Association Tests for Rare Variants Using
Sequence Data
Guimin Gao, Wenan Chen, & Xi Gao
Department of Biostatistics, VCU
Introduction to Association tests: two
hypotheses
 Common variant-common disease
 Common variant: Minor allele frequencies (MAF) >= 5%
 Using linkage disequilibrium(LD)
 Rare variant-common disease
 Rare variant: MAF < 1% (or 5%)
 High allelic heterogeneity: collectively by multiple rare
variants with moderate to high penetrances
 Associations through LD would not be suitable
Association tests for Common variants
 Test a single marker each time
 Cochran-Armitage’s trend test (CATT) (assuming additive
(ADD))
 Power: High for additive (ADD) or Multiplicative (MUL); low recessive
(REC) or Dominant (DOM)
 Genotype association test (GAT) using chi-square statistic
 Power: a little lower for ADD, higher for REC
 MAX3 = maximum of three trend test statistics across the
REC, ADD, and DOM models (Freidlin et al. 2002 Hum Hered.)
 Power: lower than CATT under ADD
 higher than CATT & CAT under REC
Association tests for Common variants
 Test for single marker (CATT, GAT, & MAX3)
 Low power when MAF <10%
 No power for rare variants with MAF<1%
 Multivariate test
 Considering a group of variants (ex. SNPs in a gene) each time
 Multiple logistic regression (or Hotelling test, Fisher’s product)
Logit
 0 
k

x ij 
j
j 1
 Xij = 0, 1, 2, the count. of the minor alleles of indiv i at locus j
 Power: higher than single-marker test;
still very low due to large d.f = No. of SNPS = k
 Need new methods for rare variants
 Collapsing SNPs into a single marker to reduce d.f.
Outline
 Introduction to association tests
 Three well-known collapsing methods for rare
variants: CAST, CMC, & Weighted Sum methods
 An evaluation using GAW 17 data
 Extension to the three collapsing methods
 Future research
Three association tests for Rare variants
 Collapsing a set of rare variants (into a single marker)
 A cohort allelic sums test (CAST) (Morgenthaler & Thilly
2007, Mutat. Res.)
 Combined Multivariate and Collapsing (CMC) (Li &
Leal, 2007, AJHG)
 Division into subgroups, collapsing in each subgroup
 Weighted Sum statistic (Madsen & Browning, 2009; PloS
Genet. Price et al. 2010, AJHG)
A cohort allelic sums test (CAST)
 A group of n variants (SNPs) in a unit (ex. one gene, LD
block)
 Collapsing the genotypes across the variants
 Indicator coding for individual j
 xj = 1, if rare alleles present at any of the n variants;
 xj = 0, otherwise
 Testing if the proportions of individuals with rare variants (xj
= 1) in cases and controls differ
 Higher power than method testing single variant each time
 Only for rare variants
Combined Multivariate and Collapsing (CMC)
Method (Li & Leal 08)
 Consider SNPs in a unit with MAF< a threshold (0.01 or
0.05)
 Division and Collapsing
 Divided into several sub-groups based on the MAF
 Ex. Subgroups : (0, 0.001], [0.001, 0.005), [0.005, 0.01)
 SNPs are collapsed in each sub-group
 xij = 1, if indiv j has rare alleles present in the i-th subgroup;
 xij = 0, otherwise
Combined Multivariate and Collapsing (CMC)
Method (Li & Leal 08)
 Multivariate test of collapsed sub-groups
 Hotelling T2 test, MANOVA, Fisher’s product method
 Power: often higher than CAST
 Different threshold may have different power
Weighted Sum Method (Madsen & Browning 09)
 A group of variants (SNPs) in a unit
 A weight for SNP i by the S.t.d of No. of minor alleles in the
sample
wi  n i  q i (1  q i )
 qi is the minor allele freq in controls
 Calculate a weighted genetic score for indiv j
L
vj 

I ij / w i
i 1
 Iij = 0, 1, 2, the count of the minor allele of indiv i at locus j
 Obtain the Rank (Vj); Sum of the ranks of affected indivs
x
 rank ( v
j A
j
)
Permutation for p-value estimation
 From observed data:
x
 rank ( v
j
)
j A
 Permutation to estimate p-value:
 Phenotype labels are permuted 1000 times, x1, …x1000
 Calculate the mean (μ) and standard deviation (σ) of 1000 xs
z 
x  u

