Sequential Kernel Association Tests for the Combined Effect of Rare and Common Variants

Journal club (Nov/13)SH Lee

Introduction

• Sequence data– Rare and unidentified variants

• Groupwise association tests– Omnibus tests– Burden test, CMC test, SKAT test• Up-weighting for rare, • down-weighting for common• Rare/common variants tested separately

Introduction• This study develops a joint test of rare/common– Combining burden/SKAT test for rare/common

• Can be applied to – whole exome sequencing + GWAS – Deep resequencing of GWAS loci

• Basically can analyse all variants including rare, low-frequency and common variants

• Simulation (type 1 error, power)• Real data, CD and Autism

Materials and Methods

Definition of rare/common• <0.01 rare• 0.01-0.05 low frequency• >0.05 common

Or• <1/sqrt(2*n) rare • >1/sqrt(2*n) common– n = 500, rare MAF < 0.031– n = 10000, rare MAF < 0.007

Materials and Methods

• Testing for the overall effect of rare and common variants– Rare for Burden test– Common for SKAT test

Weighted-sum statisticsFishers method of combining the p values

Weighted-sum statistics

• Within a region (e.g. a gene) having m variants– g(*) is a linear or logistic link function – Alpha is for covariates– X is n x m matrix– Beta is regression coefficient and random variable

Weighted sum score test(Variance component score test)

Taking the first derivative of log-likelihood respect with the variance τ

P-value from κχ2ν

κ is scale parameter, v is degree of freedom

Weighted sum score test(Variance component score test)

Wu et al (2010) AJHG 86: 929; Liu et al (2008) BMC Bioinformatics 8: 292;

Lin (1997) Biometrika 84: 309; White (1982) Econometrica 50: 1

Weighted sum score test(Variance component score test)

• ρ : the correlation between regression coefficients • If perfectly correlated (ρ = 1), they will be all the same after

weighting, and one should collapse the variants first before running regression, i.e., the burden test

• If the regression coefficients are unrelated to each other, one should use SKAT

Lee et al. (2012) AJHG 91: 224

Burden-C, SKAT-C

• Combined test statistic for rare and common– Weighting beta(p,1,25) for rare, – beta(p,0.5,0.5) for common

• Partitioning rare and common variants

Other methods

• Burden-A, SKAT-A– Adaptive combining rare/common– Searching φ for the minimum p-value

• Burden-F, SKAT-F– Fisher’s combination method

Simulation

• Sequence data on 10,000 haplotypes on 1 Mb region

• Calibrated model for the European pop• Random sample of a region of 5 or 25 kb and

simulated data with 1000-5000 individuals • Proportion of cases in the sample is 0.5

Disease model

Methods

Type I error

• The proposed methods agrees with the expectation

Power (separation cut-off)

• Using burden-C test• Power with different separation cut-offs• 1/sqrt(2n) will be used further

Power (proposed methods)

• Power for 8 different tests• The proposed combination tests outperform

Power

• Rare/common causal variants (model 1, 2, 3, 6)– The combination methods perform better

Power

• Common causal variants (model 5)– The combination methods perform better

• Rare causal variants (model 4)– The combination methods perform similarly

Power (proposed methods)

•The proposed combination methods outperform CMC for all 6 disease models•The proposed combination methods outperform the original SKAT for all 6 disease models

Power

•For model 1-4 which include only risk variants• SKAT better than Burden when prop. risk variants is small (10%)• Burden better than SKAT when prop. risk variants is large (30%)

Power

• Model 1-3 which include both rare/common• SKAT-F better than burden-F regardless of prop. risk variants

• Model 5 which include only common risk variants• SKAT better than burden regardless of prop. risk variants

Power

• Adaptive test (SKAT-A, Burden-A)– Perform worse than SKAT-C and Burden-C

• Results for a region of size 5 kb were similar

Real data

• CD NOD2 sequence data – 453 cases, 103 controls– 60 single nucleotide variations (9 of them have >

MAF 0.05)– Because only pooled frequency counts available

for each variants, sequencing data were simulated.

• Autism LRP2 sequencing data– 430 cases, 379 controls

Real data

• The combination methods powerful than others

Discussion

• The proposed combination methods– Partitioning rare/common– Powerful approach– Better than CMC (rare/common partitioning)– Better than original Burden and SKAT test – Extend to family-based designs

Discussion

• T1D HLA region – SKAT (2.7e-43)– Wald test (6.7e-49)– Likelihood ratio test (8.9e-221)

• LD between regions • Multiple different components within a region

• Thanks

Linear SKAT vs individual variant test statistics

• Linear SKAT (lower) and individual variant test (upper) is equivalent

• Three disease model for power comparison