/* Fit a linear logistic model with a clinic-specific effect to a 
   data set from a multi-center clinical trial,
   using a random-effect model
*/
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 
;

data new;
  set clin;
  do i=1 to fav;
     y=1;
     output;
  end;
  do i=1 to unfav;
     y=0;
     output;
  end;

data new2;
  set new;
  dumbtime=2-y;
  if trt='drug' then isctl=0;
  else isctl=1;

/* NLMIXED: binary data*/
proc nlmixed data=new2;
  parms intc=-0.4 b1=-0.7 v=2;
  eta = intc + b1*isctl + u;
  expNeta = exp(-eta);
  p = 1/(1+expNeta);
  model y ~ binomial(1, p);
  random u ~ normal(0, v) subject=clinic;
  title1 'Nlmixed (binary)';

data new3;
  set clin;
  if trt='drug' then isctl=0;
  else isctl=1;

/* NLMIXED: binomial data*/
proc nlmixed data=new3;
  parms intc=-0.4 b1=-0.7 v=2;
  eta = intc + b1*isctl + u;
  expNeta = exp(-eta);
  p = 1/(1+expNeta);
  model fav ~ binomial(nij, p);
  random u ~ normal(0, v) subject=clinic;
  title1 'Nlmixed (binomial)';

run;
*************                 Nlmixed (binary)  
                              Parameter Estimates
 
                       Standard
Parameter   Estimate      Error     DF   t Value   Pr > |t|    Alpha      Lower

intc         -0.4589     0.5504      7     -0.83     0.4319     0.05    -1.7605
b1           -0.7385     0.3004      7     -2.46     0.0436     0.05    -1.4488
v             1.9591     1.1903      7      1.65     0.1438     0.05    -0.8554

                              Parameter Estimates
 
                        Parameter      Upper    Gradient

                        intc          0.8426    -1.99E-7
                        b1          -0.02806    8.688E-7
                        v             4.7736    5.703E-7

****************                Nlmixed (binomial)                              
                              Parameter Estimates
 
                       Standard
Parameter   Estimate      Error     DF   t Value   Pr > |t|    Alpha      Lower

intc         -0.4589     0.5504      7     -0.83     0.4319     0.05    -1.7605
b1           -0.7385     0.3004      7     -2.46     0.0436     0.05    -1.4488
v             1.9591     1.1903      7      1.65     0.1438     0.05    -0.8554

                              Parameter Estimates
 
                        Parameter      Upper    Gradient

                        intc          0.8426    -1.99E-7
                        b1          -0.02806    8.688E-7
                        v             4.7736    5.703E-7