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A common problem in clinical trials is to test whether the effect of anexplanatory variable on a response of interest is similar between two groups,e.g. patient or treatment groups. In this regard, similarity is defined asequivalence up to a pre-specified threshold that denotes an acceptabledeviation between the two groups. This issue is typically tackled by assessingif the explanatory variable's effect on the response is similar. Thisassessment is based on, for example, confidence intervals of differences or asuitable distance between two parametric regression models. Typically, theseapproaches build on the assumption of a univariate continuous or binary outcomevariable. However, multivariate outcomes, especially beyond the case ofbivariate binary response, remain underexplored. This paper introduces anapproach based on a generalised joint regression framework exploiting theGaussian copula. Compared to existing methods, our approach accommodatesvarious outcome variable scales, such as continuous, binary, categorical, andordinal, including mixed outcomes in multi-dimensional spaces. We demonstratethe validity of this approach through a simulation study and anefficacy-toxicity case study, hence highlighting its practical relevance.

Testing for similarity of multivariate mixed outcomes using generalised joint regression models with application to efficacy-toxicity responses