| Title: | Flexible Control of the mFDP |
|---|---|
| Description: | Computes bounds for the median of the false discovery proportion (mFDP). These 50 percent confidence bounds for the FDP are simultaneously valid. The method takes a vector of p-values as input. Also provides mFDP-adjusted p-values. Can be used for flexible mFDP control. |
| Authors: | Jesse Hemerik [aut, cre] |
| Maintainer: | Jesse Hemerik <[email protected]> |
| License: | GNU General Public License |
| Version: | 0.1.0 |
| Built: | 2024-11-03 06:41:52 UTC |
| Source: | CRAN |
For a p-value rejection threshold t, compute the 50 percent confidence upper bound for the number of false positives. The bounds are simultaneous over t.
get.bound(t,c,kappa.max)get.bound(t,c,kappa.max)
t |
The p-value threshold |
c |
The tuning parameter, which influences the intercept and slope of the enveloppe. Should be numeric. |
kappa.max |
This value needs to be computes based on the p-values. Together with |
A non-negative integer, which is a median unbiased (or upward biased) estimate of the number false positives.
#Suppose the envelope that has been computed is defined by c=0.002 and kappa.max=0.001. #We can then evaluate the envelope at several thresholds t as below. #This is equivalent to simply entering the formula floor((t+c)/kappa.max). #50 percent confidence upper bound for nr of false positives, if p-value threshold of 0.01 is used: get.bound(t=0.01,c=0.002,kappa.max=0.001) #12 #50 percent confidence upper bound for nr of false positives, if p-value threshold of 0.02 is used: get.bound(t=0.02,c=0.002,kappa.max=0.001) #22 #50 percent confidence upper bound for nr of false positives, if p-value threshold of 0.03 is used: get.bound(t=0.03,c=0.002,kappa.max=0.001) #32#Suppose the envelope that has been computed is defined by c=0.002 and kappa.max=0.001. #We can then evaluate the envelope at several thresholds t as below. #This is equivalent to simply entering the formula floor((t+c)/kappa.max). #50 percent confidence upper bound for nr of false positives, if p-value threshold of 0.01 is used: get.bound(t=0.01,c=0.002,kappa.max=0.001) #12 #50 percent confidence upper bound for nr of false positives, if p-value threshold of 0.02 is used: get.bound(t=0.02,c=0.002,kappa.max=0.001) #22 #50 percent confidence upper bound for nr of false positives, if p-value threshold of 0.03 is used: get.bound(t=0.03,c=0.002,kappa.max=0.001) #32
kappa.max, which defines the mFDP envelopeBased on a vector of unadjusted(!) p-values, compute kappa.max, which together with c defines the mFDP envelope
get.kappa.max(P, c="1/(2m)", s1=0, s2=0.1)get.kappa.max(P, c="1/(2m)", s1=0, s2=0.1)
P |
A vector of p-values. |
c |
The tuning parameter, which influences the intercept and slope of the enveloppe. Should either be numeric or |
s1 |
The smallest p-value threshold of interest. Non-negative. |
s2 |
The largest p-value threshold of interest. Should be larger than |
kappa.max, which together with c defines the mFDP envelope.
set.seed(5193) ### Make some p-values m=500 #the nr of hypotheses nrfalse=100 #the nr of false hypotheses tstats = rnorm(n=m) #m test statistics tstats[1:nrfalse] = tstats[1:nrfalse] + 3 #add some signal P = 1 - pnorm(tstats) #compute p-values ### Compute kappa.max. (Taking c to be the default value 1/(2m).) kappa.max = get.kappa.max(P=P) kappa.maxset.seed(5193) ### Make some p-values m=500 #the nr of hypotheses nrfalse=100 #the nr of false hypotheses tstats = rnorm(n=m) #m test statistics tstats[1:nrfalse] = tstats[1:nrfalse] + 3 #add some signal P = 1 - pnorm(tstats) #compute p-values ### Compute kappa.max. (Taking c to be the default value 1/(2m).) kappa.max = get.kappa.max(P=P) kappa.max
Provides mFDP-adjusted p-values, given a vector of p-values.
mFDP.adjust(P, c="1/(2m)", s1=0, s2=0.1)mFDP.adjust(P, c="1/(2m)", s1=0, s2=0.1)
P |
A vector of (raw, i.e. unadjusted) p-values. |
c |
The tuning parameter, which influences the intercept and slope of the envelope. Should either be numeric or |
s1 |
The smallest p-value threshold of interest. |
s2 |
The largest p-value threshold of interest. |
A vector of mFDP-adjusted p-values. Some can be infinity - which can be interpreted as 1.
set.seed(5193) ### make some p-values m=500 #the nr of hypotheses nrfalse=100 #the nr of false hypotheses tstats = rnorm(n=m) #m test statistics tstats[1:nrfalse] = tstats[1:nrfalse] + 3 #add some signal P = 1 - pnorm(tstats) #compute p-values P.adjusted = mFDP.adjust(P=P) #mFDP-adjusted p-values. Be careful with interpretation. min(P.adjusted) #0.0208set.seed(5193) ### make some p-values m=500 #the nr of hypotheses nrfalse=100 #the nr of false hypotheses tstats = rnorm(n=m) #m test statistics tstats[1:nrfalse] = tstats[1:nrfalse] + 3 #add some signal P = 1 - pnorm(tstats) #compute p-values P.adjusted = mFDP.adjust(P=P) #mFDP-adjusted p-values. Be careful with interpretation. min(P.adjusted) #0.0208