Mining for Low-abundance Transcripts in Microarray Data

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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

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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

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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

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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

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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

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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)

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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

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0. acquire data Q, B
7. standardize ZY center spread
1. adjust for background AQ B
6. center spread
2. rank order genes Rrank(A)/(n1)
Y contrast
3. normal scores Nqnorm(R)
X mean
5. mean intensity Xmean(N)
4. contrast conditions YN1 N2
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Normal Scores Procedure

• adjusted expression A Q B
• rank order R rank(A) / (n1)
• normal scores N qnorm( R )
• average intensity X (N1N2)/2
• difference Y N1 N2
• variance Var(Y X) ??2(X)
• standardization S Y ?(X)/?(X)

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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(gh?)bd?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(gh?)?
• symmetric measurement error ??B ?Q

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Motivate Normal Scores (cont.)

• adjusted measurements A Q B d?G?
• log expression level log(G) gh?
• gene signal g 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 Nlog(G)
• normal scores almost as good

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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

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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(YX) ? ?2(X)
• can force ?2(X) to be decreasing
• similar idea for median
• E(YX) ? ?(X)

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Motivation for Spread

• log expression level log(G) gh?
• 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 g1g2g
• Var(Yg) ?2(g)
• g ? X suggests condition on X instead, but
• Var(Y X) not exactly ?2(X)
• cannot be determined without further assumptions

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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

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Robust Spread Estimation
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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 1.9510-6
• differential expression if S gt 4.62
• differential expression if Y ?(X) gt 4.62?(X)
• too conservative? weight by X?
• Dudoit (2000)

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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)/(n1),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

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Success in Capture
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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

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Capturing Changed Genes No Noise
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Capturing Changed Genes Noise
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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

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E. coli with IPTG-b
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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

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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

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Low Abundance Genes for Obesity
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Microarray ANOVAs

• Kerr (2000)
• gene by condition interaction
• Nijk genei conditionj geneconditionij
  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
• geneconditionij differential expression
• allow variance to depend on genei main effect
• replication to improve precision, catch gross
  errors

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Microarray Random Effects

• variance component for non-changing genes
• robust estimate of MS(GC) 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

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Obesity Genotype Main Effects
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Microarray QTLs

• condition may be genotype
• whole organism or pattern of genes
• genotype may be inferred rather than known
  exactly
• Nijk genei QTLj geneQTLij 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)