a glmm-based collapsing method for rare cnv analysis
DESCRIPTION
1. Jung-Ying Tzeng Bioinformatics Research Center & Department of Statistics NC State University Joint work with Jin Szatkiewicz and Patrick Sullivan @ UNC-CH. A GLMM-based Collapsing Method for Rare CNV Analysis. ENAR March 18, 2014. 2. Copy Number Variants (CNVs). - PowerPoint PPT PresentationTRANSCRIPT
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A GLMM-based Collapsing Method for Rare CNV Analysis
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Jung-Ying Tzeng
Bioinformatics Research Center & Department of Statistics
NC State University
Joint work with Jin Szatkiewicz and Patrick Sullivan @ UNC-CH
ENAR March 18, 2014
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Copy Number Variants (CNVs)• CNVs : changes in the number of DNA copies comparing to the
reference
• Although SNPs outnumber CNVs, their relative contributions to genomic variation (as measured in nucleotides) are similar (Malhotra and Sebat 2012)
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...CG ATG...
ATG......CG
ATG......CG
GAA......TTGGG......GTG
Deletion
Duplication
1bp - Mb
(Source: Ferreira and Purcell 2009)
SNPs CNVs
Estimate ~1 in 1000 bp > 1000 CNVs
Base pairs ~4 Mb ~4 Mb
% genome ~0.1% ~0.1%
Mutation rate
10-8 10-4 to 10-6
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Copy Number Variants (CNVs)
• CNVs can affect disease risk
Ex. CNVs play an important role in the etiology of multiple psychiatric disorders, e.g., developmental delay, autism, schizophrenia
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Malhotra and Sebat 2012
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Malhotra and Sebat 2012
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Collapsing Analysis for rare CNVs • Collapsing analysis serves as a key approach to
evaluate the collective effect of rare CNVs (Sullivan et al. 2012; Collins and Sullivan 2013; Malhotra & Sebat 2012)
• CNVs are typically collapsed across the genome– Ex. a greater genome-wide burden of rare CNVs
in SCZ cases than in controls (Walsh et al. 2008 Science; International Schizophrenia Consortium 2008 Nature; Kirov et al. 2009 Hum. Mol. Genet; Buizer-Voskamp et al. 2011 Biol. Psychiatry)
or within genes– Ex. the burden of rare CNVs in NRXN1 was
significantly greater in SCZ cases than in controls (Szatkiewicz et al. submitted)
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Developments in SNP Collapsing Analysis• Depending on how genotype information are modeled, SNP
collapsing methods can be roughly classified into
1. Fixed effects approaches
2. Random effects approaches
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SNP Collapsing Analysis1. Fixed effects approaches
•
• Focus on testing mean level of genetic effects
• Optimal if the effects of different loci are additive, have similar size and same direction
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1*
1 0,1,2M Mi mii iGg EY w w G G
Regress traits on weighted genotype sum of all loci
, where *
0 : 0Test for associa tionH
𝛽𝑚
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2. Random effects approaches
• Focus on testing variance level of genetic effects
•
•
, genetic similarity between and
SNP Collapsing Analysis
11 , 0,1,2i i Mi miMg EY G G G
where
Basic Idea :
0 : 0Test for associationH
~ 0, Assume N
1
)
,
[ , , ] ~ (0, )
In general ( :
where
i i
Tn n n
g EY g
g g g N S
<<<<<<<<<<<<<<
Schaid2010, Pan 2011, Wu et al. 2011,Tzeng et al. 2009,2011
𝛽𝑚
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2. Random effects approaches
• Methods differ by the choices of weights and
E.g., Global test (Goeman et al. 2004) and no weights
C-alpha method (Neale et al. 2011)and with weight = I{MAF < cut}
Kernel Machine Regression (Wu et al. 2010, 2011) = IBS at locus between and and weight = (1-MAF)24
Similarity Regression (Tzeng et al. 2009, 2011, 2014) = IBS at locus between and and weight =
• Optimal if genetic effects are interactive / non-linear among loci or
vary across loci
SNP Collapsing Approaches
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Challenges in CNV Collapsing Analysis--- Cautions about applying SNP collapsing methods1. Copy number (dosage) is not binary
– Deletion (0,1), normal copy (2) and duplication (3,4+)– SNP collapsing methods assume binary event
(i.e., mutant allele vs. not) and only keep track of number of “events”
2. CNV polymorphisms are multi-faceted– CNVs can vary in dosage, length and details of
gene intersections– Each of these ”features” affects CNVs’ impact on
disease risk. – SNP collapsing methods target only on one
feature (i.e., mutation burden).
