Quantitation of Gene Expression for High-Density Oligonucleotide Arrays: A SAFER Approach Daniel Holder, Bill Pikounis, Richard Raubertas, Vladimir Svetnik, and Keith Soper Biometrics Research Merck Research Laboratories

S cale Matters A dditive F its (probes and chips) E xperimental-Unit Variability R obustness and Resistance

Goals of Data Analysis Which genes have we detected? Which genes have changed ? –Which genes change together? Prerequisites –Quantify transcript abundance (“gene expression index”) –Quantify precision –Assess quality

Our Data Analysis Method Normalize chips for overall fluorescence (based on MM)* Transform data (linear-log hybrid scale) Fit probe-specific model using all chips (highly resistant to outliers)* Normalize for chip bias (scatterplot smooth)* Assess differences (Include between-EU variability, e.g., ANOVA)* * offers opportunities for QC

Fig 1:Hybrid Transformation (knot at c=20) f(x)=x f(x)=c*ln(x/c)+c f(x)=hybrid(0,c) x f(x)

Linear-log Hybrid Scale f(x) = a if x<a =x if x in [a,c) =c*ln(x/c)+c if x  c Typically choose a=0 Value of c chosen for additivity Improved homogeneity of variance For low expression genes compare differences, not ratios

Probe Specific Effects “Probe specific biases…are highly reproducible and predictable, and their adverse effect can be reduced by proper modeling and analysis methods” -Li and Wong (PNAS 2000) Multiplicative model for PM - MM, for each probeset, (i th chip, j th probe) –Resistance achieved by iteratively omitting extreme points (or chips) and refitting using least squares

Probe Specific Effects (Our Approach) For each probeset, resistant, additive fit to PM - MM –Use a fitting procedure that is highly resistant to extreme values (median polish) * * Since logs are undefined for non-positive values and unstable for small values, we use a linear-log hybrid scale

Adjusting for Chip Bias Initial centering of chips Chip bias may depend on gene expression level Plot chip effects vs. Overall expression level (grand median) for each probeset Omit probesets that appear to change Between group |dev|/Within group |dev| Omit probesets in top 25% Fit a resistant scatterplot smoother (loess)

Fig 4: Typical Chip Normalization Plot Grand Median Chip Effects* (Hybrid scale) 5 groups  2 chips/group, 7.1K probesets

Terry Speed questions 3. How do you tell that one approach to quantifying expression at the probe set level (e.g. SAFER), is better than another (e.g. dChip)? Compare on data for which we ‘know’ the answer –Spiking experiments (limited # genes) –Validation (eg TaqMan) –Create POS and NEG groups as best we can. How to compare (depends on down-stream usage) –repeatibility –eg. signal to noise ⇛ t-statistic ⇛ p-value –fold changes

Fibroblast/Adipocyte Mixing Expt Mixture %’s (100/0, 75/25, 50/50, 25/75, 0/100) 3 chips/mix (15 chips total, Mg74A) 3 methods (SAFER, SAFER(log), dCHIP) Create groups of probesets using 100/0 vs. 0/100 –POS (max p < 0.01, correct oligos, n=1049) –NEG (incorrect oligos, n=2611) –p-value from t-test (pooled variance, hybrid scale) We will change the POS, NEG and p-value definitions on some of the later slides

Fibroblast/Adipocyte Mixing Expt (2) Performance based on 75/25 vs 25/75 –p-values from t-test (pooled variance, hybrid) –for POS require same sign as 100/0 vs 0/100 –pos rate, false pos rate (FPR), pos rate vs FPR Linearity?

dChip SAFER log SAFER Fig 5: CDF for 0% vs 100% (all probesets) n = 12,654

POS: maxp < 0.01 (n = 1049) NEG: wrong sequence (n = 2611) 0% vs 100% POS 25% vs 75% POS 0% vs 100% NEG 25% vs 75% NEG SAFER SAFER log dChip Uniform dist. Fig 6: CDFs for POS and NEG probesets

SAFER dChip SAFER log Fig 7: Positive Rate vs ‘False’ Positive Rate 25% vs 75% POS: maxp < 0.01 (n = 1049) NEG: wrong seq. (n = 2611))

SAFER dChip SAFER log POS: maxp < 0.01 (n = 1049) NEG: wrong seq. (n = 2611) Fig 8: Positive Rate vs ‘False’ Positive Rate (log scale) 25% vs 75% log scale

Fig 9: Positive Rate vs ‘False’ Positive Rate (log scale) log scale POS: maxp < 0.01 (n = 1038) NEG: wrong seq. (n = 2611) 25% vs 75%, dChip p-values used for dChip SAFER SAFER log dChip

SAFER dChip SAFER log 25% vs 75% Fig 10: Positive Rate vs ‘False’ Positive Rate (log scale) log scale POS: rank (dChip(p))

Fig 11: Boxplot of R 2 values for POS probesets SAFER SAFER(log) dCHIP R2R2 POS: maxp < 0.01 (n = 1049)

Fig 12: Boxplot of R 2 values for POS probesets exclude 100/0 and 0/100 groups SAFER SAFER(log) dCHIP R2R2 POS: maxp < 0.01 (n = 1049)

Terry Speed questions Response: We don’t know. 1. Do you lose anything not being able to down-weight non-performing probe pairs in the way Li & Wong can with their phi's (ie, probe effect)? Li & Wong SAFER Down-weighting non-performing probes seems like a good idea. Is up-weighting ‘bright’ probes good? (variability, saturation) Possible to incorporate weighting in polishing step.

Terry Speed questions Primary goal is to quantitate mRNA detection (and error). Explicit QC methods aimed at avoiding the effects of aberrant arrays, probes, individual observations are less important when resistant methods are used. SAFER provides same raw materials (fitted values and residuals) for QC as Li and Wong. QC summaries can easily be made available. 2. Is SAFER QC as thorough as Li & Wong's (in detecting aberrant chips, probe-sets, probe pairs)? Response: QC is not as thorough, but::

Conclusions For these data, it appears that the SAFER method performs better than dChip. + Better sensitivity (ROC Curve) + Slightly Better Linearity Caveat: This is one analysis of one dataset.

Acknowledgments Biometrics Research –Bert Gunter Other –David Gerhold (Pharmacology) –John Thompson (Immunology) –Eric Muise (Immunology) –Karen Richards (Drug Metabolism) –Jian Xu (Pharmacology) –Yuhong Wang (Bioinformatics)

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chip probe grand median probe effects chip effects Example Median Polish intensities residuals

Fig 2: Choose c using P-values from Tukey Non-additivity Test P-value Hybrid(0,1)Hybrid(0,20)Hybrid(0,40)Raw Scale 5 groups  2 chips/group, 7.1K probesets

Grand effect Within Group SD Fig 3: Within Group SD, Hybrid Scale 5 groups  2 chips/group, 7.1K probesets

100*Var Between /(Var Between + Var Within ) Fig 9: Between EU variability as a percentage of Total variability All probesetsProbesets with mean>50 (hybrid) Grand Median P=known expressedLine = loess smooth 15 human livers  2 chips/liver, 1.5K probesets

dChip vs SAFER differences 0% vs 100% (all probesets)0% vs 100% (POS probesets) 25% vs 75% (all probesets)25% vs 75% (POS probesets) POS: maxp < 0.01 (n = 1049)

SAFER dChip SAFER log POS: maxp < 0.01 (n = 1049) NEG: wrong seq. & minp > 0.5 (n = 270) 25% vs 75% Positive Rate vs ‘False’ Positive Rate (log scale) log scale