Title: Variability
1Variability Statistical Analysisof Microarray
DataGCAT Georgetown July 2004
- Jo Hardin
- Pomona College
- jo.hardin_at_pomona.edu
2Variability
- key to statistics
- within slide vs. between slide
- replication
- red (Cy5) gt green dye (Cy3) dye swap
- log (base 2) transformation
3Example
- 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?
4Data Cleaning
- Individual points were median centered for each
cDNA clone and filtered for data quality. - Data values are either
5The Data
6Differential Expression Across Two Groups
- Fold Change
- t-test
- Wilcoxon Rank-Sum Test
- SAM
7Fold Change
- Of mean? Of median?
- Across treatment groups? vs. reference group?
- Small vs. large values
- What about how variable the groups are?
8An Example using one gene
9t-test
- Test statistic
-
- p-value probability of seeing your data or more
extreme if there is no difference in the groups
10t-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)
11Wilcoxon 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.
12Up regulated genes Down regulated genes
13Technical 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)
14Wilcoxon 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)
15SAM (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
16Technical 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
17False 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)
18Features 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
19Imputation
- 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