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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., Comment: 20 pages, 6 figures

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., Comment: 20 pages, 5 figures

Accurate control of autonomous marine robots still poses challenges due to the complex dynamics of the environment. In this paper, we propose a Deep Reinforcement Learning (DRL) approach to train a controller for autonomous surface vessel (ASV) trajectory tracking and compare its performance with an advanced nonlinear model predictive controller (NMPC) in real environments. Taking into account environmental disturbances (e.g., wind, waves, and currents), noisy measurements, and non-ideal actuators presented in the physical ASV, several effective reward functions for DRL tracking control policies are carefully designed. The control policies were trained in a simulation environment with diverse tracking trajectories and disturbances. The performance of the DRL controller has been verified and compared with the NMPC in both simulations with model-based environmental disturbances and in natural waters. Simulations show that the DRL controller has 53.33% lower tracking error than that of NMPC. Experimental results further show that, compared to NMPC, the DRL controller has 35.51% lower tracking error, indicating that DRL controllers offer better disturbance rejection in river environments than NMPC., Comment: ICRA 2023