Some New Methods for Family-Based Association Studies

Transcription

1 Some New Methods for Family-Based Association Studies Ingo Ruczinski Department of Biostatistics Johns Hopkins Bloomberg School of Public Health April 8, 20 http: //biostat.jhsph.edu/ iruczins/

2 Topics Some study designs to improve statistical power in association tests for rare variants. A genotypic transmission disequilibrium test that accommodates uncertain or imputed genotypes. Methods to assess de-novo copy number variants in case-parent trios. Some study designs to improve statistical power in association tests for rare variants With Rasika Mathias

3 Platelet aggregation Importance of platelets in atherosclerotic vascular disease: The aggregation of activated platelets on ruptured or eroded atherosclerotic plaques is a critical step in the initiation of thromboses of the arterial system, which subsequently results in ischemic syndromes such as myocardial infarction, stroke, and peripheral arterial occlusions. The propensity of platelets to aggregate and initiate thromboses is thought to be dependent on local vascular factors, systemic factors which may change over time (such as circadian rhythms, inflammatory processes, smoking, and neuroendocrine stress), and genetic factors which modify platelet aggregability.

4 GF GM F M F2 M2 C C2 P(C, C 2 ) = {F,M,G} P(C, C 2, F, M, F 2, M 2, GF, GM) = P(C, C 2 F, M, F 2, M 2, GF, GM) {F,M,G} P(F, M, F 2, M 2, GF, GM) = P(C F, M ) P(C 2 F 2, M 2 ) {F,M,G} P(F, M, F 2, M 2 GF, GM) P(GF, GM)

5 P(C, C 2 ) = P(C F, M ) P(C 2 F 2, M 2 ) {F,M,G} P(F, M, F 2, M 2 GF, GM) P(GF, GM) = P(C F, M ) P(C 2 F 2, M 2 ) {F,M,G} P(F ) P(M, F 2 GF, GM) P(M 2 ) P(GF ) P(GM) P(C F, M) C F M

6 P(M, F GP, GM) M,F GF GM logit(p) = α + βc P(D C) = exp(α + βc) + exp(α + βc) P(D C, D C2 ) = C,C 2 P(D C, D C2 C, C 2 ) P(C, C 2 ) = C,C 2 P(D C C ) P(D C2 C 2 ) P(C, C 2 )

7 P(C, C 2 D C, D C2 ) = P(D C, D C2 C, C 2 ) P(C, C 2 ) P(D C, D C2 ) = P(D C C ) P(D C2 C 2 ) P(C, C 2 ) C,C 2 P(D C C ) P(D C2 C 2 ) P(C, C 2 ) This defines the proportion of carriers in the cousin pairs. Population

8 Cousin pairs Power comparison

9 Power comparison

10 An alternative approach Rank the n targets by p-value (IknowIknow) and pick the top k. If there is one true positive X, then (assuming independence) P(X is in the top k) = P(p X p (k) ) = = z z P(p X p (k) p (k) = z) f p(k) (z) dz P(p X z) dbeta(k, n + k)

11 Power comparison Power comparison

12 A genotypic transmission disequilibrium test that accommodates uncertain or imputed genotypes With Terri Beaty, Margaret Taub and Holger Schwender Epidemiology of oral clefts Oral clefts are among the most common birth defects, and include three anatomical defects: cleft lip (CL); cleft lip and palate (CLP) and cleft palate (CP). Collectively, oral clefts represent half of all craniofacial malformations and create a major public health burden for both affected children and their families. The overall prevalence of oral clefts is estimated at per livebirths worldwide, with substantial variation across populations and between racial and ethnic groups. There are known environmental and genetic risk factors.

13 Case-parent trios Recruitment Site CL CLP CP Total Utah Norway Korea Maryland Pittsburgh Singapore Taiwan Iowa Denmark Philippines WuHan Shandong Province Western China Total Case-parent trios F : 2 M : 2 C : F : 2 M : 2 C : 2 F : 2 M : 2 C : 22 F : M : 2 C : F : M : 2 C : 2 F : 2 M : 22 C : 2 F : 2 M : 22 C : 22

14 Fallin et al 2002 [LOU RUC BIOM J200] [LOU RUC BAYES STAT 200 ]

15 Genotype imputation Li et al, Annu Rev Genomics Hum Genet, 0: , w (k) ij ( = Pr g (k) i ) = j lab data Genotype probabilities for member k in family i. i {,...,n}, j {0,, 2}, k {f, m, 0}. w (k) i =(w (k) i0, w (k) i, w (k) i2 ) w i =(w (m) i, w (f ) i, w (0) i )

