广义线性混合模型中组均值的估计
Estimation of group means in generalized linear mixed models
摘要：
在这篇手稿中，我们研究了治疗组平均值的平均响应的概念，以及具有受试者随机效应的广义线性模型的估计和预测。广义线性模型常用于分析分类数据。治疗组的基于模型的均值通常估计平均协变量的响应。然而，在临床试验背景下，研究人群治疗组的平均缓解至少同样重要。提出了新的方法来估计广义线性模型中的平均响应;然而，这仅在模型中没有随机效应时才能做到。我们认为，在广义线性混合模型（GLMM）中，至少有两种可能的治疗组平均应答定义可作为估计/预测目标。这些治疗组平均值的估计对于医疗保健专业人员能够理解绝对获益与风险非常重要。对于这两个治疗组的平均值，我们提出了一组新的方法，建议如何估计/预测他们在一个单变量的受试者随机效应的GLMM模型。我们的方法还提出了一种简单的方法来构建相应的置信区间和预测区间的两个可能的治疗组的手段。仿真结果表明，在大多数情况下，建议的置信区间和预测区间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的低血糖数据。
英文摘要：
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.
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