Statistical tests in medical research: traditional methods vs. multivariate npc permutation tests

Within medical research, a useful statistical tool is based on hypotheses testing in terms of the so-called null, that is the treatment has no effect, and alternative hypotheses, that is the treatment has some effects. By controlling the risks of wrong decisions, empirical data are used in order to possibly reject the null hypotheses in favour of the alternative, so that demonstrating the efficacy of a treatment of interest. The multivariate permutation tests, based on the nonparametric combination -NPC method, provide an innovative, robust and effective hypotheses testing solution to many real problems that are commonly encountered in medical research when multiple endpoints are observed. This paper discusses the various approaches to hypothesis testing and the main advantages of NPC tests, which consist in the fact that they require much less stringent assumptions than traditional statistical tests. Moreover, the related results may be extended to the reference population even in case of selectionbias, that is non-random sampling. In this work, we review and discuss some basic testing procedures along with the theoretical and practical relevance of NPC tests showing their effectiveness in medical research. Within the non-parametric methods, NPC tests represent the current " frontier" of statistical research, but already widely available in the practice of analysis of clinical data.