derive_WR.sas

/******************************************************************************
Author, date: Paul Brown, SEP2015
Macro name:   derive_WR
Description:  derive the unmatched win-ratio endpoint on simulated data.
              (developed in SAS 9.4)
Reference:    The win ratio: a new approach to the analysis of composite
              endpoints in clinical trials based on clinical priorities,
              Pocock SJ et al., EHJ, 2012
******************************************************************************/

********************************************************************;
***             Rank survival times and count ties               ***;
********************************************************************;

%macro surv_wr(indata_,var,where);
proc sort data=&indata_ (where=&where) out=&var;
  by samp &var;
run;

data rank&var;
  retain ties&var before&var count 0;
  set &var;
  by samp &var;
  if first.samp then count=0;
  else count=count+1;
  if first.&var then do;
    ties&var=1;
    before&var=count; /*can check using ties=low option in proc rank*/
  end;
  else ties&var=ties&var+1;
  keep samp subjno trt &var ties&var before&var;
run;

proc sort data=rank&var out=ties&var (keep=samp &var ties&var);
  by samp &var descending ties&var;
run;

proc sort data=ties&var nodupkey;
  by samp &var ;
run;

data rank&var.2;
  merge rank&var (drop=ties&var) ties&var;
  by samp &var;
run;

proc sort data=rank&var.2;
  by samp subjno;
run;
%mend surv_wr;

********************************************************************;
***                 Derive win-ratio score (U)                   ***;
********************************************************************;

%macro derive_wr(n=100,indata=finalsamp,outdata=out_wr,outpval=pval_wr);

%surv_wr(&indata,var1,(var1c=0));
%surv_wr(&indata,var2,(var1c=1 and var2c=0)); /*consider reh for pts who didnt die*/

*consider where pts fail;
data winratio;
  merge &indata rankvar12 rankvar22;
  by samp subjno trt;
  if var1c=0 then cat=1;      /*pt died*/
  else if var2c=0 then cat=2; /*pt didnt die, had rehosp*/
  else cat=3;
run;

*find the number of pts falling into these broad categories to enable
 calculation of no. of wins/losses/ties per pt;
ods output onewayfreqs=counts1;
proc freq data=winratio;
  ods select onewayfreqs;
  tables cat ;
  by samp;
run;

proc transpose data=counts1 out=counts1_t (drop=_name_) prefix=cat;
  var frequency;
  id cat;
  by samp;
run;

*replace missings obs with 0 (when n small have small or missing cell counts);
proc stdize data=counts1_t
            out=counts1_t2 reponly missing=0;
run;

*calculate number of wins/losses/ties for each pt, ie as if comparing each
 pt to every other pt (irrespective of trt group) as per the unmatched approach;
data &outdata;
  merge winratio counts1_t2 ;
  by samp;
  if cat=1 then do;      /*compare mortality times*/
    win=beforevar1;
    tie=tiesvar1-1; /*subtract 1 so the pt isnt tied with themselves*/
    lose=(&n-1)-win-tie;
  end;
  else if cat=2 then do; /*cant determine who died 1st, use rehosp*/
    win=cat1+beforevar2;
    tie=tiesvar2-1;
    lose=(&n-1)-win-tie;
  end;
  else if cat=3 then do; /*cant determine who died 1st, use rehosp*/
    win=cat1+cat2;
    tie=cat3-1;
    lose=(&n-1)-win-tie;
  end;
  check=win+lose+tie; /*check sum to n-1*/
  u=win-lose; /*ties have zero weight*/
  u2=u**2;
  keep samp subjno trt win lose tie u u2 check ;
  label win='No. of wins' lose='No of losses' tie='No. of ties'
        u='Win-ratio U (sum of wins/losses/ties)' u2='U^2 (for var of test stat)'
        check='Sum of wins/losses/ties (use as a check)';
run;

proc sort data=&outdata;
  by samp subjno;
run;

********************************************************************;
***                   p-value                         ***;
********************************************************************;

*calculate the p-value by hand for the unmatched win ratio
(see Finkelstein and Schoenfeld, and pocock stat appendix: the U^2
 and U are summed for the active grp. NOTE: there is a typo in
 their variance eqn i.e. it should sum U^2 from 1 to N, not 1 to n);

proc univariate data=&outdata (where=(trt='Active'));
  var u ;
  by samp;
  output out=usum sum=usum;
run;

proc univariate data=&outdata;
  var u2;
  by samp;
  output out=u2sum sum=u2sum;
run;

data &outpval;
  merge usum u2sum;
  by samp;
  T=usum; /*sum of U for active trt group*/
  V=(&n/2)*(&n/2)/(&n*(&n-1))*u2sum; /*variance of T*/
  Z=T/sqrt(V);
  nValue1=2*(1-probnorm(abs(Z))); /*p-value*/
run;

%mend derive_wr;


***end****************************************************************;