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simul_data.sas
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simul_data.sas
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/******************************************************************************
Author, date: pmbrown, feb2020
Macro name: simul_data,
iterat_simul (run simul_data iteratively in order to
obtain the desired correlations between the outcomes),
nearestcorr
Description: simulate random samples from a multivariate normal distribution,
transform variables to required types. Create a dataset containing
num random samples indicated by the variable samp=1,2,...num.
Reference:
Notes: _co=control, _ac=active
co=control grp, the base response
df=treatment difference, defines response for
ac=active grp
_sd: if var1_tp=norm or lognorm (sd for log(post/base))
tte_fu: follow-up time for censoring of TTE endpts, corresponds
to the response estimates assumed for TTE outcomes
assumed effects sizes: see email sent on 22feb2020
rough sd obtained as: (q3-q1)/1.35, from fig2 jama
Validation:
******************************************************************************/
********************************************************************;
*** define macro parameters ***;
********************************************************************;
/*!if update _df here also update in macro call below!*/
%macro simul_data(n=100, /*total sample size ie n/2 in each grp*/
num=1000, /*no. of random samples*/
numvars=4, /*number of variables*/
tte_fu=28, /*days, corresponds to assumed response for var4*/
var1_tp=NORM, var1_co=7, var1_df=-1, var1_sd=3.7, /*sofa score 96hrs */
var2_tp=NORM, var2_co=40, var2_df=-5, var2_sd=45, /*crp (ug/mL) 168hrs*/
var3_tp=NORM, var3_co=12, var3_df=-2, var3_sd=5, /*thrombomodulin (ng/mL) 168hrs*/
var4_tp=SURV, var4_co=0.75, var4_df=0.02, var4_sd=, /*mortality at d28*/
var5_tp=, var5_co=, var5_df=, var5_sd=,
corr12=0.2, corr13=0.2, corr14=0.05, corr15=0, /*initial working correlations */
corr23=0.2, corr24=0.05, corr25=0,
corr34=0.05, corr35=0,
corr45=0);
%let gtype1=%upcase(&var1_tp) ;
%let gtype2=%upcase(&var2_tp) ;
%let gtype3=%upcase(&var3_tp) ;
%let gtype4=%upcase(&var4_tp) ;
%let gtype5=%upcase(&var5_tp) ;
********************************************************************;
*** convert to normal variates ***;
********************************************************************;
data _null_;
%do i=1 %to &numvars;
%if &>ype&i=SURV %then %do;
surv_co=&&var&i._co;
surv_ac=&&var&i._co+&&var&i._df;
*--hazards;
survh_co=-log(surv_co)/&tte_fu;
survh_ac=-log(surv_ac)/&tte_fu;
*--log hazards;
survz_co=log(survh_co);
survz_ac=log(survh_ac);
*--number of deaths;
survd_co=(&n/2)*(1-surv_co);
survd_ac=(&n/2)*(1-surv_ac);
*--variance;
survv_co=1/survd_co;
survv_ac=1/survd_ac;
call symput("var&i.v_co",trim(left(put(survv_co,best.))));
call symput("var&i.v_ac",trim(left(put(survv_ac,best.))));
call symput("var&i.z_co",trim(left(put(survz_co,best.))));
call symput("var&i.z_ac",trim(left(put(survz_ac,best.))));
%end;
%else %if &>ype&i=BINO %then %do;
bino_co=&&var&i._co;
bino_ac=&&var&i._co+&&var&i._df;
*--log odds;
binoz_co=log(bino_co/(1-bino_co));
binoz_ac=log(bino_ac/(1-bino_ac));
*--variance of log odds;
binov_co=1/((&n/2)*bino_co*(1-bino_co));
binov_ac=1/((&n/2)*bino_ac*(1-bino_ac));
call symput("var&i.v_co",trim(left(put(binov_co,best.))));
call symput("var&i.v_ac",trim(left(put(binov_ac,best.))));
call symput("var&i.z_co",trim(left(put(binoz_co,best.))));
call symput("var&i.z_ac",trim(left(put(binoz_ac,best.))));
%end;
%else %if &>ype&i=NORM %then %do;
normv_co=&&var&i._sd**2;
normv_ac=&&var&i._sd**2;
normz_ac=&&var&i._co+&&var&i._df;
