Dear all
Some time ago, I posted the following message to the list:
===================================================================
Hello
I would very much appreciate receiving advice on tried and tested
methods for correction for multiple comparisons within the context of a
logistic regression analysis in which a very high number of gene-gene or
gene-environment interactions have been tested for significance. The
idea here is that whilst the p-values have already been adjusted for
confounding, they have not been corrected for chance.
I am already familiar with the Bonferroni correction and its less
conservative variants. However, I suspect that more sophisticated or
esoteric methodologies are appropriate within the setting outlined above.
Many thanks for your interest in this enquiry.
Best wishes
Margaret
I received a variety of illuminating responses and in response to a request, I have provided a summary of these responses below.
Response 1
==========
Dear Margaret,
This may be what you need
Title: CONTROLLING THE FALSE DISCOVERY RATE - A PRACTICAL AND POWERFUL
APPROACH TO MULTIPLE TESTING
Author(s): <CIW.htm>BENJAMINI Y, <CIW.htm>HOCHBERG Y
Source: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES
B-METHODOLOGICAL 57
(1): 289-300 1995
Document Type: Article
Language: English
<CIW.htm>Cited References:<CIW.htm> 14 <CIW.htm>Times
Cited:<CIW.htm>
1590 <CIW.htm>dc3f5c.jpg <javascript:void();>dc3f8b.jpg
Abstract: The common approach to the multiplicity problem calls for
controlling the familywise error rate (FWER). This approach, though,
has
faults, and we point out a few. A different approach to problems of
multiple significance testing is presented. It calls for controlling
the
expected proportion of falsely rejected hypotheses - the false
discovery
rate. This error rate is equivalent to the FWER when all hypotheses are
true but is smaller otherwise. Therefore, in problems where the control
of
the false discovery rate rather than that of the FWER is desired, there
is
potential for a gain in power. A simple sequential Bonferroni-type
procedure is proved to control the false discovery rate for independent
test statistics, and a simulation study shows that the gain in power is
substantial. The use of the new procedure and the appropriateness of
the
criterion are illustrated with examples.
Author Keywords: BONFERRONI-TYPE PROCEDURES; FAMILYWISE ERROR RATE;
MULTIPLE-COMPARISON PROCEDURES; P-VALUES
KeyWords Plus: BONFERRONI PROCEDURE
Addresses: BENJAMINI Y (reprint author), TEL AVIV UNIV, SACKLER FAC
EXACT
SCI, SCH MATH SCI, DEPT STAT, IL-69978 TEL AVIV, ISRAEL
Publisher: BLACKWELL PUBL LTD, 108 COWLEY RD, OXFORD, OXON, ENGLAND OX4
1JF
Subject Category: STATISTICS & PROBABILITY
IDS Number: QE453
ISSN: 0035-9246
Response 2
==========
Hello Margaret
I wrote a review of multiple-test procedures, and their implementation
in the Stata statistical package, in The Stata Journal a few years ago
(Newson, 2003), including an example with odds ratios from a genetics
study. I also gave a presentation on the subject to the UK Stata User
Meeting in 2003. Both the presentation and a pre-publication draft of
the paper can be downloaded from my website (see my signature below).
Newson R and the ALSPAC Study Team. Multiple-test procedures and smile
plots. The Stata Journal 2003; 3(2): 109-132. Download pre-publication
draft from my website at
www.imperial.ac.uk/nhli/r.newson/
Response 3
==========
As far as I'm aware there are no 'tried and tested' methods for
accounting for such multiple testing.
I do however have a few references that you may find useful...
Author: Marchini, J.; Donnelly, P.; Cardon, L. R.
Title: Genome-wide strategies for detecting multiple loci that
influence complex diseases
Journal: Nat. Genet.
Date: 2005
Volume: 37
Number: 4
Pages: 413-417
(The first author of the above is in the process of developing a
program for analysing data within the framework described. Its still
in development, but I contacted the author a while ago and was allowed
an early version of the source code to compile and run, its called
Bayesian Interaction Analysis, BIA).
Author: Evans, D. M.; Marchini, J.; Morris, A. P.; Cardon, L. R.
Title: Two-Stage Two-Locus Models in Genome-Wide Association.
Journal: PLoS Genet
Date: 2006
Volume: 2
Number: 9
One of the intersting findings of this paper is that despite the
increase in multiple testing exhaustive interaction analyses are
morepowerful at detecting association than two-stage strategies.
A recent approach that is increasing in popularity in the context
of genome wide association screens (and naturally by extension the
testing for interactions) which may be of interest is the False
Discovery Rate (FDR) which attempts to control the number of false
positives used. Its main application (in contradiction to the above
paper) is in two-stage study designs. A good reference is..
Author: Storey, J. D.; Tibshirani, R.
Title: Statistical significance for genomewide studies
Journal: Proc. Natl. Acad. Sci. U. S. A
Date: 2003
Volume: 100
Number: 16
Pages: 9440-9445
which is implemented as a package for R (http://www.r-project.org/)
and the home page is at http://faculty.washington.edu/~jstorey/qvalue/
Response 4
==========
Dear Margaret,
having worked in this field a couple of years ago, I came across
the following reference which might be of help; we (Kabesch et al) implemented the
Benjamini-
Liu method, which controls the false discovery rate (FDR).
Reiner, A, Yekutieli, D, and Benjamini, Y. 2003.
Identifying differentially expressed genes using false discovery rate
controlling procedures. Bioinformatics, 19(3): 368-375.
Enclose a couple of related articles which might be of interest.
Thank you to all those who emphasized the importance of the false
discovery rate and to those authors who (unknowingly) alerted me to
the peculiarities associated with testing for gene-gene and
gene-environment interactions in particular. I hope that some
others find the above info helpful.
Best wishes
Margaret
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