Some discussion on multiple hypothesis test and false discovery adjustment

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Some discussion on multiple hypothesis test and
false discovery adjustment
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P-value of NULL distribution

• 6000 genes
• 100 samples, 50 each
• All N(0,1)
• P-value uniform distribution 0,1

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P-value and hypothesis test

• P-value of any statistics the possibility that
  getting the statistics from NULL hypothesis
• P-value cutoff set an arbitrary threshold on one
  hypothesis test
• When there are multiple hypothesis tests, it may
  risk in getting too much false discovery
• e.g. in 6000 genes, if cut by p-value 0.05, there
  will be up to
• 6000 0.05 300 false discoveries
• Need some adjustment to these statistics, to
  guarantee that the False Discovery Rate in the
  finally rejected lists is lower than a
  pre-defined level f.

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FDR adjusted P-value

• Sort raw P-value
• Reject the test with the i-th smallest P-value if
  Pi lt f/i, where f is a pre-defined FDR level.

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Difficulties

• Maybe it is too stringent, especially when the
  signal is very weak, and the number of genes is
  too large
• Pre-screening may help to purify the data set and
  get better result after FDR.
• What does it mean by FDR lt 0.05, if there are
  only 10 genes being rejected?

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Pair-wise t-test of pre-post exposure

• Raw P-value of paired t-test
• Scatter plot of raw P-value and mean difference
• There are some information, but too weak berried
  under noise.

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Linear regression of gene expression versus
exposure

• Raw P-value of linear regression
• Scatter-plot of R-sqrt and raw P-value

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Alternative idea estimate the overall
distribution by permutation
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Randomly flip pre-post pair of all genes of some
sample, and get the maximum t-statistics from the
whole permuted data set
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Distribution of the maximum t-statistics in 1000
permuted data sets

• Find the gene with the true t-statistics above
  the 95 percentile of this distribution

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Consider the sets of gene, not individual ones

• Genes are correlated
• We have prior knowledge to group genes together
• GO terms
• Pathway,
• functional group
• Clustering
• Design statistics on set of gene, not individual
  genes, to be differentially expressed between
  conditions
• Combine weak information of genes in the sets,
  and reduce the number of hypothesis tests

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Moothas data