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GEE & GLMM in GWAS

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- 1. Association Study: Binomial Case GEE & GLMM Jinseob Kim GSPH, SNU July 2, 2014 Jinseob Kim (GSPH, SNU) Association Study: Binomial Case July 2, 2014 1 / 45
- 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 Jinseob Kim (GSPH, SNU) Association Study: Binomial Case July 2, 2014 2 / 45
- 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. Jinseob Kim (GSPH, SNU) Association Study: Binomial Case July 2, 2014 3 / 45
- 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 Jinseob Kim (GSPH, SNU) Association Study: Binomial Case July 2, 2014 4 / 45
- 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!! Jinseob Kim (GSPH, SNU) Association Study: Binomial Case July 2, 2014 6 / 45
- 7. Correlated = Not Independent Example Repeated Measure Jinseob Kim (GSPH, SNU) Association Study: Binomial Case July 2, 2014 7 / 45
- 8. Correlated = Not Independent Example Clustered/Multilevel study Jinseob Kim (GSPH, SNU) Association Study: Binomial Case July 2, 2014 8 / 45
- 9. Correlated = Not Independent Example Serial Correlation Jinseob Kim (GSPH, SNU) Association Study: Binomial Case July 2, 2014 9 / 45
- 10. Correlated = Not Independent Example Familial structure in Genetic Study Jinseob Kim (GSPH, SNU) Association Study: Binomial Case July 2, 2014 10 / 45
- 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 Jinseob Kim (GSPH, SNU) Association Study: Binomial Case July 2, 2014 11 / 45
- 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 Jinseob Kim (GSPH, SNU) Association Study: Binomial Case July 2, 2014 13 / 45
- 15. GEE GLMM Basic Basic Linear Regression Least Square(Œñ•) ñiD Œ: y Ü1Ð D”Æä. Figure. OLS Fitting Jinseob Kim (GSPH, SNU) Association Study: Binomial Case July 2, 2014 14 / 45
- 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... Jinseob Kim (GSPH, SNU) Association Study: Binomial Case July 2, 2014 15 / 45
- 17. GEE GLMM Basic Basic Linear Regression Maximum likelihood estimator(MLE)