In dose–response analysis, it is a challenge to choose appropriate linear or curvilinear shapes when considering multiple, differently scaled endpoints. It has been proposed to fit several marginal regression models that try sets of different transformations of the dose levels as explanatory variables for each endpoint. However, the multiple testing problem underlying this approach, involving correlated parameter estimates for the dose effect between and within endpoints, could only be adjusted heuristically. An asymptotic correction for multiple testing can be derived from the score functions of the marginal regression models. Based on a multivariate t-distribution, the correction provides a one-step adjustment of p-values that accounts for the correlation between estimates from different marginal models. The advantages of the proposed methodology are demonstrated through three example datasets, involving generalized linear models with differently scaled endpoints, differing covariates, and a mixed effect model and through simulation results. The methodology is implemented in an R package.

中文翻译：

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Tukey 趋势检验：使用多个边际模型的多重性调整

在剂量反应分析中，在考虑多个不同尺度的端点时，选择适当的线性或曲线形状是一项挑战。有人建议拟合几个边际回归模型，这些模型尝试将剂量水平的不同转换集作为每个端点的解释变量。然而，这种方法背后的多重测试问题，包括端点之间和端点内剂量效应的相关参数估计，只能进行启发式调整。多重检验的渐近校正可以从边际回归模型的得分函数中推导出来。基于多元t分布，校正提供了p的一步调整- 说明来自不同边际模型的估计之间的相关性的值。通过三个示例数据集展示了所提出方法的优点，包括具有不同缩放端点、不同协变量和混合效应模型的广义线性模型以及模拟结果。该方法在 R 包中实现。