Whilst it is possible to do PCA with a class size of n=3, comparing 4 classes is not likely to give a robust answer given the number of variables compared to the number of samples. Removing an outlier is never justified without a clear reason, for example a methodological artefact, otherwise you will be prone to biasing the data. It may be that the experiment is underpowered and you simply don't have enough observations to draw any conclusions.Your best option is to establish what is the biggest source of variation in your data (in PC1) and try to adjust for any obvious confounders. Another way to simplify the analysis is to conduct pairwise class comparisons and understand the differences if any between classes and then use this strategy to conduct feature reduction (however, this can also lead to bias and needs to be assessed).

If there is a clear difference, both univariate and multivariate analysis should find it.

My opinion is that the standard parameters you are using for your multivariate analysis are not enough, aka some tuning is needed. Indeed, there could be multiple things that could have gone wrong in your rmultivariate analysis, starting from the normalization (did you select the correct internal standard? only one? for all the compounds? or one per each class of compounds?), scaling (did you try different kind of scaling? do your data need transformation?), PCA score plot (do not resolve the 4 conditions in the first two components or in all the components? how many componenets you got?) sPLS (is there possible that the difference between two conditions is minor than the difference found for the others?).

If you can reply to this questions and still not get a good result, it might be possible that the error is in the ANOVA you performed. Did you use p-value or q-value? How significant they are?

Hope to be helpful.

Have a nice day.

Luca

Dear Luca,

Regarding the "tuning" of the statistical analysis, I dont think that is the matter of the problem and my question was not in that direction. We do normalization with a standard for PL group, we applied the scaling which fits better to our data and idem for the transformation.

The PCA does not resolve any of the four conditions I mentioned. This is, the typical coloured area of the PCA with 95% confidence overlay at any point for all of them. Same with the sPLS, that resolves 3 of the 4 groups. However, the ANOVA gives a number of significant (pvalue

Whilst it is possible to do PCA with a class size of n=3, comparing 4 classes is not likely to give a robust answer given the number of variables compared to the number of samples. Removing an outlier is never justified without a clear reason, for example a methodological artefact, otherwise you will be prone to biasing the data. It may be that the experiment is underpowered and you simply don't have enough observations to draw any conclusions.Your best option is to establish what is the biggest source of variation in your data (in PC1) and try to adjust for any obvious confounders. Another way to simplify the analysis is to conduct pairwise class comparisons and understand the differences if any between classes and then use this strategy to conduct feature reduction (however, this can also lead to bias and needs to be assessed).

Thank you Elaine,

The fact is that without the potential outlier (based on parallel information of the sample as you say) the sPLS resolves the groups, but I dont know if n=2 is acceptable from an statistical point of view. The samples are provided by collaborators so we cannot have other replicates.

On the other hand, I agree that even with the PCA and sPLS not totally resolving the groups, the ANOVA provides some features significantly different, so this pairwise comparison you mention is productive and a feature reduction should help to multivariate analysis, I have to understand better the requirements you suggest to do this.

Thank you, your answer has helped me to understand the contradiction between the multivariate analyisis (PCA,sPLS) and the ANOVA.

Ok I partially misunderstood your question.

Still my opinion:

1) "PCA does not resolve the groups" only means that there are bigger source of variation than the one you are studying... which does not implicate that your groups are not different, but only that you need a more powerful model (PLS and its variants). It would be a perfect world if PCA could solve everything... unfortunately it is not.

2) "removing a potential outlier": potential outlier is not statistics. Outlier is statistics: I mean you need to demonstrate that this is an outlier, at least applying some statistics on it (robustPCA?) and demonstrate that it falls outside the confidence area of all the remaining samples (outside its own group is not enough). Then you might think on removing it (which is never a good and easy idea, as Elaine suggested)... The fact that it does not respect its position in its group, does not mean anything.

3) N=2 is not good, especially because your k (number of variables) is hundreds (I suppose). Only literature in your field can reply to this answer; see if there are other studies where it has been accepted.

4) You did not reply on my last questions about Anova. Did you adjust your p-value (like for example with Bonferroni correction or False discovery rate?). If you did not do it, your Anova test is senseless.

5) regarding point number 2: As far as I got to understand, sPLS does not resolve one of the groups due to a possible outlier... is that possible that the variability in such group is just higher than expected?

6) without seeing your data, answering your last question is impossible. Differences between univariate and multivariate models could arise from many sources...

Hope to be helpful.

Have a nice day