A common problem in numerous research areas, particularly in clinical trials, is to test whether the effect of an explanatory variable on an outcome variable is equivalent across different groups. In practice, these tests are frequently used to compare the effect between patient groups, e.g. based on gender, age or treatments. Equivalence is usually assessed by testing whether the difference between the groups does not exceed a pre-specified equivalence threshold. Classical approaches are based on testing the equivalence of single quantities, e.g. the mean, the area under the curve (AUC) or other values of interest. However, when differences depending on a particular covariate are observed, these approaches can turn out to be not very accurate. Instead, whole regression curves over the entire covariate range, describing for instance the time window or a dose range, are considered and tests are based on a suitable distance measure of two such curves, as, for example, the maximum absolute distance between them. In this regard, a key assumption is that the true underlying regression models are known, which is rarely the case in practice. However, misspecification can lead to severe problems as inflated type I errors or, on the other hand, conservative test procedures. In this paper, we propose a solution to this problem by introducing a flexible extension of such an equivalence test using model averaging in order to overcome this assumption and making the test applicable under model uncertainty. Precisely, we introduce model averaging based on smooth AIC weights and we propose a testing procedure which makes use of the duality between confidence intervals and hypothesis testing. We demonstrate the validity of our approach by means of a simulation study and demonstrate the practical relevance of the approach considering a time-response case study with toxicological gene expression data.

翻译：众多研究领域（尤其是临床试验）中的一个常见问题是检验解释变量对结果变量的效应是否在不同组间等价。实践中，这些检验常用于比较患者组之间的效应差异，例如基于性别、年龄或治疗方法的比较。等价性通常通过检验组间差异是否不超过预设的等价阈值来评估。经典方法基于检验单一数量的等价性，如均值、曲线下面积（AUC）或其他感兴趣的值。然而，当观察到依赖特定协变量的差异时，这些方法可能不够准确。因此，考虑整个协变量范围（例如描述时间窗口或剂量范围）的完整回归曲线，并基于两条曲线之间合适的距离度量（如两者间的最大绝对距离）进行检验。在此方面，一个关键假设是真实的基础回归模型已知，但实践中很少如此。然而，模型误设可能导致严重问题，如第一类错误膨胀或检验程序过于保守。本文提出一种解决该问题的方案，通过引入基于模型平均的等价检验的灵活扩展，以克服此假设，使检验在模型不确定性下适用。具体而言，我们引入基于平滑AIC权重的模型平均，并利用置信区间与假设检验的对偶性提出一种检验程序。通过模拟研究验证该方法的有效性，并利用毒理学基因表达数据的时间响应案例研究展示该方法的实际应用价值。