**0**wrote:

(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?

**3.0k**• written 14 months ago by uriamo •

**0**

I must admit I cannot easily read what you are doing - could you reformat to better suite Biostars?

3.0kHow do you write latex/math symbols in biostars?

0You can use the formatting bar (especially the

`code`

option).You could also use these directions to include an image of the equation in your original post: How to add images to a Biostars post

78kI'll do that. but as long is Biostars will not parse that latex code, I can't see how it makes it any more clear. I can attach a link to other forums that

doparse math.0