1. 1 Two Color Microarrays EPP 245/298 Statistical Analysis of Laboratory Data

2. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 2 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

3. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 3 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

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7. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 7 File Format A slide scanned with Axon GenePix produces a file with extension.gpr that contains the results: http://www.axon.com/gn_GenePix_File_Formats.html http://www.axon.com/gn_GenePix_File_Formats.html 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

8. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 8 "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."

9. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 9 "F532 Median" "F532 Mean" "F532 SD" "B532 Median" "B532 Mean" "B532 SD" "% > B532+1SD" "% > B532+2SD" "F532 % Sat."

10. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 10 "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"

11. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 11 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

12. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 12 d41 <- read.table("037841.gpr",header=T,skip=29) d41 <- d41[,c(4,5,9,10,12,13,18,19,21,22)] d50 <- read.table("037850.gpr",header=T,skip=29) d50 <- d50[,c(4,5,9,10,12,13,18,19,21,22)] d46 <- read.table("037846.gpr",header=T,skip=29) d46 <- d46[,c(4,5,9,10,12,13,18,19,21,22)] d47 <- read.table("037847.gpr",header=T,skip=29) d47 <- d47[,c(4,5,9,10,12,13,18,19,21,22)] d48 <- read.table("037848.gpr",header=T,skip=29) d48 <- d48[,c(4,5,9,10,12,13,18,19,21,22)] d49 <- read.table("037849.gpr",header=T,skip=29) d49 <- d49[,c(4,5,9,10,12,13,18,19,21,22)] d43 <- read.table("037843.gpr",header=T,skip=29) d43 <- d43[,c(4,5,9,10,12,13,18,19,21,22)]

13. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 13 dataprep <- function(method="median",bc=F) { if ((method=="mean")&(bc)) cvec <- c(1,0,-1,0) if ((method!="median")&(bc)) cvec <- c(0,1,0,-1) if ((method=="mean")&(!bc)) cvec <- c(1,0,0,0) if ((method!="median")&(!bc)) cvec <- c(0,1,0,0) d41a <- as.matrix(d41[,3:6]) %*% cvec d41b <- as.matrix(d41[,7:10]) %*% cvec d50a <- as.matrix(d50[,3:6]) %*% cvec d50b <- as.matrix(d50[,7:10]) %*% cvec d46a <- as.matrix(d46[,3:6]) %*% cvec d46b <- as.matrix(d46[,7:10]) %*% cvec.............................. d45a <- as.matrix(d43[,3:6]) %*% cvec d45b <- as.matrix(d43[,7:10]) %*% cvec alldata <- cbind(d41a,d41b,d50a,d50b,d46a,d46b,d47a,d47b, d48a,d48b,d49a,d49b,d43a,d43b,d44a,d44b,d42a,d42b,d43a,d43b) return(alldata) }

14. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 14 alldata <- dataprep(method="median",bc=F) rownames(alldata) <- d41[,1] dye <- as.factor(rep(c("Cy5","Cy3"),10)) slide <- as.factor(rep(1:10,each=2)) treat <- c(1,0,0,1,0,1,1,0,0,3,3,0,0,3,3,0,0,1,1,0) geneID <- d41[,1:2]

15. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 15 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.

16. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 16 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

17. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 17 Group 1Group 2 Array 1Array 2Array 3Array 4 Gene 11100900425550 Gene 21109585110 Gene 380655580 Example for Normalization

18. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 18 > normex <- matrix(c(1100,110,80,900,95,65,425,85,55,550,110,80),ncol=4) > normex [,1] [,2] [,3] [,4] [1,] 1100 900 425 550 [2,] 110 95 85 110 [3,] 80 65 55 80 > 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 1 262656 262656 18.888 0.04908 * Residuals 2 27812 13906 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

19. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 19 > anova(lm(normex[2,] ~ group)) Analysis of Variance Table Response: normex[2, ] Df Sum Sq Mean Sq F value Pr(>F) group 1 25.0 25.0 0.1176 0.7643 Residuals 2 425.0 212.5 > anova(lm(normex[3,] ~ group)) Analysis of Variance Table Response: normex[3, ] Df Sum Sq Mean Sq F value Pr(>F) group 1 25.0 25.0 0.1176 0.7643 Residuals 2 425.0 212.5

20. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 20 Group 1Group 2 Array 1Array 2Array 3Array 4 Gene 1975851541608 Gene 2-1546201168 Gene 3-4516171138 Additive Normalization by Means

21. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 21 > mn <- mean(cmn) > normex - rbind(cmn,cmn,cmn)+mn [,1] [,2] [,3] [,4] cmn 974.58333 851.25 541.25 607.9167 cmn -15.41667 46.25 201.25 167.9167 cmn -45.41667 16.25 171.25 137.9167 > normex.1 <- normex - rbind(cmn,cmn,cmn)+mn

22. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 22 > mn <- mean(cmn) > anova(lm(normex.1[1,] ~ group)) Analysis of Variance Table Response: normex.1[1, ] Df Sum Sq Mean Sq F value Pr(>F) group 1 114469 114469 23.295 0.04035 * Residuals 2 9828 4914 > anova(lm(normex.1[2,] ~ group)) Analysis of Variance Table Response: normex.1[2, ] Df Sum Sq Mean Sq F value Pr(>F) group 1 28617.4 28617.4 23.295 0.04035 * Residuals 2 2456.9 1228.5 > anova(lm(normex.1[3,] ~ group)) Analysis of Variance Table Response: normex.1[3, ] Df Sum Sq Mean Sq F value Pr(>F) group 1 28617.4 28617.4 23.295 0.04035 * Residuals 2 2456.9 1228.5

23. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 23 Group 1Group 2 Array 1Array 2Array 3Array 4 Gene 1779776687679 Gene 27882137136 Gene 357568999 Multiplicative Normalization by Means

24. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 24 > normex*mn/rbind(cmn,cmn,cmn) [,1] [,2] [,3] [,4] cmn 779.16667 775.82547 687.33407 679.13851 cmn 77.91667 81.89269 137.46681 135.82770 cmn 56.66667 56.03184 88.94912 98.78378 > 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 1 8884.9 8884.9 453.71 0.002197 ** Residuals 2 39.2 19.6 > anova(lm(normex.2[2,] ~ group)) Response: normex.2[2, ] Df Sum Sq Mean Sq F value Pr(>F) group 1 3219.7 3219.7 696.33 0.001433 ** Residuals 2 9.2 4.6 > anova(lm(normex.2[3,] ~ group)) Response: normex.2[3, ] Df Sum Sq Mean Sq F value Pr(>F) group 1 1407.54 1407.54 57.969 0.01682 * Residuals 2 48.56 24.28

25. November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 25 Group 1Group 2 Array 1Array 2Array 3Array 4 Gene 1 Gene 2 Gene 3 Multiplicative Normalization by Medians