You will need one ESTIMATE statement for each attending you have in your data.  For the second level of attending, the ESTIMATE statement might look something like   estimate '2' int 1 x1 1 x2 1 | int 1 / subject 0 1 ilink e;    You include the random effects you need in your ESTIMATE statement after the | operator (the vertical bar operator).  Since we also have a SUBJECT= effect in the RANDOM statement, you specify the subject of interest for the RANDOM statement with the SUBJECT option.  Treat this effect like you would any other CLASS effect in your model.   If you have a lot of levels to the attending effect, this could get rather tedious.  You will need one ESTIMATE statement for each of those levels.  However, SAS Macro code can make writing all of these ESTIMATE statements a snap.  Try something like   %do i=1 %to 10; estimate "&i" int 1 x1 1 x2 1| int 1 / subject %do k=1 %to %eval(&i-1); 0 %end; 1 ilink e; %end;   That macro loop will generate the estimates you need for the first ten attending levels.  Just change the 10 on that %do line to generate more ESTIMATE statements.  You will need to put your PROC GLIMMIX in a macro to make this work.   I have ammended the code below to include this suggestion and to include Rick's suggestion just below my answer.       data test; call streaminit(6354153); /* initialize random number stream */ do a=1 to 10; /* 10 levels to the random effect */ ra=rand('normal',.7); /* generate random intercept adjustment for each level */ do i=1 to 20; x1=rand('uniform'); /* generate random covariates */ x2=rand('uniform'); x3=rand('normal')*.5; x4=rand('normal')*.5; trt=ceil(rand('uniform')*3); /* generate trt and group levels */ grp=ceil(rand('uniform')*5); logit=-2 + 2*x1 + x2 + x3 - x4 + (trt-2) + (grp-3) + ra; /* calculate the logit */ p=exp(-logit)/(1+exp(-logit)); /* and then the predicted probability */ if rand('uniform')>p then y=1; else y=0; /* assign the response */ output; end; end; run; proc glimmix data=test method=laplace; class a trt grp; model y=trt grp x1 x2 x3 x4 / s dist=bin link=logit; random intercept / subject=a; estimate '1' int 1 x1 1 x2 1 | int 1 / subject 1 ilink e; estimate '2' int 1 x1 1 x2 1 | int 1 / subject 0 1 ilink e; run;   %macro doests; %do i=1 %to 10; estimate "&i" int 1 x1 1 x2 1| int 1 / subject %do k=1 %to %eval(&i-1); 0 %end; 1 ilink e; %end; %mend; proc glimmix data=test method=laplace; class a trt grp; model y=trt grp x1 x2 x3 x4 / s dist=bin link=logit; random intercept / subject=a; %doests; run; ... View more

There is a lot of good information here, but one piece is missing.  Yes, you need the information (error sum of squares) contained in the group standard deviations, but you also need to take into account the variability of the group means about the overall mean in a calculation of the overall sample standard deviation.   You can write a lot of DATA Step and SAS Procedure code to come up with the answer to this question, but SQL can get you there fairly succintly.  Try this example shown below.  The initial DATA step generates sample data with 5 groups and a varying number of observations per group.  The first PROC MEANS step generates the data set described by the original poster, one with just the group n's, means, and standard deviations.  The second PROC MEANS step gives the mean and standard deviation for the overall sample.  It is this mean and standard deviation that we wish to replicate from the information in the data set GroupStats (the output data set from that first PROC MEANS).   The PROC SQL step gives us that result.  SQL is really good at doing many things.  Most are more familiar with doing joins using SQL, but it also works well at the type of calculation we need here.  The calculation of the overall standard deviation requires computing summary statistics on several different levels.  This calculation can be done in a single PROC SQL step.     There are several sources on the web for explaining the derivation of this calculation, including some Youtube videos.  See those for the why's of the SQL step below.     data test;    call streaminit(613254);    do group=1 to 5;       do rep=1 to (5+group);          y=(group*10) + rand('normal');          output;    end; end; run;   proc means data=test;    by group;    var y;    output out=GroupStats n=n mean=mean stddev=std; run;   proc means data=test mean stddev;    var y; run;   proc sql;    create table SQLFinalStats as    select distinct sum_n, OverallMean, sqrt(sum(TSS)/(sum(n)-1)) as OverallStd    from (              select n, sum(n) as sum_n,                        sum(n*mean)/sum(n) as OverallMean,                        std*std*(n-1) + n*(mean-(sum(n*mean)/sum(n)))**2 as TSS              from GroupStats); quit; ... View more

Updated solution ...   There are several good comments here, but this SAS note describes a more complete solution to the original problem.  ... View more