[BioC] How is LIMMA actually calculating the average expression value

Gordon K Smyth smyth at wehi.EDU.AU
Wed Jun 12 02:54:44 CEST 2013

Dear Miriam

> On Tue, 11 Jun 2013, Garcia Orellana,Miriam wrote:

> Dear Dr. Smyth.

> You are completely right the average expression is exact the same 
> (10.353) either using the fit2 or efit command but my new concern came 
> when I found out that the logFC differs ie. 1.333 for FAT contrast with 
> fit2 but 10.007 for same contrast when using efit command, or I am 
> havign a wrong interpretation??

Your interpretation is wrong.  The same comparison always gives the same 

> When I calculated by hand the logFC with the AveExpr given by the table 
> generated with the command summ.FAT=topTable(efit, 
> coef=1,adjust.method="BH",number=top) I was able to replicate the logFC 
> of 1.333 instead of 10.007 for the FAT contrast., Interesting to me is 
> that these AveExpr per treatments is given when using the efit command.

There is no command called "efit".  Perhaps you are refering to the use of 
contrast.fit?  In any case, there is no command which computes "AveExpr 
per treatments", as I told you in my previous email.

> From this table is that came my first original question, I mean, the 
> average of these expression values that came from the average of 3 
> arrays match for those that have high similarity values among the three 
> arrays but when they are not as similar, the values do not match when 
> comparing to a simple arithmetic mean of the GCRMA log2 values.

You are making a claim that is incorrect.  AveExpr is just the average of 
the log-expression values.

> Thanks very much for helping me with this, I deeply appreciate it.

I have done my best, but I still have little idea what your actual problem 
might be.

Best wishes

> Miriam

> ********************************
> Miriam Garcia, MS, PhD
> Department of Animal Sciences
> University of Florida

From: Gordon K Smyth [smyth at wehi.EDU.AU]
Sent: Tuesday, June 11, 2013 4:51 AM
To: Garcia Orellana,Miriam
Cc: Bioconductor mailing list
Subject: RE: How is LIMMA actually calculating the average expression value

Dear Garcia,

I'm afraid that I still don't understand what is not clear.

The average normalized expression value for the example probe
(Bt.17364.1.A1_at) is 10.353.  That is a simple average of the 18 values.

Every table you give shows the same value for AveExpr: 10.353.  It is the
same in every table, just as the documentation says it will be.

This seems to me to be simplicity itself.

What is the problem?

Best wishes

On Tue, 11 Jun 2013, Garcia Orellana,Miriam wrote:

> Dear Dr. Smyth.

> Thanks for your reply and let me apologize for probably miscalling the
> terms and/or not being clear enough when posting my question,
> microarrays data analysis is just a part of my study but definitely is
> giving me hard time to interpret my factorial with orthogonal contrast
> analysis.

> Before posting my previous question, I read the LIMMA user guide section
> 12.1 which states the the concept you are mentioning for AveEXpr in top
> table and you are right, the concept is clear with respect to the top
> table.

> However the average expression I mentioned is the one I got when using
> all the next code:

rawData <- ReadAffy()
esetgcrma <- gcrma(rawData)
eset1 <- exprs(esetgcrma)
eset2 <- eset1[!gene.rm,]
GCRMA values per each array for probe:   Bt.17364.1.A1_at
4367_SFA_HLA.CEL        4368_CTL_HLA.CEL        4381_SFA_LLA.CEL        4384_EFA_HLA.CEL        4387_EFA_HLA.CEL        4388_EFA_LLA.CEL
11.340  8.709   10.048  10.167  9.589   12.664

4394_CTL_HLA.CEL        4395_CTL_LLA.CEL        4396_SFA_HLA.CEL        4398_EFA_LLA.CEL        4399_SFA_LLA.CEL        4400_CTL_HLA.CEL
10.829  11.232  11.044  10.238  9.575   8.164

