1 / 33

Mining for Low-abundance Transcripts in Microarray Data

Mining for Low-abundance Transcripts in Microarray Data. Yi Lin 1 , Samuel T. Nadler 2 , Alan D. Attie 2 , Brian S. Yandell 1,3 1 Statistics, 2 Biochemistry, 3 Horticulture, University of Wisconsin-Madison September 2000. Basic Idea.

joylyn
Download Presentation

Mining for Low-abundance Transcripts in Microarray Data

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Miningfor Low-abundance Transcriptsin Microarray Data Yi Lin1, Samuel T. Nadler2, Alan D. Attie2, Brian S. Yandell1,3 1Statistics, 2Biochemistry, 3Horticulture, University of Wisconsin-Madison September 2000

  2. Basic Idea • DNA microarrays present tremendous opportunities to understand complex processes • Transcription factors and receptors expressed at low levels, missed by most other methods • Analyze low expression genes with normal scores • Robustly adapt to changing variability across average expression levels • Basis for clustering and other exploratory methods • Data-driven p-value sensitive to low abundance & changes in variability with gene expression

  3. DNA Microarrays • 100-100,000 items per “chip” • cDNA, oligonucleotides, proteins • dozens of technologies, changing rapidly • expose live tissue from organism • mRNA  cDNA  hybridize with chip • read expression “signal” as intensity (fluorescence) • design considerations • compare conditions across or within chips • worry about image capture of signal

  4. Low Abundance Genes • background adjustment • remove local “geography” • comparing within and between chips • negative values after adjustment • low abundance genes • virtually absent in one condition • could be important genes: transcription factors, receptors • large measurement variability • early technology (bleeding edge) • prevalence across genes on a chip • 0-20% per chip • 10-50% across multiple conditions

  5. Log Transformation? • tremendous scale range in mean intensities • 100-1000 fold common • concentrations of chemicals (pH) • fold changes have intuitive appeal • looks pretty good in practice • want transformed data to be roughly normal • easy to test if no difference across conditions • looking for genes that are “outliers” • beyond edge of bell shaped curve • provide formal or informal thresholds

  6. Exploratory Methods • Clustering methods (Eisen 1998, Golub 1999) • Self-organizing maps (Tamayo 1999) • search for genes with similar changes across conditions • do not determine significance of changes in expression • require extensive pre-filtering to eliminate • low intensity • modest fold changes • may detect patterns unrelated to fold change • comparison of discrimination methods (Dudoit 2000)

  7. Confirmatory Methods • ratio-based decisions for 2 conditions (Chen 1997) • constant variance of ratio on log scale, use normality • anova (Kerr 2000, Dudoit 2000) • handles multiple conditions in anova model • constant variance on log scale, use normality • Bayesian inference (Newton 2000, Tsodikov 2000) • Gamma-Gamma model • variance proportional to squared intensity • error model (Roberts 2000, Hughes 2000) • variance proportional to squared intensity • transform to log scale, use normality

  8. 0. acquire data Q, B 7. standardize Z=Y –center spread 1. adjust for background A=Q – B 6. center & spread 2. rank order genes R=rank(A)/(n+1) Y = contrast 3. normal scores N=qnorm(R) X = mean 5. mean intensity X=mean(N) 4. contrast conditions Y=N1 –N2

  9. Normal Scores Procedure adjusted expression A = Q – B rank order R = rank(A) / (n+1) normal scores N = qnorm( R ) average intensity X = (N1+N2)/2 difference Y = N1 – N2 variance Var(Y | X) 2(X) standardization S = [Y –(X)]/(X)

  10. Motivate Normal Scores • natural transformation to normality is log(A) • background intensity B = bd +B • measured with error  • attenuation d may depend on condition • gene measurement Q = [exp(g+h+)+b]d+Q • gene signal g • degree of hybridization h: • intrinsic noise  (variance may depend on g) • attenuation  (depends thickness of sample, etc.) • subtract background: A = Q – B • adjusted measurements A = dexp(g+h+)+ • symmetric measurement error =B –Q

  11. Motivate Normal Scores (cont.) • adjusted measurements: A = Q – B = dG+ • log expression level: log(G) = g+h+ • gene signalg confounded with hybridization h • unless hybridization h independent of condition • G is observed if • no measurement error  • no dye or array effect (no attenuation d) • no background intensity • natural under this model to consider N=log(G) • normal scores almost as good

  12. Robust Center & Spread • genes sorted based on X • partitioned into many (about 400) slices • containing roughly the same number of genes • slices summarized by median and MAD • MAD = median absolute deviation • robust to outliers (e.g. changing genes) • MAD ~ same distribution across X up to scale • MADi = i Zi, Zi ~ Z, i = 1,…,400 • log(MADi ) = log(i) + log(Zi) • median ~ same idea

