1. Microarray Normalization
Xiaole Shirley Liu
STAT115 / STAT215

2. Affymetrix Microarray Imagine Analysis
Affymetrix GeneChip Operating System (GCOS)
Gridding: based on spike-in DNA
cel file
X Y MEAN STDV NPIXELS
cdf file
Which probe at (X,Y) corresponds to which probe sequence and targeted transcript
MM probes always (X,Y+1) PM

3. Normalization
Try to preserve biological variation and minimize experimental variation, so different experiments can be compared
Assumption: most genes / probes don’t change between two conditions
Normalization can have larger effect on analysis than downstream steps (e.g. group comparisons)

4. Median Scaling Linear scaling
Ensure the different arrays have the same median value and same dynamic range
X' = (X – c1) * c2
array1
array1
array2
array2

5. LOESS
LOcally WEighted Scatterplot Smoothing, more general form is LOESS
Fit a smooth curve
Use robust local linear fits
Effectively applies different scaling factors at different intensity levels
Y = f(X)
Transform X to X' = f(X)
Y and X' are comparable

6. Quantile Normalization
Bolstad et al Bioinformatics 2003
Currently considered the best normalization method
Assume most of the probes/genes don’t change between samples
Calculate mean for each quantile and reassign each probe by the quantile mean
No experiment retain original value, but all experiments have exact same distribution
Probes
Experiments
Mean

7. How to Visualize Microarray Normalization?

8. Dilution Series RNA sample in 5 different concentrations
5 replicates scanned on 5 different scanners
Before and after quantile normalization

9. MvA Plot M=log2R- log2G log2R vs log2G A=(log2R+log2G)/2
Values should scatter
around 0
log2R vs log2G
Values should be
on diagonal

10. Before Normalization
Pairwise MA plot for 5 arrays, probe (PM)

11. After Normalization
Pairwise MA plot for 5 arrays, probe (PM)

12. Gene Expression Index

13. Affymetrix Microarray Expression Index
How to summarize probes in a probeset?
Brighter PM usually carries more information, but not always the case (cross-hybridization)

14. MAS4
GeneChip® older software Microarray Analysis Software 4.0 uses AvgDiff
A: a set of suitable pairs chosen by software
Remove highest/lowest
Calculate mean, sd from remaining probes
Eliminate probes more than 3 sd from mean
Drawback (naïve algorithm):
Can omit 30-40% probes
Can give negative values

15. MAS5 GeneChip® newest version
Tukey Biweight down-weights points far from the estimated center of the data scatter, robust statistics resistant to outliers
CT* (change threshold) a version of MM that is never bigger than PM
If MM<PM, CT* = MM
If MM>PM, estimate typical case (Tukeybiweight) MM for PM (~70% PM)
If typical MMs > PM for, set CT* = PM - 
Works OK but ad hoc

16. Li & Wong (dChip)
Important observation: relative values of probes within a probeset very stable across multiple samples.

17. Model-Based Expression Index
Look at multiple samples at a time, give different probes a different weight
Each probe signal is proportional to
Amount of target sample: qi
Affinity of specific probe sequence to the target: fj q1 q2
Probes
sample 1
sample 2
f1 f2 f3

18. Li & Wong (dChip) Model Iteratively estimate θi and φj to minimize εij
Try to minimize the sum of squared errors
Error
Concentration
Probe affinity
Sample1
Sample2
Sample3 …
φ φ2 φ3
Probe Probe Probe3 … q1 q2 q3

19. RMA = Robust Multi-chip Analysis
Irizarry & Speed, 2003
1: Probe intensity background adjustment
2: Quantile normalize the Log transformed background adjusted PM
3: Robust probe summary

20. RMA Background Subtraction
Observed PM = Signal + Background noise
Signal ~ exponential; BG ~ normal
Background estimated from MM + =

21. Why Log(PM)
Captures the fact that higher value probes are more variable
Assume probe noise is comparable on log scale

22. RMA For each probe set, PMij = qifj Fit the model:
aj is expression index, bj is probe effect
Log2n() stands for logarithm after quantile normalization of n samples

23. RMA Examples… Iteratively refit aj and bj using median polish
Alternately remove (subtract) row and column medians until sum of absolute residuals converges
For complex data structures, can efficiently find a “general picture” of the data
Robust to outliers in large data sets
Similar to dChip, but minimize error at logPM, so less weight on large PMs

24. Gene Expression Index Method Comparison

25. Method Comparison Standard
Spike-ins: introduce markers with known concentration (intensity) to RNA samples
Should cover a broad range of concentrations
Run two samples with and without spike-in, see whether algorithm can detect the spike-in (differential expression)
Dilutions:
Serial dilutions: 1:2, 1:4, 1:8…
Latin square spike-in captures both approaches above
Compare both accuracy qualitatively and expression index quantiatively

26. Latin Square Spike-ins

27. Method Comparison of Spike-in
MAS4
MAS 5
dChip
RMA
Red numbers
indicate spiked
genes
This is the first Lesson in a 3 part series:
Lesson 1 - Introduction to GeneTraffic, and Creating GeneTraffic Projects
Lesson 2 - Microarray Data Assessment
Lesson 3 - Data Analysis Using GeneTraffic

28. Summary Cel file and cdf file. Array normalization: Loess, qnorm
Assumptions
Normalization visualization: MA plots
Gene Expression Index
RMA models probe effect in expression arrays
Use MM to correct background
Qnorm log (PM)
Median polish, model probe behavior to get expression index
Method comparison