Department of Statistics, Purdue University, West Lafayette, Indiana, USA.
Biostatistics and Programming, Sanofi, Bridgewater, New Jersey, USA.
Pharm Stat. 2020 Sep;19(5):646-661. doi: 10.1002/pst.2022. Epub 2020 Apr 6.
In this study, 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 vs 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 GLMMs 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.
在这项研究中，我们研究了治疗组均值的均值响应概念，以及其在具有个体随机效应的广义线性模型中的估计和预测。广义线性模型通常用于分析分类数据。治疗组的基于模型的均值通常估计在均值协变量处的响应。然而，在临床试验背景下，对于研究人群，治疗组的均值响应至少同样重要。已经提出了新的方法来估计广义线性模型中的这种均值响应；但是，这仅在模型中没有随机效应时才完成。我们建议，在广义线性混合模型 (GLMM) 中，至少有两种可能的治疗组均值响应定义可以作为估计/预测目标。这些治疗组均值的估计对于医疗保健专业人员来说非常重要，以便能够理解绝对获益与风险。对于这两种治疗组均值，我们提出了一套新的方法，建议如何在具有单变量个体随机效应的 GLMM 中估计/预测这两种均值。我们的方法还建议了一种简单的方法来构建这两种可能的治疗组均值的置信区间和预测区间。模拟结果表明，所提出的置信区间和预测区间在大多数情况下都能提供正确的经验覆盖概率。所提出的方法也已应用于分析糖尿病临床试验中的低血糖数据。
