1. Statistical Methods for Rare Variant Association Test Using Summarized Data
Qunyuan Zhang
Ingrid Borecki, Michael A. Province
Division of Statistical Genomics

2. Motivation Next generation sequencing => rare variants
Two types of data
Individual level
Summarized level
Pooled DNA sequencing
Public data (as control)
Subject
Variant
Trait V1 V2 V3 1
case 2 3 4
control 5 6 …
Variant V1 V2 V3
Variant No. in cases 10 8 3
Variant No. in controls 2 1
No. of cases
300
No. of controls
500

3. Models for Individual-level Data
Single-variant test
(Regular GWAS)
Collective/group test
Burden/collapsing test

4. Methods for Individual-level Data
CMC (Li and Leal, 2008)
WSS (Madsen and Browning, 2009)
VT (Price et al, 2010)
aSum (Han and Pan, 2010)
KBAC (Liu and Leal, 2010)
RBT (Ionita-Laza et al, 2011)
PWST (Zhang et al, 2011)
SKAT( Wu et al, 2011)
EREC( Lin et al, 2011) … 4

5. Methods for Summarized Data
Description
Bi-directional
effects
Ref.
EFT
Exclusive Frequency Test
testing mutually exclusive allele/carrier freq. ×
Commonly-used in publications, such as
Cohen et al., 2004
TFT
Total Frequency Test
testing total allele/carrier freq.
CAST
Cohort Allele Sum Test
testing total allele/carrier number
Morgenthaler & Thilly, 2006
C-alpha
testing variance √
Neale et al., 2011

6. An Example of Summarized Data6
Jonathan C. Cohen, et al.
Science 305, 869 (2004) 6

7. An Example of Summarized Data (cont.)
Variant allele
number
Reference allele
Total
Low-HDL group 20
236
256
High-HDL group 2
254 22
490
512 7

8. QQ Plots of Existing Methods (under the null)
EFT TFT
EFT and C-alpha
inflated with false positives
TFT and CAST
no inflation, but need to assume single direction of effects
Objective
More general,
non-inflated, powerful methods …
CAST C-alpha

9. Structure of Summarized data
variant 1
variant 2 … …
variant 3
variant i
variant k
Strategy
Instead of testing total freq./number, we test the randomness of all tables.

10. Exact Probability Test (EPT)
1.Calculating the probability of each table based on
hypergeometric distribution
2. Calculating the
logarized joint
probability (L)
for multiple tables
3. Enumerating all possible
table combinations and L scores
4. Calculating p-value P= Prob.( )

11. Likelihood Ratio Test (LRT)
Binomial distribution
Maximum likelihood
estimation

12. Q-Q Plots of EPT and LRT (under the null)

13. Power Comparison significance level=0.00001
Simulation
Logistic model
N=500, 1000,3000
50% cases
50% controls
5-15 variants
MAF<1%
Positive causal: 80%
(OR=2 to 6)
Neutral :20%
Negative causal:0%
Power
Power
Power
Sample size
Sample size
Sample size

14. Power Comparison significance level=0.00001
Simulation
Logistic model
N=500, 1000,3000
50% cases
50% controls
5-15 variants
MAF<1%
Positive causal: 60%
(OR=2 to 6)
Neutral :20%
Negative causal:20%
(OR=1/6 to 1/2)
Power
Sample size

15. Power Comparison significance level=0.00001
Simulation
Logistic model
N=500, 1000,3000
50% cases
50% controls
5-15 variants
MAF<1%
Positive causal: 40%
(OR=2 to 6)
Neutral :20%
Negative causal:40%
(OR=1/6 to 1/2)
Power
Sample size

16. -LOG10 p-values of 933 cancer-related genes
Application
Cases: 460 ovarian cancer cases, germline exome data, from TCGA
Controls: ~3500 individuals from the NHBLI exome project
-LOG10 p-values of 933 cancer-related genes

17. Individual-level Data Based Methods vs. Summarized Data Based Methods
An interesting question:
If we have individual-level data, but we choose to perform summarized data based analysis, will there be any power gain or loss? 17

18. positive : neutral : negative (%)
Power Comparison individual-level data vs. summarized data N=1000, significance level=
Power
Individual-level
data based
methods:
CMC
Li & Leal, 2008
SKAT
Wu et al., 2011
Variant proportion
positive : neutral : negative (%)

19. (This study has not bee published)
Conclusions
EFT and C-alpha produce inflated p-value.
TFT and CAST produce correct p-value, but lose power in detecting bi-directional effects.
EPT produces correct p-value and maintains power regardless of effect directions, more computer time.
LRT produces slightly biased p-value for small N, can be improved by larger N, similar power of EPT, less computer time, a good alternative for large datasets.
If no confounders need to be modeled, there is no significant loss of power in the use of summarized data
(This study has not bee published)

20. (for providing the TCGA and NHBLI exome data)
Acknowledgements
Dr. Li Ding
Charles Lu
Krishna-Latha Kanchi
(for providing the TCGA and NHBLI exome data)