Eleonora Carrozzo

Union---intersection permutation solution for two-sample equivalence testing

One of the well-known problems with testing for sharp null hypotheses against two-sided alternatives is that, when sample sizes diverge, every consistent test rejects the null with a probability converging to one, even when it is true. This kind of problem emerges in practically all applications of traditional two-sided tests. The main purpose of the present paper is to overcome this very intriguing impasse by considering a general solution to the problem of testing for an equivalence null interval against a two one-sided alternative. Our goal is to go beyond the limitations of likelihood-based methods by working in a nonparametric permutation framework. This solution requires the nonparameteric Combination of dependent permutation tests, which is the methodological tool that achieves Roy’s Union–intersection principle. To obtain practical solutions, the related algorithm is presented. To appreciate its effectiveness for practical purposes, a simple example and some simulation results are also presented. In addition, for every pair of consistent partial test statistics it is proved that, if sample sizes diverge, when the effect lies in the open equivalence interval, the Rejection probability (RP) converges to zero. Analogously, if the effect lies outside that interval, the RP converges to one.

Clinical implication of tumor-associated and immunological parameters in melanoma patients treated with ipilimumab

ABSTRACT Ipilimumab, the first immune-checkpoint inhibitor extending overall survival (OS) in metastatic melanoma patients, has a survival benefit only in a proportion of patients and the development of reliable predictive biomarkers is still an unmet need. To meet this request, we used a multivariate statistical approach to test whether myeloid-derived suppressor cells (MDSC) or other tumor-associated and immunological parameters may serve as predictive or prognostic biomarkers in melanoma patients receiving ipilimumab. By using a standardized approach to determine the circulating levels of four MDSC subsets, we observed a significant expansion of three MDSC subsets at baseline, as compared to controls and, upon treatment, that high levels of CD14+/IL4Rα+ MDSCs were an independent prognostic factor of reduced OS. On the contrary, longer OS was associated to low levels of the proinflammatory proteins IL-6 and CRP and tumor-associated factors S100B and LDH both at baseline and after treatment. Increasing number of total T cells and especially of PD-1+/CD4+ T cells were associated with better prognosis, and upregulation of PD-1+ expression on CD4+ T cells upon treatment was associated with lower toxicity. As several parameters were associated to OS, we included these factors in a multivariate survival model, and we identified IL-6 and ECOG PS as independent biomarkers associated with improved OS, whereas high levels of LDH and CD14+/IL4Rα+ MDSCs were negative independent markers of reduced OS.

Generating and Comparing Multivariate Ordinal Variables by Means of Permutation Tests

In this paper we introduce a nonparametric approach based on permutation tests and nonparametric combination methodology (NPC) for testing for correlation in presence of multivariate categorical variables. After an overview of permutation inference and the NPC methodology, we discuss the nonparametric procedure and we show a simulation-based comparative study. In particular, we deal with simulations from multivariate ordinal random variables, in order to show the performance in terms of power when the assumption of normality is not satisfied. In this regard, we consider also a new proposal for generating samples from multivariate ordinal data.

Testing for Equivalence: An Intersection-Union Permutation Solution

ABSTRACT The notion of testing for equivalence of two treatments is widely used in clinical trials, pharmaceutical experiments, bioequivalence, and quality control. It is essentially approached within the intersection-union (IU) principle. According to this principle, the null hypothesis is stated as the set of effects lying outside a suitably established interval and the alternative as the set of effects lying inside that interval. The solutions provided in the literature are mostly based on likelihood techniques, which in turn are rather difficult to handle, except for cases lying within the regular exponential family and the invariance principle. The main goal of the present article is to go beyond most of the limitations of likelihood-based methods, that is, to work in a nonparametric setting within the permutation frame. To obtain practical solutions, a new IU permutation test is presented and discussed. A simple simulation study for evaluating its main properties, and three application examples are also presented.

Ranking Multivariate Populations

The need to define an appropriate ranking of several populations of interest, i.e. processes, products, and so on is very common within many areas of applied research such as Food Science, Chemistry, Engineering, Biomedicine, etc.

Customer Satisfaction Heterogeneity

The measurement of the customer satisfaction concerns the gap between the customer expectations about the product or service and the perceptions of the customer after the consumption or use. In other words, the customer satisfaction is closely related to the concept of “perceived quality”. According to the definition of Montgomery [24], it depends on how much the products or services meet the requirements of the consumers/users and it is directly connected to the homogeneity of the performance of the production process or service provision process.

The CUB Models

The CUB model [12], where CUB stands for Combination of a discrete Uniform and a shifted Binomial distributions assumes the involvement of two latent variables during an evaluation process, that have been called feeling and uncertainty. In order to justify the names for latent variables, consider the way you choose an evaluation grade from a set of 9. The final choice reflects your feeling about the evaluated item, your past experience, your knowledge about it, and so on. On the other hand, there are some aspects concern with a basic uncertainty about the evaluated item, for example you are asked to deal with it for the first time and you don’t know what grade to choose, maybe the task is too difficult or the task is annoying you. These two main components are supposed to move your final choice and they are supposed to follow respectively a shifted Binomial distribution and a Uniform distribution [12, 18].

Composite Indicators and Satisfaction Profiles

Evaluating the satisfaction about public services, organizations or products is very important in order to have a measure of their efficiency and effectiveness.

Analyzing Survey Data Using Multivariate Rank-Based Inference

Data from customer satisfaction surveys are multivariate—there are several questions resulting in as many endpoints. Furthermore, survey data typically don’t fit into simple parametric models. Indeed, the endpoints or response variables may be measured on different types of scales (metric, ordinal, binary). For these two reasons, one requires multivariate inference methods, and specifically methods that can deal with a mix of response variable types. Additionally, it would be advantageous if the procedures also performed well for small to moderate numbers of respondents, as not every survey can afford to obtain responses from hundreds of participants.

A multivariate extension of union—intersection permutation solution for two-sample testing

There are mainly two approaches to compare effects of two treatments: following the intersection–union principle (IU) or following the union–intersection principle (UI). The two approaches substantially differ by the role stated from the null and alternative hypotheses, which are mirror inverted. In particular, the IU principle considers as alternative hypothesis that the effect of a new treatment lies within a given interval around that of the comparative treatment, whereas the UI principle considers as alternative hypothesis that this effect lies outside that interval. Pesarin et al. recently discussed these two solutions and proposed a permutation approach based on the union-intersection framework.Often in pharmaceutical experiments it happens that more than one variable have to be simultaneously considered, in order to assess dissimilarity of two treatments. Generally this kind of problem is difficult to face outside the nonparametric framework, particularly due to the complex dependency structure among several variables and consequent related partial tests. Thus, the purpose of this article is to extend the existing UI-permutation solution toward a general multidimensional setting. In order to explain the performance and the applicability of the proposed method, a simulation study and application example are also shown.