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Correlation coefficients are most popular in statistical practice for measuring pairwise variable associations. Compositional data, carrying only relative information, require a different treatment in correlation analysis. For identifying the association between two compositional parts in terms of their dominance with respect to the other parts in the composition, symmetric balances are constructed, which capture all relative information in the form of aggregated logratios of both compositional parts of interest. The resulting coordinates have the form of logratios of individual parts to a (weighted) “average representative” of the other parts, and thus, they clearly indicate how the respective parts dominate in the composition on average. The balances form orthonormal coordinates, and thus, the standard correlation measures relying on the Euclidean geometry can be used to measure the association. Simulation studies provide deeper insight into the proposed approach, and allow for comparisons with alternative measures. An application from geochemistry (Kola moss) indicates that correlations based on symmetric balances serve as a sensitive tool to reveal underlying geochemical processes.

Although Scandinavian flint is one of the most important materials used for prehistoric stone tool production in Northern and Central Europe, a conclusive method for securely differentiating between flint sources, geologically bound to northern European chalk formations, has never been achieved. The main problems with traditional approaches concern the oftentimes high similarities of SiO2 raw materials (i.e. chert and flint) on different scales due to similar genetic conditions and higher intra- than inter-source variation. Conventional chert and flint provenance studies chiefly concentrate on visual, petrographic or geochemical investigations. Hence, attempts to generate characteristic fingerprints of particular chert raw materials were in most cases unsatisfying. Here we show that the Multi Layered Chert Sourcing Approach (MLA) achieves a clear differentiation between primary sources of Scandinavian flint. The MLA combines visual comparative studies, stereo-microscopic analyses of microfossil inclusions, geochemical trace element analyses applying LA-ICP-MS (Laser Ablation Inductively Coupled Plasma Mass Spectrometry) and statistical analyses through CODA (Compositional Data Analysis). For archaeologists, provenance studies are the gateway to advance interpretations of economic behavior expressed in resource management strategies entailing the procurement, use and distribution of lithic raw materials. We demonstrate the relevance of our results for archaeological materials in a case study in which we were able to differentiate between Scandinavian flint sources and establish the provenance of historic ballast flint from a shipwreck found near Kristiansand close to the shore of southern Norway from a beach source in Northern Jutland, the Vigsø Bay.

Compositional data need a special treatment prior to correlation analysis. In this paper we argue why standard transformations for compositional data are not suitable for computing correlations, and why the use of raw or log-transformed data is neither meaningful. As a solution, a procedure based on balances is outlined, leading to sensible correlation measures. The construction of the balances is demonstrated using a real data example from geochemistry. It is shown that the considered correlation measures are invariant with respect to the choice of the binary partitions forming the balances. Robust counterparts to the classical, non-robust correlation measures are introduced and applied. By using appropriate graphical representations, it is shown how the resulting correlation coefficients can be interpreted.

Compositional count data are discrete vectors representing the numbers of outcomes falling into any of several mutually exclusive categories. Compositional techniques based on the log-ratio methodology are appropriate in those cases where the total sum of the vector elements is not of interest. Such compositional count data sets can contain zero values which are often the result of insufficiently large samples. That is, they refer to unobserved positive values that may have been observed with a larger number of trials or with a different sampling design. Because the log-ratio transformations require data with positive values, any statistical analysis of count compositions must be preceded by a proper replacement of the zeros. A Bayesian-multiplicative treatment has been proposed for addressing this count zero problem in several case studies. This treatment involves the Dirichlet prior distribution as the conjugate distribution of the multinomial distribution and a multiplicative modification of the non-zero values. Different parameterizations of the prior distribution provide different zero replacement results, whose coherence with the vector space structure of the simplex is stated. Their performance is evaluated from both the theoretical and the computational point of view.

Analysis of resting-state networks using fMRI usually ignores high-frequency fluctuations in the BOLD signal - be it because of low TR prohibiting the analysis of fluctuations with frequencies higher than 0.25 Hz (for a typical TR of 2 s), or because of the application of a bandpass filter (commonly restricting the signal to frequencies lower than 0.1 Hz). While the standard model of convolving neuronal activity with a hemodynamic response function suggests that the signal of interest in fMRI is characterized by slow fluctuation, it is in fact unclear whether the high-frequency dynamics of the signal consists of noise only. In this study, 10 subjects were scanned at 3 T during 6 min of rest using a multiband EPI sequence with a TR of 354 ms to critically sample fluctuations of up to 1.4 Hz. Preprocessed data were high-pass filtered to include only frequencies above 0.25 Hz, and voxelwise whole-brain temporal ICA (tICA) was used to identify consistent high-frequency signals. The resulting components include physiological background signal sources, most notably pulsation and heart-beat components, that can be specifically identified and localized with the method presented here. Perhaps more surprisingly, common resting-state networks like the default-mode network also emerge as separate tICA components. This means that high-frequency oscillations sampled with a rather T1-weighted contrast still contain specific information on these resting-state networks to consistently identify them, not consistent with the commonly held view that these networks operate on low-frequency fluctuations alone. Consequently, the use of bandpass filters in resting-state data analysis should be reconsidered, since this step eliminates potentially relevant information. Instead, more specific methods for the elimination of physiological background signals, for example by regression of physiological noise components, might prove to be viable alternatives.

