Today, permutation tests represent a powerful and increasingly widespread tool of statistical inference for hypothesis-testing problems. To the best of our knowledge, a review of the application of permutation tests for complex data in practical data analysis for hypothesis testing is missing. In particular, it is essential to review the application of permutation tests in two-sample or multi-sample problems and in regression analysis. The aim of this paper is to consider the main scientific contributions on the subject of permutation methods for hypothesis testing in the mentioned fields. Notes on their use to address the problem of missing data and, in particular, right-censored data, will also be included. This review also tries to highlight the limits and advantages of the works cited with a critical eye and also to provide practical indications to researchers and practitioners who need to identify flexible and distribution-free solutions for the most disparate hypothesis-testing problems.

Adenoviral and mRNA vaccines encoding the viral spike (S) protein have been deployed globally to contain severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Older individuals are particularly vulnerable to severe infection, probably reflecting age-related changes in the immune system, which can also compromise vaccine efficacy. It is nonetheless unclear to what extent different vaccine platforms are impacted by immunosenescence. Here, we evaluated S protein-specific immune responses elicited by vaccination with two doses of BNT162b2 or ChAdOx1-S and subsequently boosted with a single dose of BNT162b2 or mRNA-1273, comparing age-stratified participants with no evidence of previous infection with SARS-CoV-2. We found that aging profoundly compromised S protein-specific IgG titers and further limited S protein-specific CD4⁺ and CD8⁺ T cell immunity as a probable function of progressive erosion of the naive lymphocyte pool in individuals vaccinated initially with BNT162b2. Our results demonstrate that primary vaccination with ChAdOx1-S and subsequent boosting with BNT162b2 or mRNA-1273 promotes sustained immunological memory in older adults and potentially confers optimal protection against coronavirus disease 2019.

Amongst the several consequences of the COVID-19 pandemic, we should include psychological effects on the population. The mental health consequences of lockdown are affected by several factors. The most important are: the duration of the social isolation period, the characteristics of the living space, the number of online (virtual) and offline (physical) contacts and perceived contacts’ closeness, individual characteristics, and the spread of infection in the geographical area of residence. In this paper, we investigate the possible effects of environmental, social and individual characteristics (predictors) on mental health (response) during the COVID-19 lockdown period. The relationship between mental health and predictors can be studied with a multivariate linear regression model, because “mental health” is a multidimensional concept. This work provides a contribution to the debate about the factors affecting mental health in the period of the COVID-19 lockdown, with the application of an innovative approach based on a multivariate regression analysis and a combined permutation test on data collected in a survey conducted in Italy in 2020.

In many application problems, when dealing with comparisons between two or more groups, the classical parametric inferential statistical methods are used, although in real problems the quite stringent assumptions required by such methods are rarely satisfied. In particular a parametric approach to the test on ordering of C > 2 populations is very difficult. In order to tackle this problem two alternative methods are proposed in the present paper. Both the methods consist in permutation combination based tests: the first is supposed to be more powerful and it is suitable when the main goal of the study is related to the global ordering of the populations; the second is useful when the interest is in the pairwise comparisons between the populations.

In this article the problem of comparing distributional heterogeneities for categorical variables is addressed. Specifically, the one-sided testing problem for heterogeneity comparisons is considered. For such a problem a bootstrap method is proposed and compared with a permutation method already present in literature. The power behavior of the two methods is compared through a Monte Carlo simulation study. The results of two real applications are shown.