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_cifcox.sas
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_cifcox.sas
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/******************************************************************
This macro computes the direct adjusted cumulative incidence curves
for K treatment groups, based on a proportional subdistribution
hazards model. Please note that the hazards ratio between any two
treatments is assumed to be a constant.
Macro parameters:
inputdata - the input sas data name;
time - the survival time variable;
event - 0 (censor) 1 (cause of interest) 2 (other causes);
group - the treatment group variable,
which must take values 1,...,K for K<10 groups
covlist - a list of covariate names;
outdata - the output sas data name.
The output dataset contains:
Time - the event times
CIFi, i=1,...,K
SEi, i=1,...,K
SEij, 1<=i<j<=K
Authored by Xu Zhang 2011
Re-formatted by Rodney Sparapani 02/18/2014
******************************************************************/
%*macro (inputdata, time, event, group, covlist, outdata);
%macro _cifcox(data=REQUIRED, out=REQUIRED, time=REQUIRED,
cause=REQUIRED, group=REQUIRED, x=REQUIRED,
inputdata=&data, outdata=&out, covlist=&x, event=&cause);
%_require(&data &time &event &group &out &x)
%local i j gp gp1 gp2 numcov numgroup tcov tnum;
proc means data=&inputdata noprint;
var &group;
output out=maxout max(&group)=numgroup;
run;
data _null_;
set maxout;
call symput('numgroup', numgroup);
run;
proc iml;
use &inputdata;
read all var {&covlist} into x;
close &inputdata;
numcov=ncol(x);
create ncovout from numcov[colname='numcov'];
append from numcov;
close ncovout;
run;
quit;
data _null_;
set ncovout;
call symput('numcov', numcov);
run;
%let tcov=%eval(&numgroup-1+&numcov);
proc iml;
use &inputdata;
read all var {&time} into time;
read all var {&event} into event;
read all var {&group} into group;
read all var {&covlist} into x;
close &inputdata;
numobs=nrow(time);
gmat=j(&numgroup, &numgroup-1, 0);
do i=2 to &numgroup;
gmat[i, i-1]=1;
end;
zmat=j(numobs, &numgroup-1+&numcov, 0);
do i=1 to numobs;
zmat[i,]=gmat[group[i],]||x[i,];
end;
out=time||event||zmat;
names={'time' 'cause' %do i=1 %to &numgroup-1+&numcov; "z&i" %end;};
create indata from out[colname=names];
append from out;
close indata;
run;
quit;
proc sort data=indata;
by descending time descending cause;
run;
data indata;
set indata;
atrisk+1;
run;
proc sort data=indata;
by time;
run;
data cdata;
set indata;
keep time atrisk;
where cause=0;
run;
proc sort data=cdata;
by time descending atrisk;
run;
proc freq data=cdata noprint;
tables time /out=ccount;
run;
proc sort data=ccount;
by time;
run;
data cdata;
merge cdata ccount;
by time;
drop percent ctemp;
retain ctemp 1;
if first.time;
ctemp=ctemp*(1-count/atrisk);
csurv=ctemp;
dcna=count/atrisk;
ctime=time;
time=time+0.00001;
run;
data indata;
merge indata (in=in1) cdata (keep=time csurv);
by time;
retain ctemp 1;
if csurv^=. then ctemp=csurv;
else csurv=ctemp;
if in1;
run;
data e1time;
set indata;
keep time csurv;
where cause=1;
run;
proc sort;
by time;
