BH correction with p.adjust

My understanding was that the vector was ranked, the adjusted p vector was calculated and then the vector is returned to the original order - I came across a stack overflow answer saying this:

http://stackoverflow.com/questions/10323817/r-unexpected-results-from-p-adjust-fdr

Although the code there does not appear to be the same as when I type "p.adjust" into the command line. The order shouldn't matter anyway since my data was ordered by p.

Yesterday I tried a short example of 5 numbers and it seemed to work out though today I tried to do another short example to demonstrate that the order in the p vector you input doesn't matter but didn't quite get a working example this time. Maybe due to a rounding to first significant figure or something?

smallP <- c(0.01, 0.5, 0.0001)
names(smallP) <- c("first", "second", "last")

p.adjust(smallP)
first second   last 
2e-02  5e-01  3e-04 
0.01*3/2
[1] 0.015
0.5*3/3
[1] 0.5
0.0001*3/1
[1] 3e-04
Comparing the same method might help!
p.adjust(smallP, method="BH")
[1] 0.0150 0.5000 0.0003
In any case I reconstructed a large example which can be run without real data where the figure is way off and definitely not the result of a rounding error:

exampleP <- seq(from=0.0000001, to=0.1, by=0.00000001)
length(exampleP)
[1] 9999991
examplePBH <- p.adjust(exampleP, method="BH")

exampleP[1]
[1] 1e-07
examplePBH[1]
[1] 0.1
exampleP[1]*length(exampleP)/1
[1] 0.9999991

Any help with this would be very much appreciated. It seems like it ought to be such a simple and commonly used method and yet I am struggling and not sure what to do about it.
You have the source code, how about reading it?

    }, BH = {
        i <- lp:1L
        o <- order(p, decreasing = TRUE)
        ro <- order(o)
        pmin(1, cummin(n/i * p[o]))[ro]
    }

Notice the cumulative minimum. The first element in n/i*p[o] is going to be p[n] == 0.1 (since your p is in ascending order). So no element of the result is going to be bigger than 0.1. (I presume this is because p-adjustments must be order-preserving.)
Thanks,

Scott

________________________________________
From: David Winsemius [dwinsemius at comcast.net]
Sent: 21 July 2013 03:33
To: Scott Robinson
Cc: r-help at r-project.org
Subject: Re: [R] BH correction with p.adjust

On Jul 20, 2013, at 10:37 AM, Scott Robinson wrote:

Dear List,

I have been trying to use p.adjust() to do BH multiple test correction and have gotten some unexpected results. I thought that the equation for this was:

pBH = p*n/i

Looking at the code for `p.adjust`, you see that the method is picked from a switch function

lp <- length(p)
BH = {
       i <- lp:1L
       o <- order(p, decreasing = TRUE)
       ro <- order(o)
       pmin(1, cummin(n/i * p[o]))[ro]
   }

You may not have sorted the p-values in pList.

where p is the original p value, n is the number of tests and i is the rank of the p value. However when I try and recreate the corrected p from my most significant value it does not match up to the one computed by the method p.adjust:

setwd("C:/work/Methylation/IMA/GM/siteLists")

hypTable <- read.delim("hypernormal vs others.txt")
pList <- hypTable$p
names(pList) <- hypTable$site

adjusted <- p.adjust(pList, method="BH")
adjusted[1]
cg27433479
0.05030589

pList[1]*nrow(hypTable)/1
cg27433479
0.09269194

No data provided, so unable to pursue this further.

I tried to recreate this is a small example of a vector of 5 p values but everything worked as expected there. I was wondering if there is some subtle difference about how p.adjust operates? Is there something more complicated about how to calculate 'n' or 'i' - perhaps due to identical p values being assigned the same rank or something? Does anyone have an idea what might be going on here?

--

David Winsemius
Alameda, CA, USA

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BH correction with p.adjust

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