normz_co=&&var&i._co;
call symput("var&i.v_co",trim(left(put(normv_co,best.))));
call symput("var&i.v_ac",trim(left(put(normv_ac,best.))));
call symput("var&i.z_co",trim(left(put(normz_co,best.))));
call symput("var&i.z_ac",trim(left(put(normz_ac,best.))));
%end;
%else %if &>ype&i=LOGN %then %do;
*--log ratio (post baseline/baseline);
lognz_ac=log(&&var&i._co+&&var&i._df);
lognz_co=log(&&var&i._co);
*--variance of log ratio;
lognv_co=&&var&i._sd**2;
lognv_ac=&&var&i._sd**2;
call symput("var&i.v_co",trim(left(put(lognv_co,best.))));
call symput("var&i.v_ac",trim(left(put(lognv_ac,best.))));
call symput("var&i.z_co",trim(left(put(lognz_co,best.))));
call symput("var&i.z_ac",trim(left(put(lognz_ac,best.))));
%end;
%end;
run;
********************************************************************;
*** simulate data from multivariate normal ***;
********************************************************************;
proc iml;
%nearestcorr();
*specify parameters of multivariate normal dist;
mean_co=1:&numvars; varn_co=1:&numvars;
mean_ac=1:&numvars; varn_ac=1:&numvars;
%do i=1 %to &numvars;
mean_co[&i]=&&var&i.z_co;
varn_co[&i]=&&var&i.v_co;
mean_ac[&i]=&&var&i.z_ac;
varn_ac[&i]=&&var&i.v_ac;
%end;
corr_tmp_={1 &corr12 &corr13 &corr14 &corr15,
&corr12 1 &corr23 &corr24 &corr25,
&corr13 &corr23 1 &corr34 &corr35,
&corr14 &corr24 &corr34 1 &corr45,
&corr15 &corr25 &corr35 &corr45 1};
corr_tmp=corr_tmp_[1:&numvars, 1:&numvars]; /*in case numvar < 5*/
eigval=eigval(corr_tmp);
if all(eigval>0) then corr=corr_tmp; /*if positive definite*/
else corr=NearestCorr(corr_tmp); /*otherwise find nearest pos def matrix*/
print corr;
covr_co=corr#sqrt(varn_co`*varn_co);
covr_ac=corr#sqrt(varn_ac`*varn_ac);
print covr_co; print covr_ac;
*obtain random samples (seed=feb2020);
call randseed(0220);
co=randnormal((&n/2)*&num,mean_co,covr_co);
ac=randnormal((&n/2)*&num,mean_ac,covr_ac);
*create sas datasets;
samp=colvec(repeat(T(1:&num),1,&n/2));
z=samp||co;
create rand_co from z[c={"samp" "x1" "x2" "x3" "x4" "x5"}];
append from z;
close rand_co;
z=samp||ac;
create rand_ac from z[c={"samp" "x1" "x2" "x3" "x4" "x5"}];
append from z;
close rand_ac;
quit;
*combine data for the 2 grps;
data randztmp;
format trt $10.;
set rand_co (in=c) rand_ac (in=a);
if a then trt='Active';
else if c then trt='Control';
run;
*sort data;
proc sort data=randztmp;
by samp trt;
run;
*finalise data, create patient number;
data randz;
retain subjno;
set randztmp;
by samp trt;
if first.samp then subjno=1;
else subjno=subjno+1;
run;
********************************************************************;
*** transform from normal variates ***;
********************************************************************;
data randsamp;
set randz;
%do i=1 %to &numvars;
%if &>ype&i=SURV %then %do;
var&i=round(-log(ranuni(1412))/exp(x&i),1)+1;
var&i.2=var&i; var&i.c=0;
if var&i gt &tte_fu then do;
var&i.2=&tte_fu;
var&i.c=1;
end;
label var&i="Survival endpoint &i"
var&i.2="Survival endpoint &i with censoring"
var&i.c="Survival endpoint &i censoring indicator";
%end;
%else %if &>ype&i=BINO %then %do;
if trt='Active' then do;
x&i._=(x&i-&&var&i.z_ac)/sqrt(&&var&i.v_ac);
x&i.__=tinv(1-(&&var&i._co+&&var&i._df),&n/2-1);
if x&i._ gt x&i.__ then var&i=1;
else var&i=0;
end;
else if trt='Control' then do;
x&i._=(x&i-&&var&i.z_co)/sqrt(&&var&i.v_co);
x&i.__=tinv(1-&&var&i._co,&n/2-1);
if x&i._ gt x&i.__ then var&i=1;
else var&i=0;
end;
drop x&i._ x&i.__;
label var&i="Dichotomous endpoint &i";
%end;
%else %if &>ype&i=NORM %then %do;
var&i=x&i;
label var&i="Continuous endpoint &i";
%end;
%else %if &>ype&i=LOGN %then %do;
var&i=100*(exp(x&i)-1);
label var&i="Pct change endpoint &i";
