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Documentation Example 15 for PROC MCMC

/****************************************************************/
/*          S A S   S A M P L E   L I B R A R Y                 */
/*                                                              */
/*    NAME: MCMCEX15                                            */
/*   TITLE: Documentation Example 15 for PROC MCMC              */
/*          Time Dependent Cox Model                            */
/* PRODUCT: STAT                                                */
/*  SYSTEM: ALL                                                 */
/*    KEYS:                                                     */
/*   PROCS: MCMC                                                */
/*    DATA:                                                     */
/*                                                              */
/* SUPPORT: Fang Chen                                           */
/*     REF: PROC MCMC, EXAMPLE 15                               */
/*    MISC:                                                     */
/****************************************************************/
data Myeloma;
   input Time Vstatus LogBUN HGB Platelet Age LogWBC Frac
         LogPBM Protein SCalc;
   label Time='survival time'
         VStatus='0=alive 1=dead';
   datalines;
 1.25  1  2.2175   9.4  1  67  3.6628  1  1.9542  12  10
 1.25  1  1.9395  12.0  1  38  3.9868  1  1.9542  20  18
 2.00  1  1.5185   9.8  1  81  3.8751  1  2.0000   2  15
 2.00  1  1.7482  11.3  0  75  3.8062  1  1.2553   0  12
 2.00  1  1.3010   5.1  0  57  3.7243  1  2.0000   3   9
 3.00  1  1.5441   6.7  1  46  4.4757  0  1.9345  12  10
 5.00  1  2.2355  10.1  1  50  4.9542  1  1.6628   4   9
 5.00  1  1.6812   6.5  1  74  3.7324  0  1.7324   5   9
 6.00  1  1.3617   9.0  1  77  3.5441  0  1.4624   1   8
 6.00  1  2.1139  10.2  0  70  3.5441  1  1.3617   1   8
 6.00  1  1.1139   9.7  1  60  3.5185  1  1.3979   0  10
 6.00  1  1.4150  10.4  1  67  3.9294  1  1.6902   0   8
 7.00  1  1.9777   9.5  1  48  3.3617  1  1.5682   5  10
 7.00  1  1.0414   5.1  0  61  3.7324  1  2.0000   1  10
 7.00  1  1.1761  11.4  1  53  3.7243  1  1.5185   1  13
 9.00  1  1.7243   8.2  1  55  3.7993  1  1.7404   0  12
11.00  1  1.1139  14.0  1  61  3.8808  1  1.2788   0  10
11.00  1  1.2304  12.0  1  43  3.7709  1  1.1761   1   9
11.00  1  1.3010  13.2  1  65  3.7993  1  1.8195   1  10
11.00  1  1.5682   7.5  1  70  3.8865  0  1.6721   0  12
11.00  1  1.0792   9.6  1  51  3.5051  1  1.9031   0   9
13.00  1  0.7782   5.5  0  60  3.5798  1  1.3979   2  10
14.00  1  1.3979  14.6  1  66  3.7243  1  1.2553   2  10
15.00  1  1.6021  10.6  1  70  3.6902  1  1.4314   0  11
16.00  1  1.3424   9.0  1  48  3.9345  1  2.0000   0  10
16.00  1  1.3222   8.8  1  62  3.6990  1  0.6990  17  10
17.00  1  1.2304  10.0  1  53  3.8808  1  1.4472   4   9
17.00  1  1.5911  11.2  1  68  3.4314  0  1.6128   1  10
18.00  1  1.4472   7.5  1  65  3.5682  0  0.9031   7   8
19.00  1  1.0792  14.4  1  51  3.9191  1  2.0000   6  15
19.00  1  1.2553   7.5  0  60  3.7924  1  1.9294   5   9
24.00  1  1.3010  14.6  1  56  4.0899  1  0.4771   0   9
25.00  1  1.0000  12.4  1  67  3.8195  1  1.6435   0  10
26.00  1  1.2304  11.2  1  49  3.6021  1  2.0000  27  11
32.00  1  1.3222  10.6  1  46  3.6990  1  1.6335   1   9
35.00  1  1.1139   7.0  0  48  3.6532  1  1.1761   4  10
37.00  1  1.6021  11.0  1  63  3.9542  0  1.2041   7   9
41.00  1  1.0000  10.2  1  69  3.4771  1  1.4771   6  10
41.00  1  1.1461   5.0  1  70  3.5185  1  1.3424   0   9
51.00  1  1.5682   7.7  0  74  3.4150  1  1.0414   4  13
52.00  1  1.0000  10.1  1  60  3.8573  1  1.6532   4  10
54.00  1  1.2553   9.0  1  49  3.7243  1  1.6990   2  10
58.00  1  1.2041  12.1  1  42  3.6990  1  1.5798  22  10
66.00  1  1.4472   6.6  1  59  3.7853  1  1.8195   0   9
67.00  1  1.3222  12.8  1  52  3.6435  1  1.0414   1  10
88.00  1  1.1761  10.6  1  47  3.5563  0  1.7559  21   9
89.00  1  1.3222  14.0  1  63  3.6532  1  1.6232   1   9
92.00  1  1.4314  11.0  1  58  4.0755  1  1.4150   4  11
 4.00  0  1.9542  10.2  1  59  4.0453  0  0.7782  12  10
 4.00  0  1.9243  10.0  1  49  3.9590  0  1.6232   0  13
 7.00  0  1.1139  12.4  1  48  3.7993  1  1.8573   0  10
 7.00  0  1.5315  10.2  1  81  3.5911  0  1.8808   0  11
 8.00  0  1.0792   9.9  1  57  3.8325  1  1.6532   0   8
12.00  0  1.1461  11.6  1  46  3.6435  0  1.1461   0   7
11.00  0  1.6128  14.0  1  60  3.7324  1  1.8451   3   9
12.00  0  1.3979   8.8  1  66  3.8388  1  1.3617   0   9
13.00  0  1.6628   4.9  0  71  3.6435  0  1.7924   0   9
16.00  0  1.1461  13.0  1  55  3.8573  0  0.9031   0   9
19.00  0  1.3222  13.0  1  59  3.7709  1  2.0000   1  10
19.00  0  1.3222  10.8  1  69  3.8808  1  1.5185   0  10
28.00  0  1.2304   7.3  1  82  3.7482  1  1.6721   0   9
41.00  0  1.7559  12.8  1  72  3.7243  1  1.4472   1   9
53.00  0  1.1139  12.0  1  66  3.6128  1  2.0000   1  11
57.00  0  1.2553  12.5  1  66  3.9685  0  1.9542   0  11
77.00  0  1.0792  14.0  1  60  3.6812  0  0.9542   0  12
;
title 'Cox Model with Time Dependent Covariates';
proc sort data = Myeloma;
   by descending time;
run;

