1. SPH 247 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 May 14, 2010SPH 247 Statistical Analysis of Laboratory Data2

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 May 14, 2010SPH 247 Statistical Analysis of Laboratory Data3

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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 May 14, 2010SPH 247 Statistical Analysis of Laboratory Data7

8. May 14, 2010SPH 247 Statistical Analysis of Laboratory Data8 "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"

9. 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 May 14, 2010SPH 247 Statistical Analysis of Laboratory Data9

10. 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. May 14, 2010SPH 247 Statistical Analysis of Laboratory Data10

11. 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 May 14, 2010SPH 247 Statistical Analysis of Laboratory Data11

12. May 14, 2010SPH 247 Statistical Analysis of Laboratory Data12 Group 1Group 2 Array 1Array 2Array 3Array 4 Gene 11100900425550 Gene 21109585110 Gene 380655580 Example for Normalization

13. May 14, 2010SPH 247 Statistical Analysis of Laboratory Data13 > 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

14. May 14, 2010SPH 247 Statistical Analysis of Laboratory Data14 > 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

15. May 14, 2010SPH 247 Statistical Analysis of Laboratory Data15 Group 1Group 2 Array 1Array 2Array 3Array 4 Gene 1975851541608 Gene 2-1546201168 Gene 3-4516171138 Additive Normalization by Means

16. May 14, 2010SPH 247 Statistical Analysis of Laboratory Data16 > cmn <- apply(normex,2,mean) > cmn [1] 430.0000 353.3333 188.3333 246.6667 > 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

17. May 14, 2010SPH 247 Statistical Analysis of Laboratory Data17 > 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

18. May 14, 2010SPH 247 Statistical Analysis of Laboratory Data18 Group 1Group 2 Array 1Array 2Array 3Array 4 Gene 1779776687679 Gene 27882137136 Gene 357568999 Multiplicative Normalization by Means

19. May 14, 2010SPH 247 Statistical Analysis of Laboratory Data19 > 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

20. May 14, 2010SPH 247 Statistical Analysis of Laboratory Data20 Group 1Group 2 Array 1Array 2Array 3Array 4 Gene 11000947500 Gene 2100 Gene 373686573 Multiplicative Normalization by Medians

21. May 14, 2010SPH 247 Statistical Analysis of Laboratory Data21 > cmd <- apply(normex,2,median) > cmd [1] 110 95 85 110 > normex.3 <- normex*md/rbind(cmd,cmd,cmd) > normex.3 [,1] [,2] [,3] [,4] cmd 1000.00000 947.36842 500.00000 500.00000 cmd 100.00000 100.00000 100.00000 100.00000 cmd 72.72727 68.42105 64.70588 72.72727 > anova(lm(normex.3[1,] ~ group)) Response: normex.3[1, ] Df Sum Sq Mean Sq F value Pr(>F) group 1 224377 224377 324 0.003072 ** Residuals 2 1385 693 > anova(lm(normex.3[2,] ~ group)) Response: normex.3[2, ] Df Sum Sq Mean Sq F value Pr(>F) group 1 0 0 Residuals 2 0 0 > anova(lm(normex.3[3,] ~ group)) Response: normex.3[3, ] Df Sum Sq Mean Sq F value Pr(>F) group 1 3.451 3.451 0.1665 0.7228 Residuals 2 41.443 20.722

22. 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 May 14, 2010SPH 247 Statistical Analysis of Laboratory Data22

23. May 14, 2010SPH 247 Statistical Analysis of Laboratory Data23 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) }

24. May 14, 2010SPH 247 Statistical Analysis of Laboratory Data24 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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