4402_EFA_HLA.CEL        4404_CTL_LLA.CEL        4409_EFA_LLA.CEL        4410_SFA_HLA.CEL        4413_CTL_LLA.CEL        4429_SFA_LLA.CEL
10.828  9.296   11.651  11.522  10.007  9.460
phenoDiet <- read.table("designDD_MR.txt",header=T,sep="\t")
write.exprs(esetgcrma, file="affy_ALL.gcrma.xls")
TS <- paste(phenoDiet$DD, phenoDiet$MR, sep=".")
TS <- factor(TS, levels=c("Ctl.LLA", "Ctl.HLA","SFA.LLA","SFA.HLA","EFA.LLA", "EFA.HLA"))
design <- model.matrix(~0+TS)
colnames(design) <- levels(TS)
fit <- lmFit(eset2, design, method="robust", maxit=1000000)
efit <- eBayes(fit)
#Contrast results
MatContrast=makeContrasts(FAT=(SFA.LLA + SFA.HLA + EFA.LLA + EFA.HLA)/4 - (Ctl.LLA + Ctl.HLA)/2,
                           FA=(EFA.LLA + EFA.HLA)/2 - (SFA.LLA + SFA.HLA)/2,
                           MR=(EFA.HLA+SFA.HLA+Ctl.HLA)/3 - (EFA.LLA+SFA.LLA+Ctl.LLA)/3,
                           FATbyMR=((EFA.HLA+SFA.HLA)/2 - Ctl.HLA) - ((EFA.LLA+SFA.LLA)/2-Ctl.LLA),
                           FAbyMR=(EFA.HLA-SFA.HLA)-(EFA.LLA - SFA.LLA),
#commands for tables to save the table of results: This commands resulted in the top tables containing:
**** I am listing an example for a specific probe*****

ID      FAT     FA      MR      FATbyMR FAbyMR  AveExpr F       P.Value adj.P.Val
Bt.17364.1.A1_at        1.3331  0.4183  -0.3757 1.3361  -3.0755 10.3534 14.5472 0.0001  0.0009

         ID      logFC   AveExpr t       P.Value adj.P.Val       B
5483    Bt.17364.1.A1_at        1.333   10.353  5.369   0.0002  0.0026  -2.337

         ID      logFC   AveExpr t       P.Value adj.P.Val       B
5483    Bt.17364.1.A1_at        0.418   10.353  1.530   0.15    0.59    -9.04




#Tables for the values of F statistics summ.allcontrast=topTable(efit,coef=NULL,adjust.method="BH",number=top)     # table of differentially expressed probesets
ID      Ctl.LLA Ctl.HLA SFA.LLA SFA.HLA EFA.LLA EFA.HLA AveExpr F       P.Value adj.P.Val
Bt.17364.1.A1_at        10.007  8.741   9.694   11.302  11.651  10.182  10.353  1384.0  1.01E-16        1.30E-16
summ.FAT=topTable(efit, coef=1,adjust.method="BH",number=top)
         ID      logFC   AveExpr t       P.Value adj.P.Val       B
5483    Bt.17364.1.A1_at        10.007  10.353  34.372  1.24E-13        1.62E-13        18.270

summ.FA=topTable(efit, coef=2,adjust.method="BH",number=top)
         ID      logFC   AveExpr t       P.Value adj.P.Val       B
5483    Bt.17364.1.A1_at        8.741   10.353  29.622  7.6E-13 9.4E-13 1.6E+01

summ.MR=topTable(efit, coef=3,adjust.method="BH",number=top)

summ.FATbyMR=topTable(efit, coef=4,adjust.method="BH",number=top)

summ.FAbyMR=topTable(efit, coef=5,adjust.method="BH",number=top)

ALSO, Thanks to your recommendation,

I review my code and rerun the data using 2 options of topeTable one with
the fit2 command and other with the efit as posted with the example I am
not sure how the average expression value as presented with the command

Calculating the AveExpr for each group of 3 arrays with the GCRMA log2
values, it give me quite similar results as that on the summary table for
some of the six treatments but for others average expression valus simply
do not match.

