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Re: st: strange -multproc- results


From   Roger Newson <r.newson@imperial.ac.uk>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: strange -multproc- results
Date   Wed, 17 Mar 2010 20:28:49 +0000

The paper to consult on these methods is Newson (2003), which gives a survey of all the wierd and wonderful assumptions, formulas, and features of all these procedures. The Simes procedure is less conservative than most, but the Krieger procedure is usually even less conservative, because it estimates the prior probability that a null hypothesis is true. For this to be feasible, the Krieger procedure assumes that the P-values are independent, so consistent estimation can be done. The Storey procedure is probably even less conservative than the Krieger, and is even more complicated.

I hope this helps.

Best wishes

Roger


References

Newson R. Multiple-test procedures and smile plots. The Stata Journal 2003; 3(2): 100-132. Download from
http://www.stata-journal.com/article.html?article=st0035


On 17/03/2010 20:07, Feiveson, Alan H. (JSC-SK311) wrote:
Hi - I have been using -multproc- to control the false discovery rate (FDR) on 27 significance tests. As given in the help file, there are several methods to chose from for controlling the FDR: liu1,liu2,simes,yekutieli, and krieger.


             method()          Step type    FWER/FDR    Definition or source
            userspecified     One-step     Either      pcor() option
            bonferroni        One-step     FWER        pcor=puncor/m
            sidak             One-step     FWER        pcor=1-(1-puncor)^(1/m)
                                                       (or Sidak, 1967)
            holm              Step-down    FWER        Holm, 1979
            holland           Step-down    FWER        Holland and Copenhaver, 1987
            liu1              Step-down    FDR         Benjamini and Liu, 1999a
            liu2              Step-down    FDR         Benjamini and Liu, 1999b
            hochberg          Step-up      FWER        Hochberg, 1988
            rom               Step-up      FWER        Rom, 1990
            simes             Step-up      FDR         Benjamini and Hochberg, 1995 (or
                                                       Benjamini and Yekutieli, 2001
                                                       (first method))
            yekutieli         Step-up      FDR         Benjamini and Yekutieli, 2001
                                                       (second method)
            krieger           Step-up      FDR         Benjamini, Krieger and Yekutieli, 2001

So I tried liu1, liu2, simes, yekutieli, and krieger to see what difference it would make with a specified FDR of 0.05. The two liu's and yekutieli were about the same (4 rejections, critical P-value about 0.002. But the simes and krieger were completely different (simes: 14 rejections, critical p-vlaue = 0.026) and (krieger: 15 rejections, critical p-value = 0.051). The latter two look too good to be true, especially the Krieger, where the critical p-value is actually higher than the specified FDR rate.

Anyone know what's going on here? Am I doing this correctly? What assumptions are there for Krieger, for example, that do not hold for the first three?

Al Feiveson

If anyone wants to try it - here's the data:

   h	         se	          z	         pv
1761.754	419.83	4.196352	.0000271
.0613758	.0171379	3.58129	.0003419
.0431283	.0134256	3.212402	.0013163
.0503242	.0159218	3.160711	.0015738
.0662939	.0223807	2.962102	.0030555
.0388915	.0133944	2.903562	.0036894
.0793423	.0274955	2.885645	.0039061
.0353006	.0129654	2.722682	.0064754
868.2667	323.8542	2.681042	.0073393
.0491057	.0184865	2.6563	.0079003
893.4875	341.7166	2.614703	.0089305
.0310786	.0131919	2.355878	.018479
.034885	.0150222	2.322223	.0202209
.032349	.0144647	2.236412	.0253248
.0302972	.0139816	2.166937	.0302396
.0295493	.0165115	1.789618	.0735153
-.0201654	.0129031	-1.562831	.1180923
.0255772	.017776	1.438857	.1501909
.0150236	.0122768	1.223738	.2210511
.0187261	.0165989	1.128154	.2592548
-.013579	.0127488	-1.065118	.2868224
.0142208	.0142817	.9957331	.3193798
.0099778	.0117025	.8526207	.3938697
.0071485	.0095379	.7494824	.4535665
.0130484	.021209	.6152284	.5384039
-.0067718	.0137157	-.4937261	.6214996
.0028293	.0090162	.3138045	.7536695

. multproc ,method(liu1) pvalue(pv) puncor(.05)

Method: liu1
Uncorrected overall critical P-value: .05
Number of P-values: 27
Corrected overall critical P-value: .00262649
Number of rejected P-values: 4

. multproc ,method(liu2) pvalue(pv) puncor(.05)

Method: liu2
Uncorrected overall critical P-value: .05
Number of P-values: 27
Corrected overall critical P-value: .00255198
Number of rejected P-values: 4

. multproc ,method(simes) pvalue(pv) puncor(.05)

Method: simes
Uncorrected overall critical P-value: .05
Number of P-values: 27
Corrected overall critical P-value: .02592593
Number of rejected P-values: 14

. multproc ,method(yekutieli) pvalue(pv) puncor(.05)

Method: yekutieli
Uncorrected overall critical P-value: .05
Number of P-values: 27
Corrected overall critical P-value: .00190351
Number of rejected P-values: 4

. multproc ,method(krieger) pvalue(pv) puncor(.05)

Method: krieger
Uncorrected overall critical P-value: .05
Number of P-values: 27
Corrected overall critical P-value: .05102041
Number of rejected P-values: 15


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--
Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

Opinions expressed are those of the author, not of the institution.
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