# Estimation of group means in generalized linear mixed models

## TL;DR

This paper introduces new methods for estimating and predicting treatment group means in generalized linear mixed models, addressing the importance of these estimates in clinical trial analysis.

## Contribution

It proposes novel estimation and prediction techniques for treatment group means in GLMMs with random effects, including methods for confidence and prediction intervals.

## Key findings

- Proposed intervals achieve correct empirical coverage in simulations.
- Methods successfully applied to diabetes clinical trial data.
- Two definitions of treatment group means are effectively estimated.

## Abstract

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.