Should the number of significantly DE genes rise with the number of SVs estimated (SVA package)?

Question

[Aspire]

Is there a monotonous relationship between the number of SVs one estimates (sva package), and the number of DE genes one should get as significant? In other words, is it true that the more SVs are used, the more DE genes should be significant?

(I understand that a large number of significantly DE genes is not a positive value in itself; and the more SVs one estimates, the more likely the chance to overfit. Just for understanding's sake )

[Nicolas Rosewick]

Could you rephrase your question (and maybe give an example), it's not clear. Are you asking if there is a linear relation between SV number and DE genes number ?

[Aspire]

Clarified the question.

[Kevin Blighe]

No, why should there be?

[Aspire]

From SVA manual :

The goal of the sva is to remove all unwanted sources of variation while protecting the contrasts due to the primary variables included in mod. This leads to the identification of features that are consistently different between groups, removing all common sources of latent variation.

Imho, singificantly DE genes are exactly genes that are consistently different between the groups. So, it seems that the general definition of the goal of SVA implies the definition of significantly DE genes.

Also, when I adjust for SVs using limma's removeBatchEffect, and plot the PCA/distance heatmap, the more SVs are included the better the separation between the groups. Even though the statistical method to determine DE genes (via DESeq2) is different from PCA separation, often it is the case that when the separation on the PCA is good, there are many significantly DE genes.