run;
data e1time;
set e1time;
by time;
if first.time;
run;
proc phreg data=indata out=best noprint;
model time*cause(0,2)=%do i=1 %to &numgroup-1+&numcov; z&i %end;;
run;
%let tnum=%eval(&tcov*(&tcov+1)/2);
data obs10 obs2;
set indata;
if cause in (0,1) then output obs10;
else output obs2;
run;
proc iml;
use obs10;
read all var{time} into time10;
read all var{cause} into cause10;
read all var{%do i=1 %to &numgroup-1+&numcov; z&i %end;} into z10;
read all var{%do i=&numgroup %to &numgroup-1+&numcov; z&i %end;} into zzmat01;
close obs10;
use obs2;
read all var{time} into time2;
read all var{csurv} into ckm2;
read all var{cause} into cause2;
read all var{%do i=1 %to &numgroup-1+&numcov; z&i %end;} into z2;
read all var{%do i=&numgroup %to &numgroup-1+&numcov; z&i %end;} into zzmat2;
close obs2;
use best;
read all var{%do i=1 %to &numgroup-1+&numcov; z&i %end;} into best;
close best;
use e1time;
read all var{time} into etime;
read all var{csurv} into eckm;
close e1time;
use cdata;
read all var{ctime} into ctime;
read all var{dcna} into dcna;
read all var{atrisk} into pi;
close cdata;
numctime=nrow(ctime);
numtime=nrow(etime);
numobs10=nrow(time10);
numobs2=nrow(time2);
cidx=j(numctime,1,0);
do i=1 to numctime;
if ctime[i]>etime[numtime] then cidx[i]=-1;
else do;
do j=1 to numtime until(etime[j]>=ctime[i]);
end;
cidx[i]=j;
end;
end;
eidx=j(numtime,1,0);
do i=1 to numtime;
do j=1 to numobs10 until(time10[j]=etime[i]);
end;
eidx[i]=j;
end;
b=best;
numdeath=j(numtime,1,0);
covsum=j(numtime,&tcov,0);
do i=1 to numtime;
do j=1 to numobs10;
if time10[j]=etime[i] & cause10[j]=1 then do;
numdeath[i] = numdeath[i] + 1;
covsum[i,] = covsum[i,] + z10[j,];
end;
end;
end;
incre=1;
do iter=1 to 20 until(incre<.0005);
s0_1=j(numtime,1,0);
s1_1=j(numtime,&tcov,0);
s2_1=j(numtime,&tnum,0);
score=j(1,&tcov,0);
fisher=j(&tcov,&tcov,0);
loglike=0;
expbz10=j(numobs10,1,0);
do i=1 to numobs10;
expbz10[i]=b*t(z10[i,]);
end;
expbz10=exp(expbz10);
expbz2=j(numobs2,1,0);
do i=1 to numobs2;
expbz2[i]=b*t(z2[i,]);
end;
expbz2=exp(expbz2);
pres0=0;
pres1=j(1,&tcov,0);
pres2=j(1,&tnum,0);
obsidx=numobs10;
do i=numtime to 1 by -1;
s0_1[i]=pres0;
s1_1[i,]=pres1;
s2_1[i,]=pres2;
do j=eidx[i] to obsidx;
s0_1[i] = s0_1[i] + expbz10[j];
s1_1[i,] = s1_1[i,] + z10[j,]#expbz10[j];
tonext=1;
do m=1 to &tcov;
do n=m to &tcov;
s2_1[i,tonext] = s2_1[i,tonext] + z10[j,m]#z10[j,n]#expbz10[j];
tonext = tonext + 1;
end;
end;
end;
pres0=s0_1[i];
pres1=s1_1[i,];
pres2=s2_1[i,];
obsidx=eidx[i]-1;
end;
s0_2=j(numtime,1,0);
s1_2=j(numtime,&tcov,0);
s2_2=j(numtime,&tnum,0);
do i=1 to numtime;
do j=1 to numobs2;
cweight=eckm[i]/ckm2[j];
weight=min(1,cweight);
s0_2[i] = s0_2[i] + expbz2[j]#weight;
s1_2[i,] = s1_2[i,] + z2[j,]#expbz2[j]#weight;
tonext=1;
do m=1 to &tcov;
do n=m to &tcov;
s2_2[i,tonext] = s2_2[i,tonext] + z2[j,m]#z2[j,n]#expbz2[j]#weight;
tonext = tonext + 1;
end;
end;
end;
end;
s0=s0_1+s0_2;
s1=s1_1+s1_2;
s2=s2_1+s2_2;
do i=1 to numtime;
score = score + covsum[i,] - s1[i,]#(numdeath[i]/s0[i]);
tonext=1;
do m=1 to &tcov;
do n=m to &tcov;
fisher[m,n] = fisher[m,n] + s2[i,tonext]#(numdeath[i]/s0[i])