 Assume z ~ N(0, 1) under null hypothesis
 Obtain the p-value from N(0, 1)
 Fast, p-value ~U[0,1]
Weighted Sum Method (Madsen & Browning 09)
 Power comparison:
 Simulations assuming genotypic relative risk is proportion to
MAF at disease loci (Madsen & Browning 09)
 Weighted Sum Method (WSM) > CMC > CAST
 (WSM) > CMC may not be true in other situations
 Can be applied to rare variants & common variants
 Disadvantage:
 Give very high weights to very rare alleles (singleton), very low
weights to common variants.
An evaluation of the CMC method and Weighted
sum method by using GAW 17 data
 Both methods are powerful (based on the authors’ simulation)
 Our evaluation based on simulated datasets from GAW 17
 GAW 17 data:
 a subset of genes with real sequence data available in the 1000
genome project
 Simulated phenotypes
 Unrelated individuals, families
 Dataset of 697 unrelated individuals
 24487 SNPs in 3205 genes from 22 autosomal chromosomes
 Only test for the 2196 genes with non-synonymous SNPs
GAW 17 dataset of unrelated individuals
 Four phenotypes: Q1, Q2, Q4 and disease status.
 Q1, Q2, and Q4 are quantitative traits
 Q1 associated with 39 SNP in 9 genes,
 Q2 associated with 72 SNPs in 13 genes
 Q4: not related to any genes
 Disease status is a binary trait: affected or unaffected, associated
with 37 genes
 200 simulated phenotype replicates
 Only one replicate of genotype data (original data)
Transforming Phenotypes
 Methods: case-control design
 Transform Q1, Q2, Q4 into binary traits
 Splitting at the top 30% percentile of the distributions
Criteria for evaluation of Tests
 Familywise error rate (FWER)
 2196 genes with non-synonymous SNPs, 2196 tests
 2196 null hypotheses Hj0: gene not associated with the trait
 Q1 associated in 9 genes, 9 null hypotheses are not true.
 (2196-9) null hypotheses are true
 FWER = Pr(reject at least one true null hypothesis) = Nf/200
 Nf : No. of replicates, at least one true hypothesis are rejected
 Average Power
 Mean of power for all the 9 genes that affect the phenotypes
 Evaluating power: Q1, Q2, Disease
 Evaluate FWER: Q4
Distribution of MAF in the GAW 17 dataset
Figure 1. Distribution of MAF of 24487 SNPs in GAW 17
Figure 1. Group SNPs based on MAFs for
CMC
0 - 0.01
0.01 - 0.1
Similar to Madsen & Browning (2009)
>=0.1
Table 1: Average power
Traits
CMC method
Weighted sum
method
Q1
0.144
0.112
Q2
0.00615
0.00308
Disease
0.00444
0.00500
Table 2: FWER (nominal α = 0.05)
Trait
CMC method
Weighted sum
method
Q4
0.115
0.0100
• CMC has FWER inflation
• Population stratification or admixture,
Samples from Asian, Europe,…
• Relatedness among samples
•
Similar results in Power and FWER were reported at GAW 17
Variable-Threshold Approach (Price et al 2010)
 Given a threshold T, calculate a score for indiv j
L
V
j
(T ) 

I ij
i 1
 Iij = 0, 1, 2, the count of the minor allele of indiv i at locus j
 Calculate the sum of score for cases:
N
V (T ) 
D
V
j
(T )
j 1
 Calculate Z(T) = V(T)/Var(V(T))
 Find T to maximize Z(T), Zmax = max (Z(T))
 Permutation to estimate p-value for Zmax
 Power: >CMC;
Extended to quantitative traits
A weighted approach (Price et al 2010)
 Calculate a weighted score for indiv j
L
V
j


w i I ij
i 1
 Iij = 0, 1, 2
 Calculate the sum of score for cases
N
V 
D
V
j
j 1
 Possible weight
w i  1 / q i (1  q i )
 Power: similar to the weighted sum method (Madsen & Browning 09)
A weighted approach (Price et al 2010)
 Calculate the sum of score for cases
N
V 
L
D
V
j 1
j
V
j


w i I ij
i 1
 Iij = 0, 1, 2
 Calculate weight by the prediction of functional effects
 PolyPhen-2 is used to predict damaging effects of missense
mutations with probabilistic scores.
 Probabilistic scores as weights may reduce the noise of nonfunctional variants.
 Higher Power than other methods
A data-adaptive sum test (Han & Pan 2010, Hum
Hered)
 Logistic model
Logit
 0  c
k

x ij
j 1
 xij = 0, 1, 2, the count of the minor allele of indiv i at locus j
 Effect on opposite directions
Logit
 0  
j
x ij
 If j <0, with p-value < threshold (0.1), change xij
into 2- xij
 Permutation to estimate p-value
Conclusion
 Collapsing methods have higher power than single-marker
test
 For genome-wide data analysis, collapsing methods don’t
have much power after multiple testing adjusting
 Weighted sum methods are promising, need prior
information from biological data
Future research
 Modifying the weighted sum method (in progress)
 Very high weights to very rare variants
 Smoothing weights w’ = 0.5w +0.5 (average of all w)
Thank you