Estimation of group means in generalized linear mixed models
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In this manuscript, we investigate the group mean 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. It has been argued recently in the literature that 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 only fixed effects present in the model. We propose a new set of methods that allow both estimation and prediction of the mean response for the treatment group in GLMM models with a univariate subject-wise random effect. Our methods also suggest an easy way of constructing corresponding confidence and prediction intervals for the mean response for the treatment group. Simulation shows 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.
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