exp(β) 2 exp(β)+2 exp(β) 3 exp(β)+ 4

15 Trio Logic Regression The log-likelihood is: log(l(β)) = a {β log(exp(β)+3)} + b {β log(2 exp(β)+2)} + c {β log(3 exp(β)+)} + d 4 a 0 log{ + 3 exp(β)} b 0 log{2 + 2 exp(β)} c 0 log{3 + exp(β)} d 0 4 Trio Logic Regression The first derivative of the log-likelihood is: log(l(β)) β = a (a + c 0 ) exp(β) exp(β)+3 + b (b + b 0 ) c (c + a 0 ) 2 exp(β) 2 exp(β) exp(β) 3 exp(β)+ The log-likelihood is monotonically decreasing in β. Further: lim β log(l(β)) β = a + b + c 0 and lim β + log(l(β)) β = (a 0 + b 0 + c 0 ) 0

16 Trio Logic Regression Since the derivative of the log likelihood function is a continuous function in β, it follows that the likelihood function has a maximum unless a + b + c = 0 or a 0 + b 0 + c 0 = 0. In other words, for either the exposure or the non-exposure groups, all pseudo-controls are equal to the respective probands. This might occur in a particular sample where the number of trios is small and the (or some of the) SNPs contributing to the exposure definition have extremely low minor allele frequency, however, it is not plausible that such a separation would exist in the population in truth. Missing Data

17 Simulation G SNP R 3 2 SNP R 4 2 SNPR (SNP R SNPD 6 2 ) SNPR 3 4 (SNP R 2 3 SNPD 5 2 ) SNPR (SNP D 4 SNPR 8 2 ) (SNPR 5 SNPD 6 ) 6 ((SNP R 4 2 SNPR 7 2 ) SNPR 8 3 ) (SNPR 9 2 SNPR 6 ) 7 (SNP R 3 SNPR 2 2 ) (SNPR 5 4 SNPR 5 ) (SNPR 9 2 SNPR 8 3 ) P(G) Haplotypes / block # of haplotypes # mating table rows , , 3, , 5, , 5, 5, , 8, 5, 3, 3 2, , 4, 5, 5, 3, 5 4, Simulation L/ L2/22 L/ Haplotype Frequencies population parents proband Haplotype Frequencies

18 Simulation When using conditional logistic regression to compare cases and pseudo-controls, the expected value of the parameter estimates is not the logs odds ratio β, but the log relative risk (Schaid 996). RR = P(D I G = ) P(D I G = 0) = exp(α + β)/( + exp(α + β)) exp(α)/( + exp(α)) = exp(β) ( ) + exp(α + β) + exp(α) Therefore log(rr) = β log ( ) + exp(α + β) + exp(α) Simulation log(rr) =β log! + exp(α + β) + exp(α) 4 3 2!^ 0 "!!5!3!!5!3!!5!3!!5!3!!5!3!

19 Simulation log(rr) =β log! + exp(α + β) + exp(α) 4 3 2!^ 0 "!!5!3!!5!3!!5!3!!5!3!!5!3! Software The trio logic regression methods are implemented as an augmentation in the logic regression R package LogicReg. 2 The R package trio contains functions to generate logic regression input from pedigree or genotype files, to check for Mendelian errors, to impute missing data, and to simulate case-parent trios. 3 A software vignette is also available.

20 Results Logic model exp( ˆβ) 0.67 I n o 302 D I n o 302 D 66 D I n o 302 D 66 D 48 D I n o 302 D 66 D 48 D 368 R 3.65 SNP 302 Chromosome 2 NOS SNP 66 Chromosome 8 CHRNB SNP 48 Chromosome 8 PNOC SNP 368 Chromosome 22 COMT Results Logic model exp( ˆβ) 0.67 I n o 302 D I n o 302 D 66 D I n o 302 D 66 D 48 D I n o 302 D 66 D 48 D 368 R 3.65 SNP 302 Chromosome 2 NOS SNP 66 Chromosome 8 CHRNB SNP 48 Chromosome 8 PNOC SNP 368 Chromosome 22 COMT

21 Results exp( ˆβ) ˆβ (se) z p Marginal 302 D (0.6) 4.2 4e D (0.22) Logic 302 D 66 D (0.8) 4.89 e-06 Additive 302 D (0.6) 4.5 3e D (0.22) D (0.9) 4.86 e-06 Additive 66 D (0.33) D : 66 D (0.34) Results exp( ˆβ) ˆβ (se) z p Marginal 302 D (0.6) 4.2 4e D (0.22) Logic 302 D 66 D (0.8) 4.89 e-06 Additive 302 D (0.6) 4.5 3e D (0.22) D (0.9) 4.86 e-06 Additive 66 D (0.33) D : 66 D (0.34)

22 Results exp( ˆβ) ˆβ (se) z p Marginal 302 D (0.6) 4.2 4e D (0.22) Logic 302 D 66 D (0.8) 4.89 e-06 Additive 302 D (0.6) 4.5 3e D (0.22) D (0.9) 4.86 e-06 Additive 66 D (0.33) D : 66 D (0.34) Results 0.67 I n 302 Do I {66D } 302 D 302 D D main effects only

23 Results 0.90 I n 302 Do I {66D }.09 In 302 D :66 Do 302 D 302 D D main effects + interaction Results 0.89 I n 302 D 66 Do 302 D 302 D D logic regression

24 Results 302 D 302 D 302 D 302 D 302 D 302 D D 66 D 66 D main effects only main effects + interaction logic regression Results exp( ˆβ) ˆβ(se) z p 302 D (0.6) 4.2 4e-05 Marginal 66 D (0.22) D (0.25) Logic 302 D 66 D 48 D (0.20) e-08