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When you're referring to differential analysis, I'm assuming you mean something like (in R formula notation) expression ~ condition + age + sex where you're interested in the condition effect. What that does is that your linear model does fit coefficients for age and sex, but you only use the condition coefficient for further analysis, since that one should no longer be influenced by age and sex. So you don't remove the association, you control for it.

Similarly, in factor models such as MOFA-FLEX, if you have some factors that are correlated with age and sex, you can focus your downstream analysis on the other factors, which should then not be influenced by age and sex. The guiding varia…

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@ilia-kats
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Answer selected by Pierre9344
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