FDR.FDX

Fast variable selection via elastic posterior sphere to control False Discovery Rate and False Discovery Exceedance

Example using dataset on drug ATV resistence from HIVDB

The followling demonstration is also in the "example.R" script.

Data download and preprocessing

rm(list = ls())
source("FDPbound.R")

#The following data download and preprocessing code is partly adapted 
#from the example R script at https://hivdb.stanford.edu/pages/genopheno.dataset.html

#helper function: create the design matrix X with the input mutations/positions
buildX <- function(dat, mut, ps){
  X <- matrix(NA, nrow=nrow(dat), ncol=length(mut))
  # loop through all positions
  for(p in unique(ps)){
    p1 <- substr(dat[,p],1,1)  # first mutation at this position
    p2 <- substr(dat[,p],2,2)
    for(ind in which(ps==p)){
      X[,ind] <-  as.numeric(p1==as.character(mut[ind]) | 
                               p2==as.character(mut[ind]))  
    }
  }  
  colnames(X) <- paste0(ps,mut)  
  return(X)
}

#download the dataset for PI-type drugs from the website
dataset='PI'
drug='ATV'
#min.muts is the minimum number of sequences that a mutation must appear in.
min.muts=3 
dat <- read.table("http://hivdb.stanford.edu/download/GenoPhenoDatasets/PI_DataSet.txt",
                  header=TRUE, sep="\t",stringsAsFactors=FALSE)
dat[dat=="."] <- NA
posu <- dat[,10:108]

#download PI complete mutations
PIcomplete=read.table("https://hivdb.stanford.edu/pages/published_analysis/genophenoPNAS2006/MUTATIONLISTS/COMPLETE/PI",
                      header = F,sep="\t",stringsAsFactors=FALSE)
allPImut=c('test')
for (i in 1:nrow(PIcomplete)) {
  allPImut=append(allPImut,
                  paste0(PIcomplete[i,1],unique(toupper(unlist(strsplit(PIcomplete[i,2],split = ' ')))))
  )
}
allPImut=allPImut[-1]

muts.in=allPImut
# get the amino acids and positions for the mutations to be included in the model
mut <- ifelse(nchar(muts.in)==3,toupper(substr(muts.in,3,3)),
              toupper(substr(muts.in,2,2)))
ps <- suppressWarnings(ifelse(nchar(muts.in)==3,as.numeric(substr(muts.in,1,2)),
                              as.numeric(substr(muts.in,1,1))))

# construct design matrix for OLS
X <- buildX(posu, mut, ps)#1958 rows, 224 cols

# construct dependent variable
drugcol <- which(names(dat)==drug)    
Y <- as.numeric(dat[,drugcol])  # absolute measure
Ylog10 <- log10(Y)
df.log <- data.frame(Y=Ylog10, X=X)

# remove all rows with missing values
rem.rows <- unique(which(is.na(df.log),arr.ind=TRUE)[,1])
df.log.cc <- df.log[-rem.rows,]  # complete case
if(sum(is.infinite(df.log.cc$Y))>0){
  df.log.cc=df.log.cc[-which(is.infinite(df.log.cc$Y)),]
}

# remove mutations that are rare
rare.muts <- which(colSums(df.log.cc[,-1])<min.muts)
if(length(rare.muts)>0){
  message(paste0(muts.in[rare.muts],
                 " excluded from the model because it appears in fewer than ",
                 min.muts," sequences.\n"))
  df.log.cc <- df.log.cc[,-(rare.muts+1)]  
}
print(paste(drug,'dataset shape:',dim(df.log.cc)))#1083 rows, 211 cols

# check duplicated columns from X to allow for identifiability
X=as.matrix(df.log.cc[,-1])
if(length(which(duplicated(t(X))))>0){
  print('Warning! Duplicate columns!')
  return(NA)
}

# download TSM (the approximated ground truth) for PI-type of drugs
NPTSM_PI=read.table('https://hivdb.stanford.edu/pages/published_analysis/genophenoPNAS2006/MUTATIONLISTS/NP_TSM/PI',
                    header = F,sep="\t",stringsAsFactors=FALSE)
allNPTSM_PImut=c('test')
for (i in 1:nrow(NPTSM_PI)) {
  allNPTSM_PImut=append(allNPTSM_PImut,
                        paste0(NPTSM_PI[i,1],unique(toupper(unlist(strsplit(NPTSM_PI[i,2],split = ' ')))))
  )
}
allNPTSM_PImut=allNPTSM_PImut[-1]
tp=paste0('X.',allNPTSM_PImut)#all NPTSM PI mutations

Select predictors with false discovery rate and false discovery exceedance control

fdr.target=0.2# FDR<=0.2
fdp.target=0.8# Pr(PDP<=0.2)>=0.8

# number of candidate mutations in the dataset
p = ncol(df.log.cc)-1

#---run fdpc method
set.seed(123)
lambdas=qnorm(p=1-fdr.target/(2*p)*(1:p))#the lamgba_{bh} seqeuence
# index of the selected predictors
fdpc.selected=FDPcontrolFit(x=as.matrix(df.log.cc[,-1]), y=df.log.cc[,1],
                       lambdas=lambdas,fdr.target,FDP_target=0,sigma=NA,
                       version='fdpc',isOrthogonal=F,standardize=T)


print('selection results of fdpc method:')
c('total.num.of.discoveries'=length(fdpc.selected),
  'num.of.discoveries.in.TSM'=length(intersect(names(df.log.cc)[1+fdpc.selected],tp)),
  'num.of.discoveries.not.in.TSM'=length(setdiff(names(df.log.cc)[1+fdpc.selected],tp))
  )

# output:
# total.num.of.discoveries   num.of.discoveries.in.TSM     num.of.discoveries.not.in.TSM 
#        32                            28                             4 


#---run fdpc+
set.seed(123)
lambdas=qnorm(p=1-fdr.target/(2*p)*(1:p))#the lamgba_{bh} seqeuence
# index of the selected predictors
fdpcPlus.selected=FDPcontrolFit(x=as.matrix(df.log.cc[,-1]), y=df.log.cc[,1],
                           lambdas,fdr.target,FDP_target=fdp.target,sigma=NA,
                           version='fdpc+',isOrthogonal=F,standardize=T)

print('selection results of fdpc+ method:')
c('total.num.of.discoveries'=length(fdpcPlus.selected),
  'num.of.discoveries.in.TSM'=length(intersect(names(df.log.cc)[1+fdpcPlus.selected],tp)),
  'num.of.discoveries.not.in.TSM'=length(setdiff(names(df.log.cc)[1+fdpcPlus.selected],tp))
)

# output
# total.num.of.discoveries   num.of.discoveries.in.TSM     num.of.discoveries.not.in.TSM 
#         41                            33                             8