In addition when running specific contrast as it is the FAT contrast when
using efit or fit2, both approaches give me the same AveExpr value but log
FC, T value, B, and P values. The use of fit2 give the FC values as if I
were manually calculating with the AvExpr obtained in the later table
above. So I think the right one table to use if that generate with the
fit2, but so I am wonder what is the Ftable with efit calculating as log

Thanks so much for all,


Miriam Garcia, MS, PhD
Department of Animal Sciences
University of Florida

From: Gordon K Smyth [smyth at wehi.EDU.AU]
Sent: Monday, June 10, 2013 8:36 PM
To: Garcia Orellana,Miriam
Cc: Bioconductor mailing list
Subject: How is LIMMA actually calculating the average expression value

Dear Miriam,

> Date: Sun, 9 Jun 2013 10:28:41 +0000
> From: "Garcia Orellana,Miriam" <mgarciao at ufl.edu>
> To: Bioconductor mailing list ?[bioconductor at r-project.org]?
>       <bioconductor at r-project.org>
> Subject: [BioC] How is LIMMA actually calculating the average
>       expression value?
> Dear all:

> I have found quite the same question being asked at least twice but I
> still not have clear answer about how the ebayes method in LIMMA
> calculate the average expression value for a given experimental group.

The limma package does not and never has computed the expression level for
individual experimental groups.  The AveExpr columin is the average of all
arrays (ie for all groups not for one group).  That is clearly documented,
or so it seems to me.

The limma User's Guide gives in Section 13.1 a description of all
quantities output by topTable.  It says

     "The AveExpr column gives the average log2-expression level for
     that gene across all the arrays and channels in the experiment."

That seems to be me to be completely unambiguous.  What is unclear about

The help page ?topTable says that AveExpr is

     "average log2-expression for the probe over all arrays and channels,
     same as Amean in the MarrayLM object"

The help page ?"MArrayLM-class" says that Amean is a

     "numeric vector containing the average log-intensity for each probe over
     all the arrays in the original linear model fit. Note this vector does
     not change when a contrast is applied to the fit using contrasts.fit."

Again this seem to me to be unambiguous.

I've said the same thing in response to questions on this list several
times.  What is unclear?

> I have used GCRMA to normalize my affimetrix values and then obtained
> the log2 expression values as (values below do not necessarily
> correspond to the same probe):
> 4395_CTL_LLA.CEL        :7.89
> 4404_CTL_LLA.CEL:        8.21
> 4413_CTL_LLA.CEL:       8.07
> I have calculated by excel:
> Simple mean = 8.055
> Geometric mean = 8.054
> Whereas the top table for average expression of these 3 values gave me: 8.055

There is no such thing as a "top table for average expression".  Top
tables are always for comparisons between groups.  I have no idea what you
are trying to do.

Could you please read the documentation, and have a look at the posting
guide?  If you post again, please give the whole code leading to this
output, and give expression for all arrays in your experiment, not just

Best wishes

> This values are quite the same regardless of calculation method, However
> when more variability is among values the calculated average expression
> differs differs quite largely:

> 4368_CTL_HLA.CEL:       8.26
> 4394_CTL_HLA.CEL:       7.17
> 4400_CTL_HLA.CEL:       8.70
> Simple mean = 8.042
> Geometric mean = 8.015
> Whereas the top table for average expression of these 3 values gave me: 8.263. In this case this average expression value seems to be the median but on the next set of samples not.

> 4368_CTL_HLA.CEL:       10.758
> 4394_CTL_HLA.CEL:       10.907
> 4400_CTL_HLA.CEL:       7.634
> Simple mean = 8.92
> Geometric mean = 9.766
> Whereas the top table for average expression of these 3 values gave me: 9.862, which in this case is not at all close to the median.
> I will appreciate any help on this matter. It will also be appreciated,
> any additional though on whether the adjusted average expression
> (whichever the method is) is well enough to correct for expression
> variability within a given treatment, so I do not need to be worry for
> any potential outlier expression value or should I be concerned about?
> Regards,
> Miriam
> ********************************
> Miriam Garcia, MS, PhD
> Department of Animal Sciences
> University of Florida

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