- s1[i,m]#s1[i,n]#(numdeath[i]/s0[i]##2);
tonext = tonext + 1;
end;
end;
loglike = loglike + b*t(covsum[i,])-numdeath[i]*log(s0[i]);
end;
do m=2 to &tcov;
do n=1 to m-1;
fisher[m,n]=fisher[n,m];
end;
end;
oldb=b;
b = b + score*inv(fisher);
bchange=b-oldb;
incre=max(abs(bchange));
end;
do i=1 to numobs10;
expbz10[i]=b*t(z10[i,]);
end;
expbz10=exp(expbz10);
do i=1 to numobs2;
expbz2[i]=b*t(z2[i,]);
end;
expbz2=exp(expbz2);
lambda1=j(numtime,1,0);
dlambda1=j(numtime,1,0);
ltemp=0;
do i=1 to numtime;
dlambda1[i]=numdeath[i]/s0[i];
ltemp=ltemp+dlambda1[i];
lambda1[i]=ltemp;
end;
eta_1=j(numobs10,&tcov,0);
dmart1_1=j(numobs10,numtime,0);
do i=1 to numobs10;
do j=1 to numtime;
if time10[i]>=etime[j] then dmart1_1[i,j]=-dlambda1[j]#expbz10[i];
if cause10[i]=1 & time10[i]=etime[j] then dmart1_1[i,j]=dmart1_1[i,j]+1;
eta_1[i,] = eta_1[i,] + (z10[i,]-s1[j,]/s0[j])*dmart1_1[i,j];
end;
end;
eta_2=j(numobs2,&tcov,0);
dmart1_2=j(numobs2,numtime,0);
do i=1 to numobs2;
do j=1 to numtime;
cweight=eckm[j]/ckm2[i];
weight=min(1,cweight);
dmart1_2[i,j]=-dlambda1[j]#expbz2[i]#weight;
eta_2[i,] = eta_2[i,] + (z2[i,]-s1[j,]/s0[j])*dmart1_2[i,j];
end;
end;
numobs=numobs10+numobs2;
dmart1=dmart1_1//dmart1_2;
time=time10//time2;
cause=cause10//cause2;
zmat=z10//z2;
eta=eta_1//eta_2;
psi=j(numobs,&tcov,0);
q=j(numctime,&tcov,0);
do i=1 to numctime while (cidx[i]>0);
do j=1 to numobs2 while (ctime[i]>time2[j]);
do k=cidx[i] to numtime;
q[i,]=q[i,]+(z2[j,]-s1[k,]/s0[k])#dmart1_2[j,k];
end;
end;
q[i,]=q[i,]/pi[i];
end;
dcmart=j(numobs,numctime,0);
do i=1 to numobs;
do j=1 to numctime;
if time[i]>=ctime[j] then dcmart[i,j]=-dcna[j];
if time[i]=ctime[j] & cause[i]=0 then dcmart[i,j]=dcmart[i,j]+1;
end;
psi[i,]=-dcmart[i,]*q;
end;
sigma=j(&tcov,&tcov,0);
do i=1 to numobs;
sigma = sigma + t(eta[i,]+psi[i,])*(eta[i,]+psi[i,]);
end;
naivev = inv(fisher);
robustv = inv(fisher)*sigma*inv(fisher);
se=j(&tcov,1,0);
do i=1 to &tcov;
se[i]=sqrt(robustv[i,i]);
end;
bout=t(b)||se;
hazout=etime||lambda1;
create best from bout[colname={'Estimate' 'SE'}];
append from bout;
close best;
names={%do i=2 %to &numgroup; "G&i" %end; %do i=1 %to &numcov; "Z&i" %end;};
create covest from robustv[colname=names];
append from robustv;
close covest;
create basehaz from hazout[colname={'Time' 'Base_haz'}];
append from hazout;
close basehaz;
vut=j(numctime, numtime,0);
do i=1 to numctime while (cidx[i]>0);
vtemp=0;
do j=cidx[i] to numtime;
do k=1 to numobs2;
if time2[k]<ctime[i] then vtemp=vtemp+1/s0[j]#dmart1_2[k,j];
end;
vut[i,j]=-vtemp;
end;
vut[i,]=vut[i,]/pi[i];
end;
/* variance of direct adjusted CIF */
g=j(&numgroup, &numgroup-1,0);
do i=2 to &numgroup;
g[i,i-1]=1;
end;
outmat=etime;
zzmat=zzmat01//zzmat2;
zbar=j(numtime,&tcov,0);
do i=1 to numtime;
zbar[i,]=s1[i,]/s0[i];
end;
%do gp=1 %to &numgroup;
zz=j(numobs, &numgroup-1+&numcov, 0);
do i=1 to numobs;
zz[i,]=g[&gp,]||zzmat[i,];
end;
dacif=j(numtime,1,0);
zfn1=j(numtime,1,0);
zfn2=j(numtime,&numgroup-1+&numcov,0);
do i=1 to numtime;
do j=1 to numobs;
dacif[i]=dacif[i]+1-exp(-lambda1[i]#exp(b*t(zz[j,])));
