# [BioC] Limma, SAM and Fold Change Calculation

Holger Schwender holger.schw at gmx.de
Fri Jul 13 16:55:30 CEST 2007

```Hi Peter, hi Gordon,

the reason for the fold change computation in SAM is simply that Tusher et al. also use these fold changes. In 2002, SAM was part of my diploma thesis and I tried to reproduce the results of Tusher et al. and the results that are provided by the Excel SAM version. Since then many things in sam have changed, mainly to make sam faster, more user-friendly and more flexible. But I didn't change the computation of the fold change to actually avoid the question why the fold changes differ between the siggenes SAM and the Excel SAM.

Admittedly, "because Tusher et al. do so" is not a very good reason, but I have stopped counting how often I was ask why this and that differs between Excel SAM and siggenes SAM.

Would it help you if I add another slot to the SAM object that contains the numerator of the test statistics? Note that you can compute these numerators by

> sam.out at d * (sam.out at s0 + sam.out at s)

if sam.out is the output of sam.

Best,
Holger

-------- Original-Nachricht --------
Datum: Fri, 13 Jul 2007 22:44:12 +1000 (EST)
Von: "Gordon K Smyth" <smyth at wehi.edu.au>
An: "Peter White" <pwhite at mail.med.upenn.edu>
CC: bioconductor at stat.math.ethz.ch
Betreff: [BioC] Limma, SAM and Fold Change Calculation

> Dear Peter,
>
> Since I'm the limma author, it will come as no surprise to you that I view
> the limma fold change
> (diff of log-intensities) as the more natural, consistent and useful.
>
> I don't know why SAM computes fold change as it does.  It seems to me
> somewhat inconsistent,
> because SAM uses the limma log-fold-change as numerator in its own test
> statistic for computing
> statistical significant.  So SAM reports a different fold change measure
> to that which it uses
> internally for determining statistical significance.
>
> Best wishes
> Gordon
>
> > Date: Thu, 12 Jul 2007 10:26:54 -0400
> > From: "Peter White" <pwhite at mail.med.upenn.edu>
> > Subject: [BioC] Limma, SAM and Fold Change Calculation
> > To: <bioconductor at stat.math.ethz.ch>
> >
> > I wondered if anyone could comment on what is generally considered the
> most
> > appropriate method of calculating fold change values from Affy data. I
> have
> > a data set from a test vs. control experiment (n=3 in each group)
> performed
> > on the MOE430_2 array. I used the Affy package to read in the CEL file
> data
> > and GCRMA to normalize. Finally I used limma to analyze (lmFit and
> eBayes).
> > Now the FC coefficients I get back from limma appear to be
> log2(2^(mean(test
> > replicates in log2))/(2^mean(control replicates in log2)). For example:
> >
> >> exprs(eset)[18731,1:6]
> >  TA2.CEL  TA5.CEL  TA7.CEL  TA1.CEL  TA8.CEL  TA9.CEL
> > 3.294215 4.851795 4.403851 4.782934 7.716893 9.284909
> >
> >> fit\$coefficients[18731,1:2] #returns the mean of the above log2 values
> >   Fed_MT   Fed_WT
> > 4.183287 7.261578
> >
> >> fit2\$coefficients[18731,1]
> > [1] -3.078291
> >
> >> -1/2^fit2\$coefficients[18731,1]
> > [1] -8.446136
> >
> > So we have a probe that is reporting a -8.4 fold downregulation.
> >
> > The problem is that SAM does not calculate the fold change values in the
> > same manner. It appears to take the average of the unlogged data and
> then
> > use those values to calculate fold changes. Thus:
> >
> >> 2^exprs(eset)[18731,1:6]
> >    TA2.CEL    TA5.CEL    TA7.CEL    TA1.CEL    TA8.CEL    TA9.CEL
> >   9.809738  28.875927  21.168555  27.530016 210.385700 623.786694
> >
> >> tmp <- c(mean(2^exprs(eset)[18731,1:3]),mean(2^exprs(eset)[18731,4:6]))
> >> tmp
> > [1]  19.95141 287.23414
> >
> >> tmp[1]/tmp[2]
> > [1] 0.06946043
> >
> >> -1/(tmp[1]/tmp[2])
> > [1] -14.39669
> >
> > So now we have -14.4 fold downregulation.
> >
> > The example given is of course an extreme, but using the limma method
> there
> > are 282 probes with a fold change >2, while using the sam method there
> are
> > only 159, with 141 probes in common. The probes that were called
> uniquely by
> > limma were almost all downregulated (-2 to -5 fold).
> >
> > MY QUESTION IS WHICH METHOD IS THE CORRECT WAY?
> >
> > Thanks,
> >
> > Peter
> >
> > Peter White, Ph.D.
> > Technical Director
> > Functional Genomics Core
> > Department of Genetics
> > University of Pennsylvania
> > 570 Clinical Research Building
> > 415 Curie Boulevard
> > ?
> > Tel: +1 (215) 898-0773
> > Fax: +1 (215) 573-2326
> > E-mail: pwhite at mail.med.upenn.edu
> > ?
> > http://www.med.upenn.edu/pdc/cores_fgc.html
> > http://www.med.upenn.edu/kaestnerlab/
> > http://www.betacell.org/microarrays
> > http://www.cbil.upenn.edu/EPConDB/
>
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