Glimmix did not converge or covariance matrix doesn't make sense

[Fang_Merck]

Hello,

I have several clinical data set with binary response. For all data sets, subjects are enrolled from different sites and are taking either treatment A or B (parallel design). I am trying to assess the site variation for the response variable. Since there are 2 treatment, I assume that the site variation could be different for the 2 treatments and there could be a correlation. The following is my SAS code:

proc glimmix data=dset;
class sitenum trt;
model resp= trt/dist=bin link=logit solution;
random trt/SUBJECT=SITENUM type=UN solution G;
run;

For most data sets, Proc Glimmix doesn't converge. For one data set, Glimmix does converge and I got the following covariance matrix. I think here 0.00907 is the site variance of treatment A and 3.54E-18 is the site variance of treatment B. However, the covariance between treatments A and B are even bigger than the both variance, so the correlation will be >1. Do I understand it correct? I don't know why it can happened.

Estimated G Matrix
Effect	Description of Actual Arm	Row	Col1	Col2
trt	A	1	0.00907	0.02008
trt	B	2	0.02008	3.54E-18

[ballardw]

I am a little confused by:

For most data sets, Proc Glimmix doesn't converge

I would expect that you would combine all of the data to have all of the sites in one data set to answer a question about the impact of "site" on the analysis. Why are these separate data sets analyzed one a time? Are you comparing all pairs of individual sites?

[Fang_Merck]

I meant that I have several independent clinical trial data set for
different drug. That is why I did the analysis separately.