Variability & Statistical Analysis of Microarray Data GCAT – Georgetown July 2004 Jo Hardin Pomona College

Variability key to statistics within slide vs. between slide replication red (Cy5) > green dye (Cy3): dye swap log (base 2) transformation

Example: Variation in Gene Expression Patterns in Follicular Lymphoma and the Response to Rituximab,by Bohen, Troyanskaya, Alter, Warnke, Botstein, Brown, and Levy 2 groups: those who responded to treatment, and those who did not respond to treatment. Cy5 dye used on malignant lymphoid tissues, Cy3 dye used on mRNA derived from cell lines Biopsies obtained before treatment of Rituximab Are there differences in gene expression across those who responded to treatment and those who didn’t?

Data Cleaning Individual points were median centered for each cDNA clone and filtered for data quality. Data values are either:

The Data:

Differential Expression Across Two Groups Fold Change t-test Wilcoxon Rank-Sum Test SAM

Fold Change Of mean? Of median? Across treatment groups? vs. reference group? Small vs. large values What about how variable the groups are?

An Example using one gene:

t-test Test statistic: p-value = probability of seeing your data or more extreme if there is no difference in the groups

t-test in Excel Syntax: TTEST(array1,array2,tails,type) Example:  first group is in cells c3 – k3  second group is in cells l3 – v3  we want a two sided t-test (no preconceived idea about which group is more highly expressed)  we assume the variance is unequal in cell w3 type: “=ttest(c3:k3,l3:v3,2,3)”

Wilcoxon Rank Sum Test Instead of comparing averages, this test compares rankings (or medians) In order to discount influential points, we replace the data values with their appropriate rankings. We compute a z-test (sister of the t-test) on the ranked data.

Up regulated genesDown regulated genes

Technical Details Replace values with ranks Sum the ranks in the first group Calculate hypothesized mean1 = n1*(n1+n2+1)/2 Calculate hypothesized standard deviation1 = sqrt(n1*n2*(n1+n2+1)/12) Calculate test statistic = (sum ranks – hyp mean1) / hyp stdev1 Find the p-value using the normal distribution (probability of being greater than the test statistic if there are no differences in the two groups)

Wilcoxon Rank Sum in Excel Using the rank function, translate your data into ranks  Y3: “=RANK(C3,C3:V3)” this finds the rank of C3 in the range C3-V3 (you’ll probably get a “#value” here, that’s OK because C3 is empty for gene = IMAGE:253507)  Repeat this command for Z3 to AR3 keeping the second half of the function always C3:V3  Copy the row from Y3 to AR3 and paste from Y4 to AR2366 AS2: “=SUMIF(Y3:AG3,">0",Y3:AG3)” (sum rank grp1) AT2: “=COUNT(Y3:AG3)*(COUNT(Y3:AR3)+1)/2” (mean1) AU2: “=SQRT(COUNT(Y3:AG3)*COUNT(AH3:AR3)* (COUNT(Y3:AR3)+1)/12)” (stdev1) AV2: “=(AS3-AT3)/AU3” (zscore1 = test stat) AW2: “=2*(1-NORMDIST(ABS(AV3),0,1,TRUE))” (p-value)

SAM (Significance Analysis of Microarrays) is a statistical technique for finding significant genes in a set of microarray experiements can be used in a comparison experiment can also be used with a quantitative response (like tumor size) or with one class data

Technical Details For the i th gene, comparing two groups, the test statistic is: Rank the d i and keep as test statistics Permute the data labels 100 times, and calculate expected values for the d i given no structure. Plot observed d i vs. expected d i

False Discovery Rate We know that the expected d i were computed with no group structure. Any “large” expected d i values will be false positives. If we see 30 observed d i above some cutoff and 10 expected d i above the same cutoff, we know that we probably have 10 false positives (though we can never know *which* genes are the false positives)

Features of SAM Slider – we can change the false discovery rate Fold change – in addition to the false discovery rate, we can require the genes to be at some fold change threshold (on average) Gene lists – gene lists are given along with corresponding significance levels Web Link option for more information about particular genes

Imputation Most microarray data has missing values If background is bigger than foreground, the observed signal will be negative! Poor quality spots are removed prior to analysis. SAM needs a full data set which can be computed by:  Substitution of the row average  Substitution using k-nearest neighbors