Re: st: strange -multproc- results

[Roger Newson <r.newson@imperial.ac.uk>]

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
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Tel: +44 (0)20 7352 8121 ext 3381
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Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
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Opinions expressed are those of the author, not of the institution.
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