%end;
%end;
drop x1-x&numvars ;
label trt='Treatment' samp='Rand sample no.' subjno='Patient no.';
run;
proc sort data=randsamp;
by samp trt;
run;
%mend simul_data;
********************************************************************;
*** iterations to obtain correlations ***;
********************************************************************;
%macro iterat_simul(n_=100,num_=1000,numvars_=4,criterion=0.025,maxiter=100,
var1_df_=-1,var2_df_=-5,var3_df_=-2,var4_df_=0.02,var5_df_=,
aim12=0.20, aim13=0.20, aim14=0.05, aim15=0,
aim23=0.20, aim24=0.05, aim25=0,
aim34=0.05, aim35=0,
aim45=0,
out=finalsamp, out_iter=finaliter); /*output datasets*/
%global gnumvars gnum gtype1 gtype2 gtype3 gtype4 gtype5 gprec ;
%let gnumvars=&numvars_;
%let gnum=&num_;
%let t0 = %sysfunc(datetime());
data iterations;
set _null_;
run;
%simul_data(n=&n_,num=&num_,numvars=&numvars_,
var1_df=&var1_df_,var2_df=&var2_df_,var3_df=&var3_df_,
var4_df=&var4_df_,var5_df=&var5_df_);
%let gprec=1;
%let iterat=0;
%do %while (&gprec gt &criterion and &iterat lt &maxiter);
/*prec (precision) = max difference between actual
correlation and the desired value*/
%let iterat=%eval(&iterat+1);
ods output pearsonCorr=corrns1
(keep=variable var:
rename=(var1-var&numvars_ = varc1-varc&numvars_));
proc corr data=randsamp pearson; /*pearson used even for binary outcomes,
produces the same corr
as the biserial point correlation*/
var var1-var&numvars_; /*careful to exclude var[]2 (survival vars)*/
run;
proc sort data=corrns1;
by variable;
run;
data randzc;
set randz;
rename x1-x&numvars_ = var1-var&numvars_;
run;
ods output pearsonCorr=corrns2
(keep=variable var:
rename=(var1-var&numvars_ = varcz1-varcz&numvars_));
proc corr data=randzc pearson;
var var:; /*across random samples*/
run;
proc sort data=corrns2;
by variable;
run;
data corrns;
merge corrns1 corrns2;
by variable;
run;
data iterations;
format precision 7.5 ;
retain prectmp 0;
set iterations corrns (in=a);
conv=0.005; /*conv=convergence limit*/
if a then do;
iteration=&iterat;
%do p=1 %to 5;
%do b=1 %to 5;
if variable="var&p" then do;
%if &b gt &p and &b le &numvars_ %then %do; /*corrns above diagonal*/
diff&p&b=abs(varc&b-&&aim&p&b);
prectmp=max(prectmp,diff&p&b);
if diff&p&b lt conv then c&p&b=varcz&b; /*desired corrn attained*/
else do; /*desired value not attained, thus adjust*/
if &&aim&p&b gt 0 then c&p&b=min((&&aim&p&b/varc&b)*varcz&b,1);
/*+ve corrns*/
else c&p&b=max((&&aim&p&b/varc&b)*varcz&b,-1); /*-ve corrns*/
end;
call symput("c&p&b",trim(left(put(c&p&b,best.))));
/*corrn assigned its new value*/
%end;
end;
%if &b gt &p and (&p gt &numvars_ or &b gt &numvars_) %then %do;
call symput("c&p&b",trim(left(put(0,best.)))); /*superfluous correlations*/
%end;
%end;
%end;
if variable="var&numvars_" then call symput("gprec",trim(left(put(prectmp,7.5))));
precision=prectmp; /*this precision will be compared against the criterion
and the loop terminated if satisfied*/
end;
run;
%simul_data(n=&n_,num=&num_,numvars=&numvars_,
var1_df=&var1_df_,var2_df=&var2_df_,var3_df=&var3_df_,
var4_df=&var4_df_,var5_df=&var5_df_,
corr12=&c12, corr13=&c13, corr14=&c14, corr15=&c15,
corr23=&c23, corr24=&c24, corr25=&c25,
corr34=&c34, corr35=&c35,
corr45=&c45);
%end;
%let speed=%sysfunc(datetime())-&t0;
data &out;
set randsamp;
run;
data &out_iter;
retain iteration variable varc1-varc&numvars_ precision speed ; /*put vars in order*/
format varc1-varc&numvars_ 5.2;
set iterations;
speed=put(&speed,6.2)||' secs';
keep iteration variable varc1-varc&numvars_ precision speed;
run;
proc sort data=&out_iter;
by iteration variable;
run;
%mend iterat_simul;
*** end *****************************************;