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#------------------------------------------------------------------------
# Compute c-index (c) and Brown-Hollander-Krowar-Goodman-Kruskal-Somer
# rank correlation (gamma) between X and Y with censoring indicator E
# Also returns number of relevant, concordant, and uncertain pairs
# (nrel, nconc, nuncert) and estimated s.d. of gamma (sd) using
# Quade formula (see SAS PROC MATPAR). Pairs with tied x are
# excluded if outx=.TRUE.
#
# F. Harrell 27Nov90
# Modification of SAS Procedure KGKC (1980)
#-------------------------------------------------------------------------
SUBROUTINE cidxcn(x,y,e,n,nrel,nconc,nuncert,c,gamma,sd,outx)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
DOUBLE PRECISION x(n),y(n),dx,dy
LOGICAL e(n),outx
DOUBLE PRECISION nrel,nuncert,nconc
nconc=0d0
nrel=0d0
nuncert=0d0
sumr=0d0
sumr2=0d0
sumw=0d0
sumw2=0d0
sumrw=0d0
do i=1,n {
wi=0d0
ri=0d0
do j=1,n
if(j^=i) {
dx=x(i)-x(j)
dy=y(i)-y(j)
if(dx!=0. | !outx) {
if((e(i)&dy<0.)|(e(i)&!e(j)&dy==0.)) {
if(dx<0.) {
nconc=nconc+1d0
wi=wi+1d0 }
else
if(dx==0.)nconc=nconc+.5d0
else
wi=wi-1d0
nrel=nrel+1d0
ri=ri+1d0 }
else
if((e(j)&dy>0.)|(e(j)&!e(i)&dy==0.)) {
if(dx>0.) {
nconc=nconc+1d0
wi=wi+1d0 }
else
if(dx==0.) nconc=nconc+.5d0
else
wi=wi-1d0
nrel=nrel+1d0
ri=ri+1d0 }
else
if(!(e(i)&e(j)))nuncert=nuncert+1d0 }
}
sumr=sumr+ri
sumr2=sumr2+ri*ri
sumw=sumw+wi
sumw2=sumw2+wi*wi
sumrw=sumrw+ri*wi
}
c=nconc/nrel
gamma=2.*(c-.5)
#call dblepr('sumr',4,sumr,1)
#call dblepr('sumw',4,sumw,1)
#call dblepr('sumr2',5,sumr2,1)
#call dblepr('sumw2',5,sumw2,1)
#call dblepr('sumrw',5,sumrw,1)
sd=sumr2*sumw**2-2d0*sumr*sumw*sumrw+sumw2*sumr**2
sd=2.*dsqrt(sd)/sumr/sumr
return
end
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