Dear Csenger Kovácsházi , great questions - and thanks for providing more insights.

First, answering to your specific questions:

Q1.1: How should I calculate log2 FoldChange in my log2 transformed data?

- Applying the rules of logarithm, log(A) - log (B) = log(A/B). That is, the difference between two log2 values represent in fact the log2 fold-change.

Using A = 8 and B = 16, we have log2(A) = 3 and log2(B) = 4, FC = A/B = 8/16 = 0.5, and, finally, log2FC = log2(A/B) = log2(A) - log2(B) = 3 - 4 = -1 (go over this math using different numbers to verify this relationship)

Q1.2: log2 transformation is necessary to fulfil the normal distribution criteria of the ANOVA test

- I know this wasn't a question, but, in fact, that is not generally true for this type of data. Furthermore, the biggest issue is the heterogeneity of the residuals within 'treatments' (the 3 groups you have), which is far more important for ANOVA than normality. In addition, proteomic data may include lots of zeros (BTW, how did you calculate the log2 of '0'?), which hinders this even more.

Q1.3: Also, log2FC of log2 data would be quite complicated to interpret - Do you Experts agree with this approach? - Any better idea?

- As long as you are calculating it correctly (per Q1.1), I don't see any issues with its interpretation. In fact, I really like log2FC because of its ease of interpretation.

Q2: How to create a volcano plot for this dataset? ... So what do you recommend?

Sorry, but it is what it is... You simply can't do everything in a single plot... You will have to pick your battles... If you are interested in presenting a specific contrast, your p-value should be representing that specific contrast. For ease of visualization, you may color-code your volcano plot discriminating the significant and non-significant results based on the overall p-value of the ANOVA. Thus, while you are still plotting the -log10P of the contrast, the result is color coded based on the p-value of the ANOVA.

Now, a couple of comments...

1) The process of generating proteomics data is quite messy, and it is recommended to have a data-normalization step (not related to 'normal distribution'). That is, some samples might have greater abundance and diversity of PTNs by change during the quantification process. Others may have in fact because of the 'treatment'. Thus, it is important to differentiate these two samples and not treat them the same way. See this for reference: https://pubmed.ncbi.nlm.nih.gov/27694351/

2) The transformation of data is not always needed/required/justifiable when available methods are out there. For instance, Poisson and Negative Binomial methods are popular for proteomics data, as well as the use of Zero-Inflated models within these methods. I know that it is not easy to just learn these methods and apply them to your work... But, just a tip..

Let me know if you have more questions. Thanks, Nick

Statistical analysis and visualization of multiple group proteomics data require careful consideration of the specific research question and the nature of the data. However, here are some general steps that you can follow to analyze and visualize multiple group proteomics data:

Many software tools are available for statistical analysis and visualization of multiple group proteomics data, such as R/Bioconductor, Perseus, and MaxQuant. You should consult with a bioinformatician or data analyst to select the appropriate tools and methods for your specific research question and data.

Regenerate response

Dear Nick VL Serão , Ma'Mon Abu Hammad and Samuel Oluwaseun Adeyemo

Thanks for all of you for your helpful answers.

To briefly answer the question about the log2 of missing values (zeros), I've performed the analysis mostly as Ma'Mon recommended, so data imputation was applied after the selection of proteins with poor quality (many missing values). So technically, I did not have zeros.

About log2 transformation and FC:

Nick mentioned that log(A) - log (B) = log(A/B). However, we have to take into account that I don’t have single A or B values, but averages. And

avg[log(A.1),log(A.2), … , log(A.n)] != log[avg(A.1,A.2, … ,A.n)]

where A.n are the individual samples of a group.

If I calculate Log2FC in log scale, that means:

log2FC.log = avg[log(A.1),log(A.2), … , log(A.n)] - avg[log(B.1),log(B.2), … , log(B.n)]

If I do it in normal scale, then:

Log2FC.norm = log[avg(A.1,A.2,…,A.n) / avg(B.1,B.2,…,B.n)] = log[avg(A.1,A.2,…,A.n)] - log[avg(B.1,B.2,…,B.n)].

In conclusion log2FC.log != Log2FC.norm. So the problem of how to calculate the FC is still a question.

Since our final goal is to identify biological effects and the reason of FC calculation is to identify statistically significant results without biological relevance, I would suggest that the best solution is to calculate it from the original data, regardless of its distribution. Maybe another solution can be to calculate fold change on the median since that maybe represents a Lognormal data better than mean.

About the visualization:

I must disagree in presenting data which I not used for the statistical testing (e.g. t-test between the presented values). Doing a post-hoc for those proteins where ANOVA was not significant to plot p-value, but highlight ANOVA significance could be a solution.

My conclusion is there is not a clear solution and all of them has their limitations.

About data normalization:

Nick, thank you for your comments and I will definitely look after them.

Csenger Kovácsházi , apologies for the delay.

With regards to the calculation of the log2FC, you will analyze all the log2-transformed data, and then you will contrast the “least square means” of each group to calculate the log2FC.

Thus, already think of the values I gave for A and B as the “treatment means”. Is it clearer now?

Thanks, Nick