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In multivariate clinical trials, a key research endpoint is ascertaining whether a candidate treatment is more efficacious than an established alternative. This global endpoint is clearly of high practical value for studies, such as those arising from neuroimaging, where the outcome dimensions are not only numerous but they are also highly correlated and the available sample sizes are typically small. In this paper, we develop a two-stage procedure testing the null hypothesis of global equivalence between treatments effects and demonstrate its application to analysing phase II neuroimaging trials. Prior information such as suitable statistics of historical data or suitably elicited expert clinical opinions are combined with data collected from the first stage of the trial to learn a set of optimal weights. We apply these weights to the outcome dimensions of the second-stage responses to form the linear combination z and t tests statistics while controlling the test's false positive rate. We show that the proposed tests hold desirable asymptotic properties and characterise their power functions under wide conditions. In particular, by comparing the power of the proposed tests with that of Hotelling's T(2), we demonstrate their advantages when sample sizes are close to the dimension of the multivariate outcome. We apply our methods to fMRI studies, where we find that, for sufficiently precise first stage estimates of the treatment effect, standard single-stage testing procedures are outperformed.

Original publication




Journal article


Statistics in medicine

Publication Date





253 - 268


Department of Statistics, University of Warwick, Coventry, UK.


Brain, Humans, Magnetic Resonance Imaging, Multivariate Analysis, Sample Size, Research Design, Clinical Trials as Topic, Neuroimaging