Notes 20101109 BIOL 614 McConkey Microarray Data Z-Scores

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Microarray Data

FDR (False Discovery Rate) correction
with a given confidence interval, we can infer the number of incorrect false positives
inferential statistics
- t-tests, comparisons -- infer about the population given your sample
some hypothesis with respect to the null hypothesis
genes that are differentially expressed
traditional stats: use some level of α for confidence
mean between two groups (t-test)
comparing slides

if we're only interested in a single gene, then p < 0.05 is reasonable
if we have 10,000 genes : 5% → 500 gene expressions are incorrect!
we should know our experimental error
- see Bonferroni correction (may be too harsh for microarray data)
Bonferroni correction means we set p < 5 × 10^-6 lt; something far lower --
FDR = E(count(false positives) ÷ count(total predictions))
- p < 0.05 is well accepted and is thought to be the highest amount of error allowed
in FDR, we will allow E() = 10% -- considered OK
family-wise error rate (FWER)
- control probability of making any false positive calls given desired significance
FDR
- control proportion of false positive calls in a total number of predictions

linear step up procedure -- see BH procedure
order p-values P₍₁₎ ≤ P₍₂₎ ≤ P₍₃₎ ≤ ... ≤ P_(m)
let k = i_max
- for {p(i) &leq; (i ÷ m)q}
- where q is the target FDR (default 0.10)
- we then find the maximum before the threshold -- all p-values below that are considered valid
reject the null hypotheses H₍₁₎ ≤ H₍₂₎ ≤ H₍₃₎ ≤ ... ≤ H_(i)
- up until the (i) that is the threshold

mouse brain gene expression correlation with behaviour
- 17 behavioural endpoints
- 2.7 × 10⁴ genes
behaviours are ordered by p-value
Bonferroni threshold -- 0.0029 is at p-value 0.05
FDR threshold -- foreach rank, it is 0.0029(i) for i = {1 to n}

PaGE -- Pattern of Gene Expression
- Owen: not known
SAM -- Significance Analysis of Microarrays
- Owen: works well, permutation tests
LPE -- Local Pooled-Error model test
- Owen: messy, interesting ideas, doesn't always work
Bioconductor -- Open source toolkit
- Owen: powerful, R, user-unfriendly, developer-friendly

finding meaningful patterns in the data
arrange data in the matrix
distance metric defines relatedness between points
Pearson correlation coefficient
Euclidean distance
hierarchical clustering -- grouping things in a pairwise fashion
looking for a logical separation within the microarray data
agglomerative and divisive clustering ...
UPGMA
- not as good for phylogenetic trees (assumptions made)
- very useful for microarray
- uses distance measures that are treated as one by their average value (agglomerative)