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3. Etiological heterogeneity is often observed in CNVs – Different dosage may have different effects
Ex. 22q11.2 deletion is a risk factor for SCZ (Bassett et al. 2005; Murphy et al. 1999) whereas 22q11.2 duplication is a protective factor (Rees et al. 2014)
Ex. In gene VIPR2, triplication has higher risk than duplication for SCZ (Vacic et al. 2011)
– Collapsing with random effects methods have greater potentials than fixed effect methods for CNV analyses (for between-locus heterogeneity)
– Cautions are still needed for within-locus heterogeneity
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Challenges in CNV Collapsing Analysis--- Cautions about applying SNP collapsing methods
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Current CNV Collapsing Methods(All are fixed effects methods)
1. PLINK Burden Tests (International Schizophrenia Consortium 2008; Kirov et al. 2009)– Dichotomize CNV genotypes based on the event of
interests, e.g.,• CNV () vs. no CNVs ()• Del (<2) vs. No Del• Dup (>2) vs. No Dup• Genes intersected (GI) by CNVs vs. no GI
– Compare the event rates between cases and controls – Drawbacks:
• Need to dichotomize data based on event of interests• Do not address the issue of etiological heterogeneity• Only evaluate marginal effects of a CNV feature, which
subjects to spurious association (Raychaudhuri et al. 2010)
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Cases ControlsScenario CNV rate Mean size (kb) CNV rate Mean size (kb)
S0 0.25 100 0.25 100S1 0.25 100 0.05 100S2 0.25 60 0.25 100S3 0.25 100 0.05 60S4 0.25 60 0.05 100
Under no GI effect (Raychaudhuri et al. 2010) 14
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Current CNV Collapsing Methods2. PLINK Enrichment Tests (Raychaudhuri et al. 2010)
–
– Pros: assess conditional effect of CNV features and avoid spurious association
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Total # of CNVs
# of genes intersected (GI) by a CNVMean CNV size
(kb)
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Cases ControlsScenario CNV rate Mean size (kb) CNV rate Mean size (kb)
S0 0.25 100 0.25 100S1 0.25 100 0.05 100S2 0.25 60 0.25 100S3 0.25 100 0.05 60S4 0.25 60 0.05 100
Under no GI effect (Raychaudhuri et al. 2010) 16
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Current CNV Collapsing Methods2. PLINK Enrichment Tests (Raychaudhuri et al. 2010)
–
– Pros: assess conditional effect of CNV features and avoid spurious association
– Cons: • Need to dichotomize data based on event of
interests• Do not address the issue of etiological
heterogeneity
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Total # of CNVs
# of genes intersected (GI) by a CNVMean CNV size
(kb)
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Proposed CNV Collapsing Method
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Plan
• Use random effects model approaches– To account for between-locus and within-locus
etiological heterogeneity• Model multiple features of CNVs
– To assess the conditional effect of a CNV feature• Accommodate multi-nominal nature of dosage
– To avoid dichotomizing data
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(0) Start with a PLINK format CNV file
(1) Define CNV region (CNVR): – Clusters of CNV segments with ≥1bp overlap
– Retain region-specific effect when collapsing
1. Input Data Format
CNVR2CNVR1
12345…
--------------------------------------------------------------------------------------------------
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(2) Create design matrix for each CNV feature: dosage, length, and gene intersection– Dosage (DS) :
– Length (Len):
1. Input Data Format
¿CNVR CNVR
0,1,2,3,4}
¿CNVR CNVR
length∈kb
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(2) Create design matrix for each CNV feature: dosage, length, and gene intersection– Gene intersection (GI) :
1. Input Data Format
¿Gene Gene
∈ { 0 : no GI1 :GI by a Del2 :GI by a Dup}
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• For subject , be the continuous or binary trait, be a covariate vector including the intercept, and design vector of feature ,
• Model
• Assume exponential family with density
where and
models the effect of CNV feature
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2. Model
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• Example of – Ex. Linear regression: – Ex. Random effect: and – Ex. In Raychaudhuri et al (2010),
• (total of CNVs of subject ) • ( of GI by CNV for subject ).
• Propose to model the covariates and background CNV features using fixed effects and model the CNV feature of interests using random effects
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2. Model
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• GLM Model:
where matrix with
similarity between – mean CNV length in kb
– Dosage effect can be evaluated by testing – Test statistic: follows a weighted distribution
Example: Assessing Dosage Effect
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• The GLMM has a direct connection with kernel machine regression (Kwell et al. 2008; Wu et al. 2010) and gene-trait similarity regression (Tzeng et al. 2009; 2011)
• Under the kernel machine framework,
the GLMM is equivalent to set
with being the unknown parameters (the dual representation)• Under the similarity regression framework,
regression coefficient of genetic similarity that is quantified by the
similarity metric .
