[BioC] limma posterior variance - revisited

[Charles C. Berry]

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
> 
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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