  13. Robust Center & Spread • MAD ~ same distribution across X up to scale • log(MADi ) = log(i) + log(Zi), I = 1,…,400 • regress log(MADi) on Xi with smoothing splines • smoothing parameter tuned automatically • generalized cross validation (Wahba 1990) • globally rescale anti-log of smooth curve • Var(Y|X)  2(X) • can force 2(X) to be decreasing • similar idea for median • E(Y|X)  (X)

  14. Motivation for Spread • log expression level: log(G) = g+h+ • hybridization h negligible or same across conditions • intrinsic noise  may depend on gene signal g • compare two conditions 1 and 2 • Y = N1 – N2 log(G1) – log(G2) = g1 –g2+ 1 -2 • no differential expression: g1=g2=g • Var(Y|g) = 2(g) • gX suggests condition on X instead, but: • Var(Y | X) not exactly 2(X) • cannot be determined without further assumptions

  15. Simulation of Spread Recovery • 10,000 genes: log expression Normal(4,2) • 5% altered genes: add Normal(0,2) • no measurement error, attenuation • estimate robust spread

  16. Robust Spread Estimation

  17. Bonferroni-corrected p-values • standardized normal scores • S = [Y –(X)]/(X) ~ Normal(0,1) ? • genes with differential expression more dispersed • Zidak version of Bonferroni correction • p = 1 – (1 – p1)n • 13,000 genes with an overall level p = 0.05 • each gene should be tested at level 1.95*10-6 • differential expression if S > 4.62 • differential expression if |Y –(X)| > 4.62(X) • too conservative? weight by X? • Dudoit (2000)

  18. Simulation Study • simulations with two conditions • 10,000 genes • g1 ,g2 ~ Normal(4,2) for nonchanging genes • 5% with differential expression • gc ~ Normal(4,2) + Normal(3-rank(X)/(n+1),1/2) • up- or down-regulated with probability 1/2 • intrinsic noise  ~ Normal(0,0.5) • attenuation  = 1 • measurement error variance= 0, 1, 2, 5, 10, 20

  19. Success in Capture

  20. Comparison of Methods • differential expression for two conditions • Newton (2000) J Comp Biol • Gamma-Gamma-Bernouli model • Bayesian odds of differential expression • Chen (1997) • constant ratio of expressions • underlying log-normality • normal scores (Lin 2000) • some (unknown) transformation to normality • robust, smooth estimate of spread & center • Bonferroni-style p-values

  21. Capturing Changed Genes: No Noise

  22. Capturing Changed Genes: Noise

  23. Comparison with E. coli Data • 4,000+ genes (whole genome) • Newton (2000) J Comp Biol • Bayesian odds of differential expression • IPTG-b known to affect only a few genes • ~150 genes at low abundance • including key genes

  24. E. coli with IPTG-b

  25. Diabetes & Obesity Study • 13,000+ gene fragments (11,000+ genes) • oligonuleotides, Affymetrix gene chips • mean(PM) - mean(NM) adjusted expression levels • six conditions in 2x3 factorial • lean vs. obese • B6, F1, BTBR mouse genotype • adipose tissue • influence whole-body fuel partitioning • might be aberrant in obese and/or diabetic subjects • Nadler (2000) PNAS

  26. Low Abundance Obesity Genes • low mean expression on at least 1 of 6 conditions • negative adjusted values • ignored by clustering routines • transcription factors • I-kB modulates transcription - inflammatory processes • RXR nuclear hormone receptor - forms heterodimers with several nuclear hormone receptors • regulation proteins • protein kinase A • glycogen synthase kinase-3 • roughly 100 genes • 90 new since Nadler (2000) PNAS

  27. Low Abundance Genes for Obesity

  28. Microarray ANOVAs • Kerr (2000) • gene by condition interaction • Nijk = genei + conditionj + gene*conditionij + rep errorijk • conditions organized in factorial design • experimental units may be whole or part of array • genes are random effects • focus on outliers (BLUPs), not variance components • gene*conditionij = differential expression • allow variance to depend on genei main effect • replication to improve precision, catch gross errors

  29. Microarray Random Effects • variance component for non-changing genes • robust estimate of MS(G*C) using smoothed MAD • rescale normal score response N by spread (X) • look for differential expression • or use clustering methods • variance component for replication • robust estimate of MSE using smoothed MAD • look for outliers = gross errors

  30. Obesity Genotype Main Effects

  31. Microarray QTLs • condition may be genotype • whole organism or pattern of genes • genotype may be inferred rather than known exactly • Nijk = genei + QTLj + gene*QTLij + individualijk • QTL genotype depends on flanking markers • mixture model across possible QTL genotypes • single vs. multiple QTL • single QTL may influence numerous genes • epistasis = inter-genic interaction • modification of biochemical pathway(s)

More Related