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Fei Zou Department of Biostatistics University of North Carolina-Chapel Hill

Bayesian Variable Selection in Semiparametric Regression Modeling with Applications to Genetic Mappping. Fei Zou Department of Biostatistics University of North Carolina-Chapel Hill Email: fzou@bios.unc.edu June 2012 Finland.

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Fei Zou Department of Biostatistics University of North Carolina-Chapel Hill

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  1. Bayesian Variable Selection in Semiparametric Regression Modeling with Applications to Genetic Mappping Fei Zou Department of Biostatistics University of North Carolina-Chapel Hill Email: fzou@bios.unc.edu June 2012 Finland

  2. http://www.cs.unc.edu/Courses/comp590-090-f06/Slides/CSclass_Threadgill.ppthttp://www.cs.unc.edu/Courses/comp590-090-f06/Slides/CSclass_Threadgill.ppt

  3. The Central Dogma of Molecular Biology

  4. tall short • Significant difference in genotype distributions? http://psb.stanford.edu/psb06/presentations/association_mapping.pdf • Copied (with modifications) from psb.stanford.edu/psb06/presentations/association_mapping.pdf

  5. Mendel’s Experiment

  6. Mendel’s Experiment

  7. Experimental Crosses: F2 Parents P1 P2

  8. Experimental Crosses • F2 Backcross(BC) P2 P1 P1 P2 AA AA BB BB P1 F1 F1 F1 AA AB AB AB BB AB AB AB AA AB F2: BC:

  9. F2 Data Format 0: homozygous AA, 2: homozygous BB, 1: heterozygote AB.

  10. Data Structure • For each subject i (i=1,2,…,n) • Phenotype: yi • Genotypes: xij (coded as 0, 1, 2 for genotypes AA, AB and BB, respectively) at marker j(j=1,2,…,m) • Genetic map: locations of markers • Other non-genetic covariates, such as age, sex, environmental conditions

  11. Locations of markers

  12. Linkage Analysis • Quantitative trait loci (QTL): a particular region of the genome containing one or more genes that are associated with the trait being assayed or measured

  13. QTL Mapping of Experimental Crosses • Single QTL Mapping • Single marker analysis • Interval mapping: Lander & Botstein (1989, Genetics) • Multiple QTL mapping • Composite interval mapping • Multiple interval mapping • Bayesian analysis

  14. Single Marker Analysis

  15. Correlations of marker genotypes in experimental crosses

  16. Interval Mapping • Traditional QTL mapping method • Treat QTL position as unknown and use marker genotypes to infer conditional probabilities of QTL genotypes • Profile LOD scores calculated across whole genome • LOD score is a measure for strength of support for QTL • LOD = LRT/4.8 • In any region where the profile exceeds a (genome-wide) significance threshold, a QTL is declared at the position with the highest LOD score.

  17. Profile LOD

  18. QTL • Old believe: one trait one gene • very unlikely • Most traits have a significant environmental exposure component • The vast majority of biological traits are caused by complex polygenic interactions • also context dependent

  19. Multiple QTL Mapping • Most complicated traits are caused by multiple (potentially interacting) genes, which also interact with environmental stimuli • Single QTL interval mapping • Ghost QTL • Low power if multiple QTLs affect the trait

  20. Two QTL Data Two QTL with opposite effects Two QTL with effects in same direction

  21. Multiple QTL Mapping • Available Methods • Composite interval mapping: searching for a putative QTL in a given region while simultaneously fitting partial regression coefficients for "background markers" to adjust the effects of other QTLs outside the region • which background markers to include; window size etc • Multiple interval mapping: fitting multiple QTLs simultaneously • Computationally very intensive; how many QTLs to fit?

  22. Multiple QTL Mapping

  23. Multiple QTL Mapping

  24. Multiple QTL Mapping

  25. Bayesian QTL Mapping • Reversible jump Markov chain Monte Carlo (MCMC) (Green 1995): treat the number of QTLs as a parameter • Change of dimensionality, the acceptance probability for such dimension change, which in practice, may not be handled correctly (Ven 2004) • Bayesian variable selection procedures • composite model space (Yi 2004) • stochastic search variable selection (SSVS) (George and McCulloch 1993)

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