[BioC] Comparison of correlation coefficients - Details

[Christian.Stratowa at vie.boehringer-ingelheim.com]

Dear all

Maybe, my last mail did not explain my problem correctly:
Since we are interested, which genes have similar expression profiles
in a certain tissue or in different tissues, we have calculated the 
correlation coefficients between all 46,000 x 46,000 genes of the 
HG_U133A/B chipset for about 70 tissues, where the number of samples 
per tissue ranges from 10 to more than 200.

While writing an R-function to display the correlation coefficients
between gene A and B in the different tissues as bar-graph, I realized
that it may not be correct to compare the different correlation coefficients
directly, since the number of samples per tissue varyies between 10 and 200.

Thus, the question is: Is there a way to compare different correlation
coefficients and/or apply some kind of normalization?

Assuming that this might be a well known statistical problem I was browsing
statistics books and the web for more information, but could only find the
function "compcorr" which gives a p-value how well you can trust the 
comparison of two correlation coefficients from different samples.

Even though this might currently not be a direct Bioconductor question, it
is certainly a microarray analysis related question. Any suggestions how
to solve this problem would be greatly appreciated.

Best regards
Christian Stratowa

==============================================
Christian Stratowa, PhD
Boehringer Ingelheim Austria
Dept NCE Lead Discovery - Bioinformatics
Dr. Boehringergasse 5-11
A-1121 Vienna, Austria
Tel.: ++43-1-80105-2470
Fax: ++43-1-80105-2782
email: christian.stratowa at vie.boehringer-ingelheim.com



-----Original Message-----
From: Stratowa,Dr.,Christian FEX BIG-AT-V 
Sent: Tuesday, July 13, 2004 14:40
To: 'bioconductor at stat.math.ethz.ch'
Subject: Comparison of correlation coefficients



Dear Bioconductor expeRts

Is it possible to compare correlation coefficients or to normalize 
different correlation coefficients?

Concretely, we have the following situation:
We have gene expression profiles for different tissues, where the 
number of samples per tissue are different, ranging from 10 to 250. 
We are able to determine the correlation between two genes A and B 
for each tissue separately, using "cor.test". However, the question 
arises if the correlation coefficients between different tissues can 
be compared or if they must somehow be "normalized", since the 
number of samples per tissue varyies. 

Searching the web I found the function "compcorr", see:
http://www.fon.hum.uva.nl/Service/Statistics/Two_Correlations.html
http://ftp.sas.com/techsup/download/stat/compcorr.html
and implemented it in R:

compcorr <- function(n1, r1, n2, r2){
# compare two correlation coefficients
# return difference and p-value as list(diff, pval)

#	Fisher Z-transform
	zf1 <- 0.5*log((1 + r1)/(1 - r1))
	zf2 <- 0.5*log((1 + r2)/(1 - r2))

#	difference
	dz <- (zf1 - zf2)/sqrt(1/(n1 - 3) + (1/(n2 - 3)))

#	p-value
	pv <- 2*(1 - pnorm(abs(dz)))

	return(list(diff=dz, pval=pv))
}

Would it make sense to use the resultant p-value to "normalize" the 
correlation coefficients, using: corr <- corr * compcorr()$pval

Is there a better way or an alternative to "normalize" the correlation 
coefficients obtained for different tissues?

Thank you in advance for your help.
Since in the company I am not subscribed to bioconductor-help, could you 
please reply to me (in addition to bioconductor-help)

P.S.: I have posted this first at r-help and it was suggested to me to 
post it here, too.

Best regards
Christian Stratowa

==============================================
Christian Stratowa, PhD
Boehringer Ingelheim Austria
Dept NCE Lead Discovery - Bioinformatics
Dr. Boehringergasse 5-11
A-1121 Vienna, Austria
Tel.: ++43-1-80105-2470
Fax: ++43-1-80105-2782
email: christian.stratowa at vie.boehringer-ingelheim.com