/* Fit a linear logistic model with a clinic-specific effect to a 
   data set from a multi-center clinical trial.
  (1) Using a random-effect model
  (2) Using the conditional likelihood approach
*/
options ls=80 center pagesize=60 number label;

data clin;
  input clinic trt $ fav unfav ;
  nij=fav+unfav;
  datalines;
1 drug 11 25
1 cntl 10 27
2 drug 16  4
2 cntl 22 10
3 drug 14  5
3 cntl  7 12
4 drug  2 14
4 cntl  1 16
5 drug  6 11
5 cntl  0 12
6 drug  1 10
6 cntl  0 10
7 drug  1  4
7 cntl  1  8 
8 drug  4  2
8 cntl  6  1 
;

%inc '/home/gopher/sasmacros/glimxv12.sas' / nosource;

/* no convergence: 
%glimmix(data=clin,
   procopt=method=reml,
   stmts=%str(
      class clinic trt;
      model fav/nij = trt/ solution;
      random clinic / solution;
   ),
   error=binomial,
   link=logit,
   converge=1e-6,
   maxit=400
)
*/
/* to increase convergence: */
data new;
  set clin;
  do i=1 to fav;
     y=1;
     output;
  end;
  do i=1 to unfav;
     y=0;
     output;
  end;

%glimmix(data=new,
   procopt=method=reml,
   stmts=%str(
      class clinic trt;
      model y = trt/ solution;
      random clinic / solution;
   ),
   error=binomial,
   link=logit
)

/* Conditional likelihood approach */
data new2;
  set new;
  dumbtime=2-y;
  if trt='drug' then isctl=0;
  else isctl=1;

proc phreg data=new2;
model dumbtime*y(0) = isctl / ties=discrete;
strata clinic;
title1 "Conditional likelihood";

*************Random-effects model:

                              Cov
                              Parm         Estimate
                             CLINIC      2.05663184

                              Parameter Estimates                              
   Effect       TRT       Estimate     Std Error     DF         t    Pr > |t|
   INTERCEPT               -0.4243        0.5555      7     -0.76      0.4699
   TRT          cntl       -0.7273        0.2882    264     -2.52      0.0122
   TRT          drug        0.0000         .          .       .         .    

                            Random Effects Estimates                           
   Effect    CLINIC      Estimate       SE Pred     DF         t    Pr > |t|
   CLINIC      1          -0.1376        0.5788    264     -0.24      0.8122
   CLINIC      2           1.8181        0.5968    264      3.05      0.0026
   CLINIC      3           0.9581        0.6008    264      1.59      0.1120
   CLINIC      4          -1.3470        0.6935    264     -1.94      0.0531
   CLINIC      5          -0.5982        0.6495    264     -0.92      0.3579
   CLINIC      6          -1.6712        0.7960    264     -2.10      0.0367
   CLINIC      7          -0.7526        0.7653    264     -0.98      0.3263
   CLINIC      8           1.7305        0.7192    264      2.41      0.0168

                             Tests of Fixed Effects                            

                  Source    NDF    DDF    Type III F    Pr > F
                   TRT       1     264          6.37    0.0122

***************Conditional likelihood 

                     Testing Global Null Hypothesis: BETA=0
 
                   Without        With   
    Criterion    Covariates    Covariates    Model Chi-Square

    -2 LOG L        257.398       250.907       6.491 with 1 DF (p=0.0108)  
    Score              .             .          6.384 with 1 DF (p=0.0115)  
    Wald               .             .          6.246 with 1 DF (p=0.0124)  

                    Analysis of Maximum Likelihood Estimates
 
                    Parameter     Standard      Wald         Pr >          Risk
 Variable   DF       Estimate       Error    Chi-Square   Chi-Square      Ratio

 ISCTL       1      -0.756259      0.30259      6.24638       0.0124      0.469