多重检验中的FDR错误控制方法与p-value的校正

  • A+
所属分类:Statistics

数据分析中常碰见多重检验问题(multiple testing).Benjamini于1995年提出一种方法,通过控制FDR(False Discovery Rate)来决定P值的域值. 假设你挑选了R个差异表达的基因,其中有S个是真正有差异表达的,另外有V个其实是没有差异表达的,是假阳性的.实践中希望错误比例Q=V/R平均而言不能超过某个预先设定的值(比如0.05),在统计学上,这也就等价于控制FDR不能超过5%.
根据Benjamini在他的文章中所证明的定理,控制fdr的步骤实际上非常简单。

设总共有m个候选基因,每个基因对应的p值从小到大排列分别是p(1),p(2),...,p(m),则若想控制fdr不能超过q,则只需找到最大的正整数i,使得 p(i)<= (i*q)/m.然后,挑选对应p(1),p(2),...,p(i)的基因做为差异表达基因,这样就能从统计学上保证fdr不超过q。

The False Discovery Rate (FDR) of a set of predictions is the expected percent of false predictions in the set of predictions. For example if the algorithm returns 100 genes with a false discovery rate of .3 then we should expect 70 of them to be correct.

The FDR is very different from a p-value, and as such a much higher FDR can be tolerated than with a p-value. In the example above a set of 100 predictions of which 70 are correct might be very useful, especially if there are thousands of genes on the array most of which are not differentially expressed. In contrast p-value of .3 is generally unacceptabe in any circumstance. Meanwhile an FDR of as high as .5 or even higher might be quite meaningful.

计算方法 请参考:

http://stat.ethz.ch/R-manual/R-devel/library/stats/html/p.adjust.html

> p<-c(0.0003,0.0001,0.02)
>  p
[1] 3e-04 1e-04 2e-02
> 
> p.adjust(p,method="fdr",length(p))
[1] 0.00045 0.00030 0.02000
> 
> p*length(p)/rank(p)
[1] 0.00045 0.00030 0.02000
> length(p)
[1] 3
> rank(p)
[1] 2 1 3
 sort(p)
[1] 1e-04 3e-04 2e-02
avatar

发表评论

:?: :razz: :sad: :evil: :!: :smile: :oops: :grin: :eek: :shock: :???: :cool: :lol: :mad: :twisted: :roll: :wink: :idea: :arrow: :neutral: :cry: :mrgreen: