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A Quantitative Overview to Gene Expression Profiling in Animal Genetics

A Quantitative Overview to Gene Expression Profiling in Animal Genetics. Analysis of (cDNA) Microarray Data : Part IV. Mixed-Model Equations I. Armidale Animal Breeding Summer Course, UNE, Feb. 2006. A Quantitative Overview to Gene Expression Profiling in Animal Genetics.

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A Quantitative Overview to Gene Expression Profiling in Animal Genetics

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  1. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Analysis of (cDNA) Microarray Data: Part IV. Mixed-Model Equations I Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  2. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations Setting the scene (1/3): Kerr & Churchill, 2001 PNAS 98:8961-8965 Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  3. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations Setting the scene (2/3): Wolfinger et al, 2001 J Comp Biol 8:625 Two-Step Mixed-Model Assumes most genes are not DE. Otherwise some important effects are lost. One for each gene! Source: G Rosa 2003. Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  4. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations Setting the scene (2/3): Wolfinger et al, 2001 J Comp Biol 8:625 Two-Step Mixed-Model Step 1. Global Normalisation Step 1. Gene Models Source: G Rosa 2003. Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  5. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations Setting the scene (2/3): Wolfinger et al, 2001 J Comp Biol 8:625 Two-Step Mixed-Model Source: G Rosa 2003. Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  6. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations Setting the scene (3/3): Hoeschele & Li, 2005 Biostatistics 6:183 Joint versus Gene-Specific Mixed-Models • Flexibility on how the (co)variance structure is modelled and different formulations can be compared, eg. Homo- vs Hetero-geneous within-gene variance) • Allows the evaluation of gene-specific treatment contrasts that include main effects • Allows model evaluation and residual analysis • Low Power (fewer degrees of freedom), but exact if: • Genes have the same number of probes in each array; • Residual variance must be homogeneous across genes; and • Large number of genes. Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  7. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations Examples: Joint vs Gene-Specific Mixed-Models Joint AI vs IVF vs NT Embrios Variety has been fitted as an additional fixed effect Gene-Specific (Two-Step) Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  8. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations Illustration: A 1 B 2 Arrays, 5 Genes/Array, Genes spotted five times, 2 Treatments (A, B) 2 1 2 3 4 5 2 3 4 5 1 3 4 5 1 2 4 5 1 2 3 5 1 2 3 4 This could represent a row (or column) of the second array. x 5 (to generate entire data) Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  9. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations Illustration: A 1 B 2 Arrays, 5 Genes/Array, Genes spotted five times, 2 Treatments (A, B) 2 Model: Y = Array + Dye + Gene*Treatment + Error Random SAS Code: DATA test; INFILE ‘h:\UNE_data\Test\c1c2’; INPUT array gene dye $ treat $ intens; RUN; PROC GLM; CLASS array dye gene treat; MODEL intens = array dye gene*treat; RANDOM gene*treat; LSMEANS array dye gene*treat / pdiff; RUN; x 5 (to generate entire data) Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  10. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations Illustration: A 1 B 2 Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  11. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations Illustration: A 1 B 2 Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  12. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations The Diets experiment: Byrne et al, 2005 J Anim Sci 83:1-12 Log2 Intensities yijkgtr = Ci Component of Design (Reference, All-Pairs) + Aj Array slide (1, 2, …, 14) + Dk Dye (Red, Green) + Tt Treatment (Diets: High, Medium, Low) + (AD)jk Array * Dye + Gg Main effect of Gene + (AG)jg Gene * Array + (DG)kg Gene * Dye + (TG)tg Gene * Treatment + ijkgtr Random Error Random effects Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  13. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations Byrne et al, 2005 J Anim Sci 83:1-12 The Diets experiment: • The terms C, A, D, T, and AD account for all effects that are not gene specific, have no biological significance, and the fitting of which aims at normalizing the data by accounting for systematic effects. • The random gene effect G contains the average level of gene expression (averaged over the other factors). • The random gene  array in (AG) models the effects for each spot and it serves to account for the spot-to-spot variability inherent in spotted microarray data. It allows us to extract appropriate information about the treatments and obviates the need to form ratios (Wolfinger et al., 2001). • The random gene  dye in (DG) models the gene specific dye effects occurring when some genes exhibit higher fluorescent signal when labeled with one dye or the other, regardless of the treatment (Kerr et al., 2002). • The effect of interest was the random interaction between genes and diet treatments, (TG) because it captured differences from overall averages that were attributable to specific combination of diet and gene. Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  14. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations The Diets experiment: Byrne et al, 2005 J Anim Sci 83:1-12 Log2 Intensities yijkgtr = Ci + Aj + Dk + Tt + (AD)jk + Gg Main effect of Gene  Between Genes + (AG)jg Gene * Array  B/w G within Array + (DG)kg Gene * Dye  B/w G within Dye + (TG)tg Gene * Treatment  B/w G within Trt + ijkgtr Random Error  Within Gene Decomposition of Total Variance Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  15. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations Byrne et al, 2005 J Anim Sci 83:1-12 The Diets experiment: Log2 Intensities yijkgtr = Ci + Aj + Dk + Tt + (AD)jk + Gg + (AG)jg + (DG)kg + (TG)tg + ijkgtr Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  16. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations Byrne et al, 2005 J Anim Sci 83:1-12 The Diets experiment: REML Estimates %Total Variance Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  17. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations Byrne et al, 2005 J Anim Sci 83:1-12 The Diets experiment: Residual Plots Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  18. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations The Diets experiment: Byrne et al, 2005. J Anim Sci 83:1-12 Measures of (possible) Differential Expression HIGH vs LOW Contrast Alternatively: Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  19. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations The Diets experiment: Byrne et al, 2005. J Anim Sci 83:1-12 %Total Variance (SD = 0.454) ± 2 SD ± 3 SD Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  20. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations The Diets experiment: Byrne et al, 2005. J Anim Sci 83:1-12 Histogram of p-values for a Test of dg assuming Normality (Using 100 bins at 0.01 interval) 331 If we set our cutoff for significance at c = 0.01, we could estimate FDR to be 73.43/331 = 0.32. We estimate 73.43 true Null p-values per bin Armidale Animal Breeding Summer Course, UNE, Feb. 2006

  21. A Quantitative Overview to Gene Expression Profiling in Animal Genetics Mixed-Model Equations Concluding Remarks on DE Genes: • The assumption of Normality of dg is questionable • Hence, resorting to “tabled values” (ie. 2, 3, SD from the mean) could be suboptimal • Instead, using the proportion of the total variation that is attributed to the Gene by Treatment (diet) interaction could be safer option. • We let the mixed-model tell us how many genes are likely to be DE • CLAIM: The proportion of the total variation that is attributed to the Gene by Treatment (diet) interaction allows us to control the FDR • CLAIM: The proportion of the total variation that is attributed to the Gene by Treatment (diet) interaction provides a lower bound for the mixing proportion in the extreme cluster(s) in a model based clustering via mixtures of distributions. Armidale Animal Breeding Summer Course, UNE, Feb. 2006

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