data _null_;
   set Myeloma nobs=_n;
   call symputx('N', _n);
   stop;
run;

ods select none;
proc freq data=myeloma;
   tables time / out=freqs;
run;
ods select all;

proc sort data = freqs;
   by descending time;
run;

data myelomaM;
   set myeloma;
   ind = _N_;
run;

data myelomaM;
   merge myelomaM freqs(drop=percent); by descending time;
   retain stop;
   if first.time then do;
      stop = _n_ + count - 1;
   end;
run;

%macro array(list);
   %global mcmcarray;
   %let mcmcarray = ;
   %do i = 1 %to 32000;
      %let v = %scan(&list, &i, %str( ));
      %if %nrbquote(&v) ne %then %do;
         array _&v[&n];
         %let mcmcarray = &mcmcarray array _&v[&n] _&v.1 - _&v.&n%str(;);
         do i = 1 to stop;
            set myelomaM(keep=&v) point=i;
            _&v[i] = &v;
         end;
      %end;
      %else %let i = 32001;
   %end;
%mend;

data z;
   set myelomaM;
   %array(logbun hgb platelet);
   drop vstatus logbun hgb platelet count stop;
run;

data myelomaM;
   merge myelomaM z; by descending time;
run;
proc mcmc data=myelomaM outpost=outi nmc=50000 ntu=3000 seed=17
          missing=ac;
   ods select PostSummaries PostIntervals;
   array beta[6];
   &mcmcarray
   parms (beta:) 0;
   prior beta: ~ normal(0, prec=1e-6);

   b = (beta1 + beta2 * time) * logbun +
       (beta3 + beta4 * time) * hgb +
       (beta5 + beta6 * time) * platelet;
   S = 0;
   do i = 1 to stop;
      S = S + exp( (beta1 + beta2 * time) * _logbun[i] +
                   (beta3 + beta4 * time) * _hgb[i] +
                   (beta5 + beta6 * time) * _platelet[i]);
   end;
   loglike = vstatus * (b - log(S));

   model general(loglike);
run;
proc mcmc data=myelomaM outpost=outa nmc=50000 ntu=3000 seed=17 jointmodel;
   ods select none;
   array beta[6];      array timeA[&n];      array vstatusA[&n];
   array logbunA[&n];  array hgbA[&n];       array plateletA[&n];
   array stopA[&n];    array bZ[&n];         array S[&n];

   begincnst;
      timeA[ind]=time;          vstatusA[ind]=vstatus;
      logbunA[ind]=logbun;      hgbA[ind]=hgb;
      plateletA[ind]=platelet;  stopA[ind]=stop;
   endcnst;

   parms (beta:) 0;
   prior beta: ~ normal(0, prec=1e-6);

   jl = 0;
   do i = 1 to &n;
      v1 = beta1 + beta2 * timeA[i];
      v2 = beta3 + beta4 * timeA[i];
      v3 = beta5 + beta6 * timeA[i];
      bZ[i] = v1 * logbunA[i] + v2 * hgbA[i] + v3 * plateletA[i];

      /* sum over risk set without considering ties in time. */
      S[i] = exp(bZ[i]);
      if (i > 1) then do;
         do j = 1 to (i-1);
            b1 = v1 * logbunA[j] + v2 * hgbA[j] + v3 * plateletA[j];
            S[i] = S[i] + exp(b1);
         end;
      end;
   end;

   /* make correction to the risk set due to ties in time. */
   do i = 1 to &n;
      if(stopA[i] > i) then do;
         v1 = beta1 + beta2 * timeA[i];
         v2 = beta3 + beta4 * timeA[i];
         v3 = beta5 + beta6 * timeA[i];
         do j = (i+1) to stopA[i];
            b1 = v1 * logbunA[j] + v2 * hgbA[j] + v3 * plateletA[j];
            S[i] = S[i] + exp(b1);
         end;
      end;
      jl = jl + vstatusA[i] * (bZ[i] - log(S[i]));
   end;
   model general(jl);
run;
proc compare data=outi compare=outa;
   ods select comparesummary;
   var beta1-beta6;
run;
proc phreg data=Myeloma;
   ods select PostSummaries PostIntervals;
   model Time*VStatus(0)=LogBUN z2 hgb z3 platelet z4;
   z2 = Time*logbun;
   z3 = Time*hgb;
   z4 = Time*platelet;
   bayes seed=1 nmc=10000 outpost=phout;
run;