1. Association Study: Binomial Case
GEE & GLMM
Jinseob Kim
GSPH, SNU
July 2, 2014
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2. Contents
1 Correlated = Not Independent
Concept
Example
2 GEE & GLMM Basic
Basic Linear Regression
GEE
GLMM
Comparison
3 GEE & GLMM in GWAS
Concepts of GWAS
Genetic Correlation
Use GEE & GLMM
4 Conclusion
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3. Objective
1 Correlated data structure| ttä.
2 GEE, GLMMX P, õµ, (tÐ t ttä.
3 GWASÐ GEE, GLMMX ©äD ttä.
4 Binomial caseÐ GEE, GLMMD t©XÀ »hD Àä.
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4. Correlated = Not Independent
Contents
1 Correlated = Not Independent
Concept
Example
2 GEE GLMM Basic
Basic Linear Regression
GEE
GLMM
Comparison
3 GEE GLMM in GWAS
Concepts of GWAS
Genetic Correlation
Use GEE GLMM
4 Conclusion
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5. Correlated = Not Independent Concept
iid??
i iid N(0; 2) or N(0; 2In)
Independent
Identically distributed
i N(0; 2
i )
Independent
Not Identically distributed
@ ¨Ñèt DÈä!!
äL ÜÐ..
Jinseob Kim (GSPH, SNU) Association Study: Binomial Case July 2, 2014 5 / 45

6. Correlated = Not Independent Concept
Variance-covariance matrix
var () =
0
BBB@
2 0 0 0
0 2 0 0
...
...
...
. . .
...
0 0 0 2
1
CCCA
= 2
0
1 0 0 0
0 1 0 0
BBB@
...
...
...
. . .
...
0 0 0 1
1
CCCA
= 2In
‰, covariance 0 DÌ ƒt X˜|Ä ˆt correlated data!!
‰, ÁÄ 0 DÌ ƒt X˜|Ä ˆt correlated data!!
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7. Correlated = Not Independent Example
Repeated Measure
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8. Correlated = Not Independent Example
Clustered/Multilevel study
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9. Correlated = Not Independent Example
Serial Correlation
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10. Correlated = Not Independent Example
Familial structure in Genetic Study
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11. Correlated = Not Independent Example
Genetic correlation
0
BBB@
1 12 13 1n
21 1 23 2n
...
...
...
. . .
...
n1 n2 n3 1
1
CCCA
0
1 0:5 0:25 0
0:5 1 1 0:5
BBB@
...
...
...
. . .
...
0 0:5 0 1
1
CCCA
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12. GEE GLMM Basic
Contents
1 Correlated = Not Independent
Concept
Example
2 GEE GLMM Basic
Basic Linear Regression
GEE
GLMM
Comparison
3 GEE GLMM in GWAS
Concepts of GWAS
Genetic Correlation
Use GEE GLMM
4 Conclusion
Jinseob Kim (GSPH, SNU) Association Study: Binomial Case July 2, 2014 12 / 45

13. GEE GLMM Basic Basic Linear Regression
Remind

14. estimation in linear regression
1 Ordinary Least Square(OLS): semi-parametric
2 Maximum Likelihood Estimator(MLE): parametric
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15. GEE GLMM Basic Basic Linear Regression
Least Square(Œñ•)
ñiD Œ: y Ü1Ð D”Æä.
Figure. OLS Fitting
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16. GEE GLMM Basic Basic Linear Regression
Likelihood??
¥Ä(likelihood) VS U`(probability)
Discrete: ¥Ä = U` - ü¬ X8 1˜, U`@ 16
Continuous: ¥Ä != U` - 01 Ð + X˜ QXD L 0.7|
U`@ 0...
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17. GEE GLMM Basic Basic Linear Regression
Maximum likelihood estimator(MLE)