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(WARNING: Not a statistician - do not get mad)

We have two different treatments $A,B$, each was tested separately ($A$ treated group vs control, $B$ treated group vs control). In each comparison, the same set of features was tested for differential expression ($f_{1},...,f_{n}$) using the appropriate test statistics and FDR and the effect direction of each feature (log2(fold change) of treated group vs control), and we ended up with two lists of significantly discriminating features for each of the two comparisons.

Now, we want to explain the ``similarity'' of the effects of the two treatments (see what they have in common), under the null hypothesis that nothing is common between the effects. Since the two experiments were conducted in different batches we cannot directly analyze the actual values using standard approaches (say MANOVA + post hoc).

Our approach to answer the question of mutual effects is to:

Take the set of significantly discriminating features from treatment $A$ comparison: $S_{A}$. See the correlation between the log2(fold change) values of the features in $S_{A}$ i.e

  • $x=\log_{2}\left(\text{fold change of } f_{i} \text{ in treatment }A\right)$
  • $y=\log_{2}\left(\text{fold change of } f_{i} \text{ in treatment }B\right)$ where $f_{i}\in S_{A}$.

Under our $H_{0}$, $x,y$ as defined should be uncorrelated.

Another thing we are interested in is to see whether the size of the set of correlated features (that going up or down together between features) out of $S_{A}$ is "significantly larger than a random choice" that is, say that out of $S_{A}$ we have $N$ features that go up/down together, what is the probability of getting $M>N$ correlated features when taking a random sample of $\left|S_{A}\right|$ features (out of $f_{1},...,f_{n}$)? (To answer this question I think I can use direct permutation test ).

Are these ideas reasonable? Any other suggestions?

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