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, e.g. 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 response, remain underexplored. This paper introduces an approach based on a generalised 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.

翻译：临床试验中的一个常见问题是检验解释变量对感兴趣结局的影响在两组之间（例如患者组或治疗组）是否相似。在此方面，相似性被定义为在预设阈值范围内的等价性，该阈值表示两组之间可接受的偏差。这个问题通常通过评估解释变量对结局的影响是否相似来解决。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适当距离。通常，这些方法建立在单变量连续或二元结局变量的假设之上。然而，多元结局，尤其是超出二元双变量响应的情况，仍未得到充分探索。本文介绍了一种基于广义联合回归框架的方法，该框架利用高斯连接函数（Gaussian copula）。与现有方法相比，我们的方法适用于各种结局变量尺度，例如连续、二元、分类和有序变量，包括多维空间中的混合结局。我们通过模拟研究和一项疗效-毒性案例研究证明了该方法的有效性，从而突出了其实用价值。