Improved family-wise error rate control in multiple equivalence testing.

Equivalence testing is an important component of safety assessments, used for example by the European Food Safety Authority, to allow new food or feed products on the market. The aim of such tests is to demonstrate equivalence of characteristics of test and reference crops. Equivalence tests are typically univariate and applied to each measured analyte (characteristic) separately without multiplicity correction. This increases the probability of making false claims of equivalence (type I errors) when evaluating multiple analytes simultaneously. To solve this problem, familywise error rate (FWER) control using Hochberg's method has been proposed. This paper demonstrates that, in the context of equivalence testing, other FWER-controlling methods are more powerful than Hochberg's. Particularly, it is shown that Hommel's method is guaranteed to perform at least as well as Hochberg's and that an "adaptive" version of Bonferroni's method, which uses an estimator of the proportion of non-equivalent characteristics, often substantially outperforms Hommel's method. Adaptive Bonferroni takes better advantage of the particular context of food safety where a large proportion of true equivalences is expected, a situation where other methods are particularly conservative. The different methods are illustrated by their application to two compositional datasets and further assessed and compared using simulated data.

Permutation-based true discovery proportions for functional magnetic resonance imaging cluster analysis.

We propose a permutation-based method for testing a large collection of hypotheses simultaneously. Our method provides lower bounds for the number of true discoveries in any selected subset of hypotheses. These bounds are simultaneously valid with high confidence. The methodology is particularly useful in functional Magnetic Resonance Imaging cluster analysis, where it provides a confidence statement on the percentage of truly activated voxels within clusters of voxels, avoiding the well-known spatial specificity paradox. We offer a user-friendly tool to estimate the percentage of true discoveries for each cluster while controlling the family-wise error rate for multiple testing and taking into account that the cluster was chosen in a data-driven way. The method adapts to the spatial correlation structure that characterizes functional Magnetic Resonance Imaging data, gaining power over parametric approaches.

On optimal two-stage testing of multiple mediators.

Mediation analysis in high-dimensional settings often involves identifying potential mediators among a large number of measured variables. For this purpose, a two-step familywise error rate procedure called ScreenMin has been recently proposed. In ScreenMin, variables are first screened and only those that pass the screening are tested. The proposed data-independent threshold for selection has been shown to guarantee asymptotic familywise error rate. In this work, we investigate the impact of the threshold on the finite-sample familywise error rate. We derive a power maximizing threshold and show that it is well approximated by an adaptive threshold of Wang et al. (2016, arXiv preprint arXiv:1610.03330). We illustrate the investigated procedures on a case-control study examining the effect of fish intake on the risk of colorectal adenoma. We also apply our procedure in the context of replicability analysis to identify single nucleotide polymorphisms (SNP) associated with crop yield in two distinct environments.

Cross-sectional serum metabolomic study of multiple forms of muscular dystrophy.

Muscular dystrophies are characterized by a progressive loss of muscle tissue and/or muscle function. While metabolic alterations have been described in patients'-derived muscle biopsies, non-invasive readouts able to describe these alterations are needed in order to objectively monitor muscle condition and response to treatment targeting metabolic abnormalities. We used a metabolomic approach to study metabolites concentration in serum of patients affected by multiple forms of muscular dystrophy such as Duchenne and Becker muscular dystrophies, limb-girdle muscular dystrophies type 2A and 2B, myotonic dystrophy type 1 and facioscapulohumeral muscular dystrophy. We show that 15 metabolites involved in energy production, amino acid metabolism, testosterone metabolism and response to treatment with glucocorticoids were differentially expressed between healthy controls and Duchenne patients. Five metabolites were also able to discriminate other forms of muscular dystrophy. In particular, creatinine and the creatine/creatinine ratio were significantly associated with Duchenne patients performance as assessed by the 6-minute walk test and north star ambulatory assessment. The obtained results provide evidence that metabolomics analysis of serum samples can provide useful information regarding muscle condition and response to treatment, such as to glucocorticoids treatment.

Exact testing with random permutations.

When permutation methods are used in practice, often a limited number of random permutations are used to decrease the computational burden. However, most theoretical literature assumes that the whole permutation group is used, and methods based on random permutations tend to be seen as approximate. There exists a very limited amount of literature on exact testing with random permutations, and only recently a thorough proof of exactness was given. In this paper, we provide an alternative proof, viewing the test as a "conditional Monte Carlo test" as it has been called in the literature. We also provide extensions of the result. Importantly, our results can be used to prove properties of various multiple testing procedures based on random permutations.