16 Let g (k) i {0,, 2} be the (unknown) genotypes for the affected proband (k = 0) and the three pseudo-contols (k, 2, 3). Let x be the predictor variable that encodes the genetic effect. For example, x (k) i = g (k) i for an additive model. Let x i =(x (0) i, x () i, x (2) i, x (3) i ) be the vector of these predictors for family i. Let y i =(, 0, 0, 0) be the vector of these response variables for family i. Log-likelihood l(β) = n log f (y i x i = x l, β)pr(x i = x l w i ) xl X i= Here, X is the set of possible values of x i given the assumed genetic model and Mendelian constraints of the observed parental mating type.

17 l(β) β = n i= x l X f (y i x i = x l, β)pr(x i = x l w i ) x l X f (y i x i = x l, β)pr(x i = x l w i ). = n i= x l X { f } (y i x i = x l, β) f (y i x i = x l, β) Pr(x i = x l w i, β, y i ) Under a conditional logistic regression model we have ( ) (0) exp(βx l ) f (y i x i = x l, β) = =: c 3 (k) l (β). k=0 exp(βx l ) l(β) β = x l X { c l (β) c l (β) } n Pr(x i = x l w i, β, y i ) i= = x l X c l (β) c l (β) n Pr(x i = x l w i ). i= Assuming independent genotype estimates, we have Pr(x i =(0, 0,, ) w i ) w (f ) i0 w (m) i w (0) i0 + w (f ) i w (m) i0 w (0) i0. Denote for an additive model α = n Pr(x i =(0, 0,, ) w i ). i= See next slide.

18 Affected Pseudo- Weight c l (β add ) Sum α l of family Parents child controls in likelihood probabilities 0, 0 0,, 0, 0,0,,2,2,2,2 2,,2, 0,,2, 0,,2, 2 0,, 0,0 0 0,0,0 0,2,, 2,2 2 2,2,2 2+2exp(β add ) α exp(β add ) 2+2exp(β add ) α 2 2+2exp(β add ) α 3 exp(β add ) 2+2exp(β add ) α 4 (+exp(β add )) 2 α 5 exp(β add ) (+exp(β add )) 2 α 6 exp(2β add ) (+exp(β add )) 2 α 7 4 α 8 4 α 9 4 α 0 Setting l(β) β equal to 0, we obtain Hypothesis testing ( α 2 + α 4 + α 6 + 2α 7 ˆβ add = logit α + α 2 + α 3 + α 4 + 2α 5 + 2α 6 + 2α 7 ). Similar calculations lead to ( ) Den ŜE ˆβ add = (Den Num) Num The parameter erstimates and estimated standard errors for the dominant and recessive models also have closed form solutions, but are a bit more complicated. This can also easily be extended to test for G E with binary E.

19 CPU time [TAU SCH BEA LOU RUC TECH REP 20 ] Genotyped Imputed [TAU SCH BEA LOU RUC TECH REP 20 ]

20 [TAU SCH BEA LOU RUC TECH REP 20 ] Trio logic regression [LI LOU FAL RUC TEC REP 200 ] [SCH BOW FAL RUC ANN HUM GEN 20 ]

21 Simulating case-parent trios log(rr) =β log ( ) + exp(α + β) + exp(α) ^ Simulations based on an interaction between 3 SNPs. [ LI LOU FAL RUC TEC REP 200 ] Schizophrenia study 0.90 I { 302 D } I { 66 D }.09 I { 302 D :66 D } 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 0.67 I { 302 D } I { 66 D } 0.89 I { 302 D 66 D } [LI FAL LOU RUC GEN EPI 200 ]

22 Methods to assess de-novo copy number variants in case-parent trios. With Rob Scharpf Copy number estimates are noisy

23 Plate effects SNP_A25622 SNP_A plate plate 2 23 log 2 (B) log 2 (A) + log 2 (B) log 2 (A) plate2 plate plates ordered by median date Genotype estimates are robust Birdseed CRLMM

24 Allele specific copy numbers Allele specific copy numbers At locus i, for subject j in plate p, we have for allele k {A, B} I kijp = ν kip δ kijp +φ kip c kijp ɛ kijp { } ( ) = ĉ kijp = max Ikijp ˆν ˆφ kip, 0 kip [SCH IRI RIT CAR RUC TECH REP 20 ] [SCH RUC CAR DOA CHA IRI BIOSTAT 20 ]

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32 http: //biostat.jhsph.edu/ iruczins/