1. Sequential Kernel Association Tests for the Combined Effect of Rare and Common Variants Journal club (Nov/13) SH Lee

2. 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

3. 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

4. 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

5. Materials and Methods Testing for the overall effect of rare and common variants – Rare for Burden test – Common for SKAT test Weighted-sum statistics Fishers method of combining the p values

6. 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

7. Weighted sum score test (Variance component score test) Taking the first derivative of log-likelihood respect with the variance τ P-value from κχ 2 ν κ is scale parameter, v is degree of freedom

8. 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

9. 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

10. 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

11. Other methods Burden-A, SKAT-A – Adaptive combining rare/common – Searching φ for the minimum p-value Burden-F, SKAT-F – Fishers combination method

12. 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

13. Disease model

14. Methods

15. Type I error The proposed methods agrees with the expectation

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

17. Power (proposed methods) Power for 8 different tests The proposed combination tests outperform

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

19. Power Common causal variants (model 5) – The combination methods perform better Rare causal variants (model 4) – The combination methods perform similarly

20. 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

21. 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%)

22. 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

23. 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

24. 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

25. Real data The combination methods powerful than others

26. 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

27. 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

28. Thanks

29. Linear SKAT vs individual variant test statistics Linear SKAT (lower) and individual variant test (upper) is equivalent

30. Three disease model for power comparison