zfn1[i]=zfn1[i]+exp(-lambda1[i]#exp(b*t(zz[j,]))+b*t(zz[j,]));
zfn2[i,]=zfn2[i,]+zz[j,]#exp(-lambda1[i]#exp(b*t(zz[j,]))+b*t(zz[j,]));
end;
end;
dacif=dacif/numobs;
zfn1=zfn1/numobs;
zfn2=zfn2/numobs;
htz=j(numtime,&tcov,0);
do i=1 to numtime;
htemp=j(1,&tcov,0);
do j=1 to i;
htemp=htemp+(zfn2[i,]-zfn1[i]#zbar[j,])#dlambda1[j];
end;
htz[i,]=htemp;
end;
cifv=j(numtime,1,0);
cifse=j(numtime,1,0);
w1temp=j(numobs,1,0);
do i=1 to numtime;
w1=j(numobs,1,0);
w2=j(numobs,1,0);
w3=j(numobs,1,0);
do j=1 to numobs;
w1temp[j]=w1temp[j]+1/s0[i]#dmart1[j,i];
w1[j]=w1temp[j]#zfn1[i];
w2[j]=htz[i,]*naivev*t(eta[j,]+psi[j,]);
w3[j]=w3[j]+dcmart[j,]*vut[,i]#zfn1[i];
tempw=w1[j]+w2[j]+w3[j];
cifv[i]=cifv[i]+tempw#tempw;
end;
end;
cifse=cifv##0.5;
outmat=outmat||dacif||cifse;
%end;
/* variance of the difference between direct adjusted CIF's */
%do gp1=1 %to &numgroup-1;
%do gp2=&gp1+1 %to &numgroup;
zz1=j(numobs, &numgroup-1+&numcov, 0);
zz2=j(numobs, &numgroup-1+&numcov, 0);
do i=1 to numobs;
zz1[i,]=g[&gp1,]||zzmat[i,];
zz2[i,]=g[&gp2,]||zzmat[i,];
end;
zfn1=j(numtime,1,0);
zfn2=j(numtime,&numgroup-1+&numcov,0);
do i=1 to numtime;
do j=1 to numobs;
zfn1[i]=zfn1[i]+exp(-lambda1[i]#exp(b*t(zz1[j,]))+b*t(zz1[j,]))
-exp(-lambda1[i]#exp(b*t(zz2[j,]))+b*t(zz2[j,]));
zfn2[i,]=zfn2[i,]+zz1[j,]#exp(-lambda1[i]#exp(b*t(zz1[j,]))+b*t(zz1[j,]))
-zz2[j,]#exp(-lambda1[i]#exp(b*t(zz2[j,]))+b*t(zz2[j,]));
end;
end;
zfn1=zfn1/numobs;
zfn2=zfn2/numobs;
htz=j(numtime,&tcov,0);
do i=1 to numtime;
htemp=j(1,&tcov,0);
do j=1 to i;
htemp=htemp+(zfn2[i,]-zfn1[i]#zbar[j,])#dlambda1[j];
end;
htz[i,]=htemp;
end;
cif_diff_v=j(numtime,1,0);
cif_diff_se=j(numtime,1,0);
w1temp=j(numobs,1,0);
do i=1 to numtime;
w1=j(numobs,1,0);
w2=j(numobs,1,0);
w3=j(numobs,1,0);
do j=1 to numobs;
w1temp[j]=w1temp[j]+1/s0[i]#dmart1[j,i];
w1[j]=w1temp[j]#zfn1[i];
w2[j]=htz[i,]*naivev*t(eta[j,]+psi[j,]);
w3[j]=w3[j]+dcmart[j,]*vut[,i]#zfn1[i];
tempw=w1[j]+w2[j]+w3[j];
cif_diff_v[i]=cif_diff_v[i]+tempw#tempw;
end;
end;
cif_diff_se=cif_diff_v##0.5;
outmat=outmat||cif_diff_se;
%end;
%end;
names={'Time' %do i=1 %to &numgroup; "CIF&i" "SE&i" %end;
%do i=1 %to &numgroup; %do j=&i+1 %to &numgroup; "SE&i.&j" %end; %end;};
create &outdata from outmat[colname=names];
append from outmat;
close &outdata;
run;
quit;
data name;
time=0;
%do i=1 %to &numgroup;
CIF&i=0;
SE&i=0;
%do j=&i+1 %to &numgroup; SE&i.&j=0; %end;
%end;
output;
run;
data &outdata;
set name &outdata;
by time;
run;
data name;
%do i=2 %to &numgroup;
Variable="G&i";
output;
%end;
%do i=1 %to &numcov;
Variable="Z&i";
output;
%end;
run;
data best;
merge name best;
drop zstat;
zstat=abs(Estimate/SE);
Prob=2*probnorm(-zstat);
run;
data covest;
merge name covest;
run;
title 'Cox model for a subdistribution function';
title2 'WORK.BEST: Estimates of the regression parameters';
proc print data=best;
run;
title2 'WORK.COVEST: Estimated variance-covariance matrix';
proc print data=covest;
run;
title2 'WORK.BASEHAZ: Estimated baseline cumulative hazard function';
proc print data=basehaz;
run;
title2 "&outdata: Direct adjusted cumulative incidence functions";
proc print data=&outdata;
run;
%mend;