In order to assess whole-brain resting-state fluctuations at a wide range of frequencies, resting-state fMRI data of 20 healthy subjects were acquired using a multiband EPI sequence with a low TR (354 ms) and compared to 20 resting-state datasets from standard, high-TR (1800 ms) EPI scans. The spatial distribution of fluctuations in various frequency ranges are analyzed along with the spectra of the time-series in voxels from different regions of interest. Functional connectivity specific to different frequency ranges (<0.1 Hz; 0.1-0.25 Hz; 0.25-0.75 Hz; 0.75-1.4 Hz) was computed for both the low-TR and (for the two lower-frequency ranges) the high-TR datasets using bandpass filters. In the low-TR data, cortical regions exhibited highest contribution of low-frequency fluctuations and the most marked low-frequency peak in the spectrum, while the time courses in subcortical grey matter regions as well as the insula were strongly contaminated by high-frequency signals. White matter and CSF regions had highest contribution of high-frequency fluctuations and a mostly flat power spectrum. In the high-TR data, the basic patterns of the low-TR data can be recognized, but the high-frequency proportions of the signal fluctuations are folded into the low frequency range, thus obfuscating the low-frequency dynamics. Regions with higher proportion of high-frequency oscillations in the low-TR data showed flatter power spectra in the high-TR data due to aliasing of the high-frequency signal components, leading to loss of specificity in the signal from these regions in high-TR data. Functional connectivity analyses showed that there are correlations between resting-state signal fluctuations of distant brain regions even at high frequencies, which can be measured using low-TR fMRI. On the other hand, in the high-TR data, loss of specificity of measured fluctuations leads to lower sensitivity in detecting functional connectivity. This underlines the advantages of low-TR EPI sequences for resting-state and potentially also task-related fMRI experiments.

Introduction We investigated whether governmental measures and lockdowns during the COVID‐19 pandemic had an impact on the number and histopathologic stages of melanoma. Methods The number and thickness (Breslow) of all diagnosed melanomas per day, month, or period at the ‘Institute for Pathology in the Centre’ in 2019 and 2020 were compared. For 2020, we defined four time periods: Period 1: 1 January–15 March; Period 2: 16 March–15 May (Lockdown 1); Period 3: 16 May–2 November; Period 4: 3 November–7 December (Lockdown 2). Results We found similar melanoma numbers in 2019 (577) and 2020 (608). The mean number of diagnoses per day during Lockdown 1 (Period 2) was significantly lower (0.87 melanomas/day; p = 0.005) when compared to the respective time periods in 2019 and to the other three periods in 2020 (Period 1: 1.65 melanomas/day, Period 3: 1.77 melanomas/day, and Period 4: 2.49 melanomas/day). Tumour thickness in July 2020 (1.9 mm) was significantly higher (p = 0.02) than in July 2019 (1.1 mm). Discussion The significant lower number of histopathologic diagnoses of melanoma during ‘Lockdown 1’ may be explained by postponed or missed patient consultations. This assumption is supported by the demonstration of a higher tumour thickness in July and August 2020, compared to 2019.

Microbiome data analysis often relies on the identification of a subset of potential biomarkers associated with a clinical outcome of interest. Robust ZeroSum regression, an elastic-net penalized compositional regression built on the least trimmed squares estimator, is a variable selection procedure capable to cope with the high dimensionality of these data, their compositional nature, and, at the same time, it guarantees robustness against the presence of outliers. The necessity of discovering “true” effects and to improve clinical research quality and reproducibility has motivated us to propose a two-step robust compositional knockoff filter procedure, which allows selecting the set of relevant biomarkers, among the many measured features having a nonzero effect on the response, controlling the expected fraction of false positives. We demonstrate the effectiveness of our proposal in an extensive simulation study, and illustrate its usefulness in an application to intestinal microbiome analysis.

Outlier detection based on the Mahalanobis distance (MD) requires an appropriate transformation in case of compositional data. For the family of logratio transformations (additive, centered and isometric logratio transformation) it is shown that the MDs based on classical estimates are invariant to these transformations, and that the MDs based on affine equivariant estimators of location and covariance are the same for additive and isometric logratio transformation. Moreover, for 3-dimensional compositions the data structure can be visualized by contour lines. In higher dimension the MDs of closed and opened data give an impression of the multivariate data behavior.