Mathematical Institute, Heinrich Heine University Düsseldorf, Düsseldorf, 40225, Germany.
Institute of Medical Statistics and Computational Biology (IMSB), Faculty of Medicine, University of Cologne, Cologne, 50923, Germany.
Biometrics. 2024 Jul 1;80(3). doi: 10.1093/biomtc/ujae077.
A common problem in clinical trials is to test whether the effect of an explanatory variable on a response of interest is similar between two groups, for example, patient or treatment groups. In this regard, similarity is defined as equivalence up to a pre-specified threshold that denotes an acceptable deviation between the two groups. This issue is typically tackled by assessing if the explanatory variable's effect on the response is similar. This assessment is based on, for example, confidence intervals of differences or a suitable distance between two parametric regression models. Typically, these approaches build on the assumption of a univariate continuous or binary outcome variable. However, multivariate outcomes, especially beyond the case of bivariate binary responses, remain underexplored. This paper introduces an approach based on a generalized joint regression framework exploiting the Gaussian copula. Compared to existing methods, our approach accommodates various outcome variable scales, such as continuous, binary, categorical, and ordinal, including mixed outcomes in multi-dimensional spaces. We demonstrate the validity of this approach through a simulation study and an efficacy-toxicity case study, hence highlighting its practical relevance.
临床试验中的一个常见问题是检验两个组（例如，患者组或治疗组）之间某个解释变量对感兴趣的响应的影响是否相似。在这方面，相似性被定义为在预先指定的阈值内等效，该阈值表示两组之间可接受的偏差。通常通过评估解释变量对响应的影响是否相似来解决这个问题。这种评估基于例如差异的置信区间或两个参数回归模型之间的合适距离。通常，这些方法基于单变量连续或二分类因变量的假设。然而，多元结果，尤其是在二元二分类响应之外的情况，仍然研究不足。本文提出了一种基于广义联合回归框架的方法，利用高斯 Copula。与现有方法相比，我们的方法可以适应各种因变量尺度，如连续、二分类、分类和有序，包括多维空间中的混合结果。我们通过模拟研究和疗效-毒性案例研究证明了该方法的有效性，从而突出了其实用性。
