[BioC] limma posterior variance - revisited

[Naomi Altman]

Thanks, Chuck.

I noticed this after my first set of e-mails and fixed it.

It was the source of the original problem (variance inflation instead of 
variance stabilization) but not the 2nd problem - 97% of the genes appear 
to differentially express (FDR=.01) and that percentage is HIGHER than the 
percentage of genes with ebayes or ordinary p-value less than .01.

--Naomi

At 06:14 PM 6/9/2004 +0000, you wrote:

>Excuse me if I missed something here, but should not
>
> >
> >contrast.matrix
> >
> >      c1 c2 c3 c4 c5
> >trt1  1  1 1  1 1
> >trt2 -1  1 1  1 1
> >trt3  0 -2  1  1 1
> >trt4  0  0 -3  1  1
> >trt5  0  0 0 -5  1
> >trt6  0  0 0  0 -5
>
>(Note '-5' in c4)
>
>Be
>
>contrast.matrix
>
>       c1 c2 c3 c4 c5
>trt1  1  1 1  1 1
>trt2 -1  1 1  1 1
>trt3  0 -2  1  1 1
>trt4  0  0 -3  1  1
>trt5  0  0 0 -4  1
>trt6  0  0 0  0 -5
>
>Is this merely a typo in your email or is this the source of the
>problem?
>
>Chuck
>
>On Wed, 9 Jun 2004, Gordon Smyth wrote:
>
> > At 06:43 AM 9/06/2004, Naomi Altman wrote:
> > >The problem remains, but I have added a few lines of code that were
> > >missing in the original posting.
> > >
> > >I have just run limma and am getting p-values after eBayes that are
> > >smaller than the p-values before, leading to 100% of my genes being
> > >declared significant at any value of FDR you care to use.
> >
> > It seems very surprising to get 100% of genes significant, but nothing in
> > the output that you give below suggests that anything is wrong. It all
> > seems as it should be. You should tend to get smaller p-values after 
> eBayes
> > than before because the degrees of freedom increase, but not uniformly so
> > because many of the residual standard deviations also increase.
> >
> > >The design is a 1-way ANOVA with 6 treatments and 2 reps/treatment (which
> > >I know is not great but ...)
> > >
> > >I thought that the denominator adjustment would make the posterior
> > >sigma^2 > unadjusted MSE,  but this is not the case.
> >
> > Empirical Bayes methods, like all shrinkage methods, shrink estimators
> > towards a common value. This means that some values will go up, and some
> > will go down. The help page says that eBayes() "uses an empirical Bayes
> > method to      shrink the gene-wise sample variances towards a common
> > value". What is happening is that the precisions (the inverse sample
> > variances) are being set to their posterior means. You can see the
> > complete, pretty simple, formula by following the URL for the reference
> > given on the help page.
> >
> > Gordon
> >
> > >   Here are the commands I used to fit the model and do the ebayes
> > > adjustment.
> > >
> > >design=model.matrix(~-1+factor(c(1,1,2,2,3,3,4,4,5,5,6,6)))
> > >colnames(design)=c("trt1","trt2","trt3","trt4","trt5","trt6")
> > >
> > >fitRMA=lmFit(RMAdata,design)
> > >
> > >contrast.matrix
> > >
> > >      c1 c2 c3 c4 c5
> > >trt1  1  1 1  1 1
> > >trt2 -1  1 1  1 1
> > >trt3  0 -2  1  1 1
> > >trt4  0  0 -3  1  1
> > >trt5  0  0 0 -5  1
> > >trt6  0  0 0  0 -5
> > >
> > >fitCont=contrasts.fit(fitRMA,contrast.matrix)
> > >fitAdj=eBayes(fitCont)
> > >
> > >ls.print(lsfit(fitRMA$sigma^2,fitAdj$s2.post))
> > >Residual Standard Error=0
> > >R-Square=1
> > >F-statistic (df=1, 22744)=1.632754e+35
> > >p-value=0
> > >
> > >           Estimate Std.Err      t-value Pr(>|t|)
> > >Intercept   0.0093       0 1.026963e+17        0
> > >X              0.5628       0 4.040735e+17        0
> > >
> > >mean(fitAdj$s2.post)
> > >[1] 0.02991697
> > >
> > >mean(fitRMA$sigma^2)
> > >[1] 0.03656270
> > >
> > >fitAdj$s2.prior
> > >[1] 0.02136298
> > >
> > >
> > >Naomi S. Altman                                814-865-3791 (voice)
> > >Associate Professor
> > >Bioinformatics Consulting Center
> > >Dept. of Statistics                              814-863-7114 (fax)
> > >Penn State University                         814-865-1348 (Statistics)
> > >University Park, PA 16802-2111
> >
> > _______________________________________________
> > Bioconductor mailing list
> > Bioconductor at stat.math.ethz.ch
> > https://www.stat.math.ethz.ch/mailman/listinfo/bioconductor
> >
>
>Charles C. Berry                        (858) 534-2098
>                                          Dept of Family/Preventive Medicine
>E mailto:cberry at tajo.ucsd.edu            UC San Diego
>http://hacuna.ucsd.edu/members/ccb.html  La Jolla, San Diego 92093-0717
>
>

Naomi S. Altman                                814-865-3791 (voice)
Associate Professor
Bioinformatics Consulting Center
Dept. of Statistics                              814-863-7114 (fax)
Penn State University                         814-865-1348 (Statistics)
University Park, PA 16802-2111