######################################################################
##     AFC is an association test to test genetic associations      ##
##     between multiple phenotypes and a genetic variant.           ##
##                                                                  ##
##     In the function AFC,                                         ##
##     x: represents the genotype (number of minor alleles) vector. ##
##     y: represents the trait value matrix. Each row represents    ##
##        an individual and each column represents a phenotype.     ##      
##     numper: represents the number of permutations to             ##
##             obtain the p-value of the test statistic AFC.        ##
######################################################################

AFC=function(x,y,numper)
{
  m=ncol(y)
  n=nrow(y)
  yvar=apply(y,2,var)
  Tstat=n*cov(y,x)/sqrt(n*yvar*var(x))
  P0=1-pchisq(Tstat^2,1)
  pv=sort(P0)
  T0=-cumsum(log(pv))
  
  Tper=matrix(NA,numper,m)
  for(l in 1:numper){
    x.new=sample(x,size=n,replace=FALSE)
    Tstat=n*cov(y,x.new)/sqrt(n*yvar*var(x.new))
    P0=1-pchisq(Tstat^2,1)
    pvper=sort(P0)
    Tper[l,]=-cumsum(log(pvper))
  }
  TT=rbind(T0,Tper)
  T1=apply(TT,2,rank)
  T2=apply(T1,1,max)  	
  pvalue=sum(T2[-1]>T2[1])/numper+sum(T2[-1]==T2[1])/numper/2
  return(pvalue)
}