Variability

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Variability Statistical Analysisof Microarray
DataGCAT Georgetown July 2004

• Jo Hardin
• Pomona College
• jo.hardin_at_pomona.edu

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Variability

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

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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
  didnt?

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Data Cleaning

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

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The Data
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Differential Expression Across Two Groups

• Fold Change
• t-test
• Wilcoxon Rank-Sum Test
• SAM

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Fold Change

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

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An Example using one gene
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t-test

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

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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(c3k3,l3v3,2,3)

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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.

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Up regulated genes Down regulated genes
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Technical Details

• Replace values with ranks
• Sum the ranks in the first group
• Calculate hypothesized mean1 n1(n1n21)/2
• Calculate hypothesized standard deviation1
  sqrt(n1n2(n1n21)/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)

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Wilcoxon Rank Sum in Excel

• Using the rank function, translate your data into
  ranks
• Y3 RANK(C3,C3V3) this finds the rank of C3
  in the range C3-V3
• (youll probably get a value here, thats OK
  because C3 is empty for gene IMAGE253507)
• Repeat this command for Z3 to AR3 keeping the
  second half of the function always C3V3
• Copy the row from Y3 to AR3 and paste from Y4 to
  AR2366
• AS2 SUMIF(Y3AG3,"gt0",Y3AG3) (sum rank
  grp1)
• AT2 COUNT(Y3AG3)(COUNT(Y3AR3)1)/2 (mean1)
• AU2 SQRT(COUNT(Y3AG3)COUNT(AH3AR3)
  (COUNT(Y3AR3)1)/12) (stdev1)
• AV2 (AS3-AT3)/AU3 (zscore1 test stat)
• AW2 2(1-NORMDIST(ABS(AV3),0,1,TRUE))
• (p-value)

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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

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Technical Details

• For the ith gene, comparing two groups, the test
  statistic is
• Rank the di and keep as test statistics
• Permute the data labels 100 times, and calculate
  expected values for the di given no structure.
• Plot observed di vs. expected di

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False Discovery Rate

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

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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

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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