Identifiyng mutual trends between treatments

Question

[uriamo]

(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?

[Kristoffer Vitting-Seerup]

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

[uriamo]

How do you write latex/math symbols in biostars?

[GenoMax]

You can use the formatting bar (especially the code option).

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

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

[uriamo]

I'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 do parse math.

Answer 1

[Kristoffer Vitting-Seerup]

Reading the link to where it was formatted to be readable I think those ideas sound good.

For the the correlation analysis I would also make the scatterplot of the log2FC vs Log2FC along with a trend line. Two things you could consider:

1. To use DESeq2's log2FC shrinkage (see this section of the vignette) to minimize the effect of outliers cased by low experssion
2. You could also do the analysis for the union of the DE genes

For the the set size analysis you could also just do a fishers test only considering the genes actually tested in both conditions. This is nice because you also get the odds ratio of the overlap being as large as it is.

Lastly if you want to argue that the effect in the two conditions have the same biological consequences/function you can do the same two types of analysis after you have done a gene-set enrichment analysis in each condition (just plotting odds ratios instead of log2FCs).

Good luck Kristoffer