1. EPP 245 Statistical Analysis of Laboratory Data
12/19/2019
Two Color Microarrays
EPP 245
Statistical Analysis of
Laboratory Data

2. EPP 245 Statistical Analysis of Laboratory Data
12/19/2019
Two-Color Arrays
Two-color arrays are designed to account for variability in slides and spots by using two samples on each slide, each labeled with a different dye.
If a spot is too large, for example, both signals will be too big, and the difference or ratio will eliminate that source of variability
November 15, 2007
EPP 245 Statistical Analysis of Laboratory Data

3. EPP 245 Statistical Analysis of Laboratory Data
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Dyes
The most common dye sets are Cy3 (green) and Cy5 (red), which fluoresce at approximately 550 nm and 649 nm respectively (red light ~ 700 nm, green light ~ 550 nm)
The dyes are excited with lasers at 532 nm (Cy3 green) and 635 nm (Cy5 red)
The emissions are read via filters using a CCD device
November 15, 2007
EPP 245 Statistical Analysis of Laboratory Data

4. EPP 245 Statistical Analysis of Laboratory Data
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EPP 245 Statistical Analysis of Laboratory Data

5. EPP 245 Statistical Analysis of Laboratory Data
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EPP 245 Statistical Analysis of Laboratory Data

6. EPP 245 Statistical Analysis of Laboratory Data
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EPP 245 Statistical Analysis of Laboratory Data

7. EPP 245 Statistical Analysis of Laboratory Data
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File Format
A slide scanned with Axon GenePix produces a file with extension .gpr that contains the results:
This contains 29 rows of headers followed by 43 columns of data (in our example files)
For full analysis one may also need a .gal file that describes the layout of the arrays
November 15, 2007
EPP 245 Statistical Analysis of Laboratory Data

8. EPP 245 Statistical Analysis of Laboratory Data
"Block"
"Column"
"Row"
"Name"
"ID"
"X"
"Y"
"Dia."
"F635 Median"
"F635 Mean"
"F635 SD"
"B635 Median"
"B635 Mean"
"B635 SD"
"% > B635+1SD"
"% > B635+2SD"
"F635 % Sat."
"F532 Median"
"F532 Mean"
"F532 SD"
"B532 Median"
"B532 Mean"
"B532 SD"
"% > B532+1SD"
"% > B532+2SD"
"F532 % Sat."
"Ratio of Medians (635/532)"
"Ratio of Means (635/532)"
"Median of Ratios (635/532)"
"Mean of Ratios (635/532)"
"Ratios SD (635/532)"
"Rgn Ratio (635/532)"
"Rgn R² (635/532)"
"F Pixels"
"B Pixels"
"Sum of Medians"
"Sum of Means"
"Log Ratio (635/532)"
"F635 Median - B635"
"F532 Median - B532"
"F635 Mean - B635"
"F532 Mean - B532"
"Flags"
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November 15, 2007
EPP 245 Statistical Analysis of Laboratory Data

9. EPP 245 Statistical Analysis of Laboratory Data
12/19/2019
Analysis Choices
Mean or median foreground intensity
Background corrected or not
Log transform (base 2, e, or 10) or glog transform
Log is compatible only with no background correction
Glog is best with background correction
November 15, 2007
EPP 245 Statistical Analysis of Laboratory Data

10. EPP 245 Statistical Analysis of Laboratory Data
12/19/2019
Array normalization
Array normalization is meant to increase the precision of comparisons by adjusting for variations that cover entire arrays
Without normalization, the analysis would be valid, but possibly less sensitive
However, a poor normalization method will be worse than none at all.
November 15, 2007
EPP 245 Statistical Analysis of Laboratory Data

11. Possible normalization methods
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Possible normalization methods
We can equalize the mean or median intensity by adding or multiplying a correction term
We can use different normalizations at different intensity levels (intensity-based normalization) for example by lowess or quantiles
We can normalize for other things such as print tips
November 15, 2007
EPP 245 Statistical Analysis of Laboratory Data

12. EPP 245 Statistical Analysis of Laboratory Data
12/19/2019
Example for Normalization
Group 1
Group 2
Array 1
Array 2
Array 3
Array 4
Gene 1
1100
900
425
550
Gene 2
110 95 85
Gene 3 80 65 55
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EPP 245 Statistical Analysis of Laboratory Data

13. EPP 245 Statistical Analysis of Laboratory Data
12/19/2019
> normex <- matrix(c(1100,110,80,900,95,65,425,85,55,550,110,80),ncol=4)
> normex
[,1] [,2] [,3] [,4]
[1,]
[2,]
[3,]
> group <- as.factor(c(1,1,2,2))
> anova(lm(normex[1,] ~ group))
Analysis of Variance Table
Response: normex[1, ]
Df Sum Sq Mean Sq F value Pr(>F)
group *
Residuals
---
Signif. codes: 0 `***' `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
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EPP 245 Statistical Analysis of Laboratory Data

14. EPP 245 Statistical Analysis of Laboratory Data
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> anova(lm(normex[2,] ~ group))
Analysis of Variance Table
Response: normex[2, ]
Df Sum Sq Mean Sq F value Pr(>F)
group
Residuals
> anova(lm(normex[3,] ~ group))
Response: normex[3, ]
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EPP 245 Statistical Analysis of Laboratory Data

15. EPP 245 Statistical Analysis of Laboratory Data
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Additive Normalization by Means
Group 1
Group 2
Array 1
Array 2
Array 3
Array 4
Gene 1
975
851
541
608
Gene 2
-15 46
201
168
Gene 3
-45 16
171
138
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EPP 245 Statistical Analysis of Laboratory Data

