[BioC] Nonorthogonal multiple comparisons in Limma/ Books on Bayesian Statistics

[Richard Friedman]

Gordon,

	Thank you for answering my questions. The last equation in your paper 
makes intuitive sense to me.

	I'm wondering if you can take the time to answer two  more questions:

1. Say I have the following case:

Level A (3 replicates)
Level B (2 replicates)
Level C(1 replicate)
Level D(1 replicate)

Can I legitimately calculate a P value for the contrast Level A to 
level C in the linear model even though I have only one replicate on 
Level C. I am not talking about just Limma here. I am talking about the 
linear model in general. Also,
I realize that one replicate is poor experimental design. This is what 
I was given to analyze.

2. If I wished to apply a multiple test correction to the pvalues from 
non-orthogonal contrasts, would the following procedure be legitimate::

	1. Generate a pvalue for each contrast in the set of nonothogonal 
contrasts for each gene  using classifyTestsF().
	2. Correct the pvalues using a multiple test correction such as FDR.

I realize that no multiple-test correction is entirely satisfactory, I 
just want to get an approximate estimate of the p-values for each 
contrast as a guide to further experimentation and literature 
searching.

Best wishes,
Rich

On Aug 5, 2004, at 9:26 PM, Gordon Smyth wrote:

> At 03:12 AM 6/08/2004, Richard Friedman wrote:
>> Fellow  Expressionists,
>>
>>         Does Limma automatically perform a multiple
>> comparison adjustment for non-orthogonal contrasts?
>
> Yes. classifyTestsF() is a classification which takes full account of 
> non-orthogonality. Unpublished method though. Also "holm" and some 
> other options are valid even across non-orthogonal contrats.
>
>>         If not, can you recommend another program that can
>> be used in conjunction with Limma to do this?
>>
>>         Also, I find the Bayesian theory in the paper
>> by Gordon Smyth ("Linear Models and Empirical
>> Bayes Methods..." tough going) Can anyone
>> please recommend a book or books on Bayesian methods
>> that can bridge the gap between basic statistics texts
>> (e.g. Hoel, "An Introduction to Mathematical Statistics" and
>> Zar "Biostatistical Analysis" and this article)?
>
> I don't know of any accessible refs, even for stat majors I'm afraid. 
> And unfortunately Bayes refs may not be much help. The empirical Bayes 
> arithmetic requires different quantities to be computed compared to 
> full Bayes.
>
> I hope that the final formula in the paper make intuitive sense even 
> though the math derivation might be hard.
>
> Gordon
>
>> Thanks and best wishes,
>> Rich
>
>
------------------------------------------------------------
Richard A. Friedman, PhD
Associate Research Scientist
Herbert Irving Comprehensive Cancer Center
Oncoinformatics Core
Lecturer
Department of Biomedical Informatics
Box 95, Room 130BB or P&S 1-420C
Columbia University Medical Center
630 W. 168th St.
New York, NY 10032
(212)305-6901 (5-6901) (voice)
friedman at cancercenter.columbia.edu
http://cancercenter.columbia.edu/~friedman/

In Memoriam, Francis Crick