  In this manuscript, we investigate the concept of the mean response for a
treatment group mean as well as its estimation and prediction for generalized
linear models with a subject-wise random effect. Generalized linear models are
commonly used to analyze categorical data. The model-based mean for a treatment
group usually estimates the response at the mean covariate. However, the mean
response for the treatment group for studied population is at least equally
important in the context of clinical trials. New methods were proposed to
estimate such a mean response in generalized linear models; however, this has
only been done when there are no random effects in the model. We suggest that,
in a generalized linear mixed model (GLMM), there are at least two possible
definitions of a treatment group mean response that can serve as
estimation/prediction targets. The estimation of these treatment group means is
important for healthcare professionals to be able to understand the absolute
benefit versus risk. For both of these treatment group means, we propose a new
set of methods that suggests how to estimate/predict both of them in a GLMM
models with a univariate subject-wise random effect. Our methods also suggest
an easy way of constructing corresponding confidence and prediction intervals
for both possible treatment group means. Simulations show that proposed
confidence and prediction intervals provide correct empirical coverage
probability under most circumstances. Proposed methods have also been applied
to analyze hypoglycemia data from diabetes clinical trials.