16. EPP 245 Statistical Analysis of Laboratory Data
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> cmn <- apply(normex,2,mean)
> cmn
[1]
> mn <- mean(cmn)
> normex - rbind(cmn,cmn,cmn)+mn
[,1] [,2] [,3] [,4]
cmn
cmn
cmn
> normex.1 <- normex - rbind(cmn,cmn,cmn)+mn
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EPP 245 Statistical Analysis of Laboratory Data

17. EPP 245 Statistical Analysis of Laboratory Data
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> anova(lm(normex.1[1,] ~ group))
Analysis of Variance Table
Response: normex.1[1, ]
Df Sum Sq Mean Sq F value Pr(>F)
group *
Residuals
> anova(lm(normex.1[2,] ~ group))
Response: normex.1[2, ]
Df Sum Sq Mean Sq F value Pr(>F)
group *
Residuals
> anova(lm(normex.1[3,] ~ group))
Response: normex.1[3, ]
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EPP 245 Statistical Analysis of Laboratory Data

18. EPP 245 Statistical Analysis of Laboratory Data
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Multiplicative Normalization by Means
Group 1
Group 2
Array 1
Array 2
Array 3
Array 4
Gene 1
779
776
687
679
Gene 2 78 82
137
136
Gene 3 57 56 89 99
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EPP 245 Statistical Analysis of Laboratory Data

19. EPP 245 Statistical Analysis of Laboratory Data
> normex*mn/rbind(cmn,cmn,cmn)
[,1] [,2] [,3] [,4]
cmn
cmn
cmn
> normex.2 <- normex*mn/rbind(cmn,cmn,cmn)
> anova(lm(normex.2[1,] ~ group))
Response: normex.2[1, ]
Df Sum Sq Mean Sq F value Pr(>F)
group **
Residuals
> anova(lm(normex.2[2,] ~ group))
Response: normex.2[2, ]
group **
Residuals
> anova(lm(normex.2[3,] ~ group))
Response: normex.2[3, ]
Df Sum Sq Mean Sq F value Pr(>F)
group *
Residuals
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EPP 245 Statistical Analysis of Laboratory Data

20. EPP 245 Statistical Analysis of Laboratory Data
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Multiplicative Normalization by Medians
Group 1
Group 2
Array 1
Array 2
Array 3
Array 4
Gene 1
1000
947
500
Gene 2
100
Gene 3 73 68 65
November 15, 2007
EPP 245 Statistical Analysis of Laboratory Data

21. EPP 245 Statistical Analysis of Laboratory Data
> cmd <- apply(normex,2,median)
> cmd
[1]
> normex.3 <- normex*md/rbind(cmd,cmd,cmd)
> normex.3
[,1] [,2] [,3] [,4]
cmd
cmd
cmd
> anova(lm(normex.3[1,] ~ group))
Response: normex.3[1, ]
Df Sum Sq Mean Sq F value Pr(>F)
group **
Residuals
> anova(lm(normex.3[2,] ~ group))
Response: normex.3[2, ]
Df Sum Sq Mean Sq F value Pr(>F)
group
Residuals
> anova(lm(normex.3[3,] ~ group))
Response: normex.3[3, ]
group
Residuals
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November 15, 2007
EPP 245 Statistical Analysis of Laboratory Data

22. Intensity-based normalization
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Intensity-based normalization
Normalize by means, medians, etc., but do so only in groups of genes with similar expression levels.
lowess is a procedure that produces a running estimate of the middle, like a robustified mean
If we subtract the lowess of each array and add the average of the lowess’s, we get the lowess normalization
November 15, 2007
EPP 245 Statistical Analysis of Laboratory Data

23. EPP 245 Statistical Analysis of Laboratory Data
12/19/2019
norm <- function(mat1) {
mat2 <- as.matrix(mat1)
p <- dim(mat2)[1]
n <- dim(mat2)[2]
cmean <- apply(mat2,2,mean)
cmean <- cmean - mean(cmean)
mnmat <- matrix(rep(cmean,p),byrow=T,ncol=n)
return(mat2-mnmat) }
November 15, 2007
EPP 245 Statistical Analysis of Laboratory Data

24. EPP 245 Statistical Analysis of Laboratory Data
12/19/2019
lnorm <- function(mat1,span=.1) {
mat2 <- as.matrix(mat1)
p <- dim(mat2)[1]
n <- dim(mat2)[2]
rmeans <- apply(mat2,1,mean)
rranks <- rank(rmeans,ties.method="first")
matsort <- mat2[order(rranks),]
r0 <- 1:p
lcol <- function(x)
lx <- lowess(r0,x,f=span)$y }
lmeans <- apply(matsort,2,lcol)
lgrand <- apply(lmeans,1,mean)
lgrand <- matrix(rep(lgrand,n),byrow=F,ncol=n)
matnorm0 <- matsort-lmeans+lgrand
matnorm1 <- matnorm0[rranks,]
return(matnorm1)
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EPP 245 Statistical Analysis of Laboratory Data

25. EPP 245 Statistical Analysis of Laboratory Data
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EPP 245 Statistical Analysis of Laboratory Data

26. EPP 245 Statistical Analysis of Laboratory Data
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EPP 245 Statistical Analysis of Laboratory Data

27. EPP 245 Statistical Analysis of Laboratory Data
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November 15, 2007
EPP 245 Statistical Analysis of Laboratory Data