A good question. The book on microarray expression data by McLachlan, Do and Ambroise contains a review of FDR methods in Chapter 5, but a more detailed review is much needed. BTW, Yoav Benjamini has shown me that one can substitute a particular first order approximation to pi0 into the BH method without harming the ability of the method to work for small numbers of genes. So far, I haven't been motivated enough to do that because the improvement is usually relatively small for microarray data sets. Cheers Gordon At 01:13 PM 16/01/2006, Naomi Altman wrote: >This discussion convinced me to read through my collection of FDR >papers, and I am finding it heavy going. Is there a review paper >somewhere that goes through these methods + Storey et al (and maybe >the Simes and Bonferroni FWER methods) and explains their >applicability to the types of dependence structures typically found >in e.g. factorial ANOVA where we may be testing main effects and >interactions, or 1-way ANOVA with all pairwise comparisons, or >eBayes tests like limma, where dependence is induced by the >denominator adjustment? > >Thanks, >Naomi > > >At 04:32 PM 1/14/2006, Gordon K Smyth wrote: >>Actually I don't think the number of genes is a problem. Neither >>BH nor BY use an estimate of pi0 >>(the true proportion of hull hypotheses). Whenever pi0 would >>appear as a multiplier in the >>formulae, they use 1 instead. The methods are therefore somewhat >>conservative if pi0 is not >>large, but they continue to control the FDR at below the requested level. >> >>This means that BY gives rigorous control of expected FDR for any >>dependence structure and any >>number of genes, given only that the p-value distribution is valid >>under the null hypothesis. BH >>is the same except that it is theoretically valid only for certain >>dependence structures (positive >>regression dependence). >> >>I think that Rebecca's question is about the particular (negative) >>dependence structure which is >>found between the set of pairwise contrasts for a particular >>gene. Yes, I think this does >>theoretically invalidate BH. However in practical situations >>you'll actually find the main >>problem to be conserativism rather than the other way around >>because there are more pairwise >>comparisons than there are independent comparisons to be made. So, >>personally, this wouldn't make >>me move to BY. >> >>Hope this helps >>Gordon >> >> > Date: Fri, 13 Jan 2006 16:57:28 -0500 >> > From: Naomi Altman <naomi at="" stat.psu.edu=""> >> > Subject: Re: [BioC] adjustment for dependent hypotheses when pairwise >> > testing >> > To: pmt1rew at leeds.ac.uk, "bioconductor at stat.math.ethz.ch" >> > <bioconductor at="" stat.math.ethz.ch=""> >> > >> > I do not think you will be able to use these methods with such a >> > small number of genes. A large number of genes are required to >> estimate pi0. >> > >> > --Naomi >> > >> > At 07:52 AM 1/13/2006, pmt1rew at leeds.ac.uk wrote: >> >>Dear all, >> >> >> >>I data for 13 genes with the samples from 4 different tissue >> >>types. Would like >> >>to compare the normal means of the different tissue types using pairwise >> >>testing with an adjustment for fdr. >> >> >> >>Having considered the Benjamini and Yekutieli reference on the >> p.adjust help >> >>page I am unsure as to whether my dependency structure satisfies >> the criteria >> >>to just use the regular "BH" adjustment or if the "BY" >> adjustment would be >> >>more appropriate? >> >> >> >>Any suggestions for me please? >> >> >> >>Many thanks >> >> >> >>Rebecca Walls >> >> >> > Naomi S. Altman 814-865-3791 (voice) >> > Associate Professor >> > Dept. of Statistics 814-863-7114 (fax) >> > Penn State University 814-865-1348 (Statistics) >> > University Park, PA 16802-2111 > >Naomi S. Altman 814-865-3791 (voice) >Associate Professor >Dept. of Statistics 814-863-7114 (fax) >Penn State University 814-865-1348 (Statistics) >University Park, PA 16802-2111 >