[BioC] Testing for no difference

[Albyn Jones]

There are several procedures, I'm not sure which is best.  Take a look
at Chapter 7 of 

   Testing Statistical Hypotheses of Equivalence and Noninferiority, 
   Second Edition by Stefan Wellek
   CRC/Chapman & Hall

albyn

On Tue, Jul 24, 2012 at 09:02:52AM +0200, Gustavo Fernández Bayón wrote:
> Hi Albyn.  
> 
> As I have already answered to W. Huber in this thread, I think that TOST could be a good choice here. I think I am going to give it a try. Problem is, I am comfortable with the two sample description of TOST but, what about multiple groups? Should I do a similar procedure to the one I was doing before? That is, leave-one-out methods for each of the probes, but doing TOST's instead of common tests…
> 
> Thanks for your answer.
> 
> Regards,
> Gus
> 
> 
> 
> ---------------------------
> Enviado con Sparrow (http://www.sparrowmailapp.com/?sig)
> 
> 
> El lunes 23 de julio de 2012 a las 17:29, jones escribió:
> 
> > You might look into "tests of equivalence", one common procedure
> > involves defining an interval (-a,a) and doing two one sided
> > tests ("TOST") for H_0: delta > a and delta < -a, which is equivalent
> > to checking that the CI for the difference is contained in
> > the specified interval.
> >  
> > albyn
> >  
> > On 7/23/12 12:52 AM, Gustavo Fernández Bayón wrote:
> > > Hi everybody.
> > >  
> > > I have a set of only 5 samples of Illumina27k methylation data. We
> > > have extracted some info from the probes, but now the researcher in
> > > charge of the project wants something that could support his idea of
> > > the five samples to be practically equivalent wrt to their  
> > > methylation
> > > levels.
> > >  
> > > I know that the sample is quite small. Intuitively, if you plot
> > > densities from the 5 samples, they are almost equal. Problem is, I do
> > > not know a way in which I could give a statistical significance about
> > > this fact (yes, as always, there is the "I need a p-value" problem).
> > >  
> > > 1) I did PCA on both beta values and m-values, and found that the
> > > first principal component accounts for between 90 and 91% of the  
> > > total
> > > variance. In the biplot, the five samples appear to be very close.
> > >  
> > > 2) I asked for advice to a statistician friend, and we tried to do
> > > the following: probe by probe, we tried a Leave-One-Out approach, by
> > > calculating a confidence interval for 4 of the samples and seeing if
> > > the remaining probe falls within the interval. Then, for each probe,  
> > > I
> > > summed the number of times a methylation value fell out of the
> > > confInt, only to find out that nearly 53% of the probes contain -in
> > > this sense- 'outliers'.
> > >  
> > > At first it surprised me, but then I noticed -by plotting the
> > > outliers against the samples- that these 'outliers' were uniformly
> > > distributed among samples, which I think is again intuitive, i.e.,
> > > there are indeed differences (statistical differences, maybe not
> > > biological) among samples, but there is no global difference of one  
> > > of
> > > the samples w.r.t. the others.
> > >  
> > > These differences might be related to technical noise, so I was
> > > thinking of imposing a minimum difference in order to test again for
> > > outliers. Would this be ok?
> > >  
> > > Is there any method I can use to try to show there is no difference
> > > among the samples? Or should I stay with the graphs and the intuitive
> > > description on the text?
> > >  
> > > Thanks. Any help or hint would be much appreciated.
> > >  
> > > Regards,
> > > Gustavo
> > >  
> > > ---------------------------
> > > Enviado con Sparrow (http://www.sparrowmailapp.com/?sig)
> > >  
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> 
> 
> 

-- 
Albyn Jones
Reed College
jones at reed.edu