Remark 1: Connection with Other Random Effects Methods
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Use the -th order polynomial function
is the pre-specified weight for locus based on, e.g., MAF• Cannot directly use in the kernel function
(both and are deviated from “normal reference”)• Solution: factorize dosage
– for – for 3– Then, which retains dosage-specific effect when
collapsing
Remark 2: Quantifying Similarity b/w
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Simulation Studies
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Simulation Scheme• Obtain CNV data from TwinGene Project (Heijmans 2005;
Silventoinen et al. 2006)– Cross-sectional sampling design
– 2000 unrelated samples (rarest CNV = )
– 1757 CNVRs
– 688 genes (69 genes intersected by CNVs)
– Sample with replacement to form an individual’s CNV
– Determine based on CNV features of interests
– Simulate individuals (1000 cases and 1000 controls)
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Simulation Scheme
Scheme A. Different dosage effects of Dup and Del
A1. Between-locus heterogeneity
– Randomly select 300 Dup-only CNVRs and 300 Del-only CNVRs as causal loci
A2. Within-locus heterogeneity
– Select the 38 CNVRs with both Dup and Del as causal
Scheme B. Different gene-Intersection effect of Dup and Del (i.e., heterogeneous effect of genes intersected by Dup and by Del)
B1. Across-gene heterogeneity
– Randomly select 26 genes with Dup intersection on only and 26 genes with Del intersection only as causal
B2. Within-gene heterogeneity
– Select the 8 genes with both Dup and Del intersection as causal
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Type I Error for (A) Dosage Analysis
• Compare the proposed GLMM methods with
plink.all = PLINK CNV rates
plink.dup = PLINK Duplication rates
plink.del = PLINK Deletion rates
• Type I error rates:
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Model GLMMPlink.a
llplink.dup Plink.del
Between-Locus
Heterogeneity
0.035 0.046 0.057 0.041
Within-Locus Heterogeneit
y0.041 0.051 0.057 0.043
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Simulation Scheme
Scheme A. Different dosage effects of Dup and Del
A1. Between locus heterogeneity
– Randomly select 300 Dup-only CNVRs and 300 Del-only CNVRs as causal
A2. Within locus heterogeneity
– Select the 38 CNVRs with both Dup and Del as causal
Scheme B. Different gene-intersection effect of Dup and Del
B1. Across-gene heterogeneity
– Randomly select 26 genes with Dup intersection only and 26 genes with Del intersection only as causal
B2. Within-gene heterogeneity
– Select the 8 genes with both Dup and Del intersection as causal
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Type I Error for Gene Intersection (GI) Analysis
• Compare the proposed GLMM methods with
PLINK Enrichment test (Raychaudhuri et al. 2010)
• Type I error rates:
33
Model GLMM Plink.enrichment
Between-Locus
Heterogeneity0.041 0.044
Within-Locus Heterogeneity 0.043 0.051
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Power Analysis for (A) Dosage Effects
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Po
wer
(v
s. p
link
2 si
ded
)35
50% Dup causal (Del causal) are harmful and 50% are protective
All Dup causal are harmfulAll Del causal are protective
All Dup causal are protectiveAll Del causal are harmful No Heterogeneity
A1. (Dosage effect) Between-Locus Heterogeneity
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A2. (Dosage effect) Within-Locus HeterogeneityP
ow
er
(vs.
plin
k 2
sid
ed)
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B. Power Analysis for (B) GI Effects
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B1. (GI effect) Between-Gene HeterogeneityP
ow
er
(vs.
plin
k.en
rich
men
t)38
50% Dup causal (Del causal) are harmful and 50% are protective
All Dup causal are harmfulAll Del causal are protective
All Dup causal are protectiveAll Del causal are harmful No Heterogeneity
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B2. (GI effect) Within-Gene HeterogeneityP
ow
er
(vs.
plin
k.en
rich
men
t)39
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SummaryFor CNV collapsing analysis:• Developments in SNP collapsing can be applied in CNV collapsing with
modification to account for the nature of CNVs, e.g., defining “locus” using CNVR or gene,
calculating similarity based on factorized dosage / GI details, adjust for background CNV features
• Random effect modeling has more potential to address etiological heterogeneity– For DS, random effects model has robustness across different
scenarios– For GI, GLMM is more powerful than plink.enrichment
• Note that GLMM has the same model as plink.enrichment except that GI effect is modeled using random effect with factorized coding
• Current work: a fixed-effect imputation method to speed up the EM computation (for estimation the variance components) when using random effects on all CNV features
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Testing with
Type I error rate ( at nominal level 0.05
Power ( at nominal level 0.05
Fixed-effect Imputation
EM Algorithm
Fixed-effect Imputation
EM Algorithm
0.051
(4.9 min)
0.048
(32.6 min)
0.282
(2.2 min)
0.287
(18.7 min)
0.052
(5.8 min)
0.049
(18.2 min)
0.278
(2.4 min)
0.282
(12.0 min)
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Thank you
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Kirov et al 2009
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Cases ControlsScenario CNV rate Mean size (kb) CNV rate Mean size (kb)
S0 0.25 100 0.25 100S1 0.25 100 0.05 100S2 0.25 60 0.25 100S3 0.25 100 0.05 60S4 0.25 60 0.05 100
Under no GI effect (Raychaudhuri et al. 2010)
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Multi-faceted Nature of CNVs
Kirov et al 2009
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A2. (Dosage effect) Within-Locus HeterogeneityP
ow
er
(vs.
plin
k 2
sid
ed)
48
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50% Dup causal (Del causal) are harmful and 50% are protective
Po
wer
(v
s. p
link
1 si
ded
)49
All Dup causal are harmfulAll Del causal are protective
All Dup causal are protectiveAll Del causal are harmful No Heterogeneity
A1. (Dosage effect) Between-Locus Heterogeneity