[limma] [Rfit] [samr] Gene expression distribution using lmFit and eBayes
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@jerome-lane-6256
Last seen 7.7 years ago
Hi, The 3/4 of my microarray gene expressions have non normal distribution with most of p-values after Shapiro test under 10x-5. I tried linear ranked regression from rfit (no normality assumption for residues) from Rfit package for adjustment of covariables + SAM (non parametric) from samr package but results where not as biologically relevant as lmFit + eBayes could provide. I know that lmFit function can analyses gene expression not strictly normal, but what is the limit ? Is it statistically relevant to use lmFit + eBayes according to my data ? Best regards, J??r??me Lane
Microarray Regression Microarray Regression • 1.7k views
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@gordon-smyth
Last seen 30 minutes ago
WEHI, Melbourne, Australia

Dear Jerome,

The Shapiro test is only applicable to iid samples, so it is difficult to see how it could be used to test normality of expression values in a linear modelling context. If you have applied the test to the normalized expression values for each gene, then I suspect that the test is actually picking up differential expression rather than non-normality.

The limma code is very robust against non-normality. All the usual microarray platforms and standard preprocessing procedures produce data that is normally distributed to a good enough approximation. Much effort has been devoted to developing good preprocessing and normalization algorithms.

The concept of "robustness" in statistical analysis goes back a 1953 paper by George Box in Biometrika. In that paper, Box wrote of the "remarkable property of robustness to non-normality which [tests for comparing means] possess". The tests done by limma inherit the robustness property that Box was referring to. Box made the point that the robustness of the two sample t-test was not improved by checking first for equal variances. He said

"To make the preliminary test on variances is rather like putting to sea in a rowing boat to find out whether conditions are sufficiently calm for an ocean liner to leave port!"

I rather think that, if Box was still alive today, he might say something similar about a preliminary Shapiro test!

Best wishes Gordon

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Dear Gordon,

Thanks for the reply, I appreciated it very much.

Is there a way to determine the "quality" of normalization for genes?

Best regards, Jerome

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