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I have RNA-seq data in response to treatment vs non response; By machine learning I selected three principle components likely can predict the response based on the gene expression. Now I have something like this

> head(pca$rotation[1:10,1:6])
               PC1          PC2          PC3          PC4           PC5          PC6
ACTB   -0.01858031 -0.005810636  0.014939832 -0.009594126 -0.0118313644 -0.011534401
ATP5F1 -0.01822611  0.014851900 -0.016401920 -0.015616379  0.0254850111 -0.010225516
DDX5   -0.02477827 -0.020573978  0.002199966 -0.009296852  0.0006222345  0.014506614
EEF1G  -0.02803284  0.001126758 -0.010570521 -0.017035205  0.0007583815  0.011225639
GAPDH  -0.02691309  0.005503228  0.006446502 -0.012686738 -0.0289737909  0.007036631
NCL    -0.03019765 -0.003011778 -0.015534611 -0.002019556 -0.0126401245  0.013977142
> 
> dim(pca$rotation)
[1] 3962   56
>

Machine learning says PC 6, PC 21 and PC 39 are better; how I know from 3962 genes in each of these PCs which genes is more contribute to response to treatment?

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    $\begingroup$ Have you looked at the loadings in those PCs? $\endgroup$
    – Devon Ryan
    Oct 4, 2019 at 9:43
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    $\begingroup$ Hi @Fereshteh you should know this, you have enough experience in ML. PCA cannot solve this but you can use the classification for supervised learning which will tell you $\endgroup$
    – M__ ♦
    Oct 4, 2019 at 9:45
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    $\begingroup$ Like @DevonRyan mentioned, you can go by the loadings, which will be sort( abs(pca$rotation[,"PC6"]),decreasing=T) for example in your case. But it kind of defeats the purpose of PCA right? You use PCA to get linear combinations of the genes.. $\endgroup$
    – StupidWolf
    Oct 4, 2019 at 9:55
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    $\begingroup$ Yes the genes with the higher loadings in the better PCs should contribute more towards response / non-response. My point is, it should be a combination of the genes. For example, if PC6 has strong +ve loadings for gene 1,2,3 and strong -ve loadings for gene 4,5,6, I would interpret it as, a strong expression of genes 1-3 and low expression of genes 4-6 contribute towards a response phenotype $\endgroup$
    – StupidWolf
    Oct 4, 2019 at 11:31
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    $\begingroup$ What exactly is the goal of your analysis? If it is to predict and then point out a few potential causative genes, then the PCA approach you have is ok. I would be cautious about using up to PC39 (which explains very little of the variance in gene expression). $\endgroup$
    – StupidWolf
    Oct 4, 2019 at 11:33

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