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Concept: Skewness


Despite the fact that 2015 was the international year of light, no mention was made of the fact that radiation contains entropy as well as energy, with different spectral distributions. Whereas the energy function has been vastly studied, the radiation entropy distribution has not been analysed at the same speed. The Mode of the energy distribution is well known -Wien’s law- and Planck’s law has been analytically integrated recently, but no similar advances have been made for the entropy. This paper focuses on the characterization of the entropy of radiation distribution from an statistical perspective, obtaining a Wien’s like law for the Mode and integrating the entropy for the Median and the Mean in polylogarithms, and calculating the Variance, Skewness and Kurtosis of the function. Once these features are known, the increasing importance of radiation entropy analysis is evidenced in three different interdisciplinary applications: defining and determining the second law Photosynthetically Active Radiation (PAR) region efficiency, measuring the entropy production in the Earth’s atmosphere, and showing how human vision evolution was driven by the entropy content in radiation.

Concepts: Energy, Mode, Median, Arithmetic mean, Mean, Standard deviation, Skewness, Statistical mechanics


Underwater noise from human activities appears to be rising, with ramifications for acoustically sensitive marine organisms and the functioning of marine ecosystems. Policymakers are beginning to address the risk of ecological impact, but are constrained by a lack of data on current and historic noise levels. Here, we present the first nationally coordinated effort to quantify underwater noise levels, in support of UK policy objectives under the EU Marine Strategy Framework Directive (MSFD). Field measurements were made during 2013-2014 at twelve sites around the UK. Median noise levels ranged from 81.5-95.5 dB re 1 μPa for one-third octave bands from 63-500 Hz. Noise exposure varied considerably, with little anthropogenic influence at the Celtic Sea site, to several North Sea sites with persistent vessel noise. Comparison of acoustic metrics found that the RMS level (conventionally used to represent the mean) was highly skewed by outliers, exceeding the 97(th) percentile at some frequencies. We conclude that environmental indicators of anthropogenic noise should instead use percentiles, to ensure statistical robustness. Power analysis indicated that at least three decades of continuous monitoring would be required to detect trends of similar magnitude to historic rises in noise levels observed in the Northeast Pacific.

Concepts: European Union, Median, Atlantic Ocean, United Kingdom, Europe, Arithmetic mean, Mean, Skewness


BACKGROUND: Excessive daytime sleepiness (EDS) is a common condition worldwide that has many negative effects on people who were afflicted with it, especially on their health-related quality of life (HRQOL). The Epworth Sleepiness Scale (ESS) is a commonly used method for evaluating EDS in English-speaking countries. This paper reported the prevalence of subjective EDS in China as assessed by the Mandarin version of the ESS; tested the scale’s response rate, reliability and validity; and investigated the relationship between ESS scores and HRQOL. METHODS: A population-based sample of 3600 residents was selected randomly in five cities in China. The demographic information was collected, subjective EDS was assessed by the Mandarin version of the ESS (ESS scores >10), and HRQOL was evaluated by the Mandarin version of the 36-item Short Form Health Survey (SF-36). RESULTS: The Mandarin version of ESS had very few missing responses, and the average response rate of its eight items was 97.92 %. The split-half reliability coefficient and Cronbach’s alpha coefficient were 0.81 and 0.80, respectively. One factor was identified by factor analysis with an eigenvalue of 2.78. The ESS scores showed positive skewness in the selected sample, with a median (Q1, Q3) of 6 (3, 0). 644 (22.16 %) respondents reported subjective EDS, and all of the scores of the eight dimensions of the SF-36 were negatively correlated with ESS scores. CONCLUSIONS: The Mandarin version of ESS is an acceptable, reliable, and valid tool for measuring EDS. In addition, subjective EDS is common in China, based on the ESS results, and impairs HRQOL.

Concepts: Psychometrics, Factor analysis, Reliability, Skewness, Cronbach's alpha, Epworth Sleepiness Scale, Excessive daytime sleepiness, Internal consistency


The efficacy of rituximab (RTX) as the sole therapy for preventing relapses of nephrotic syndrome (NS) is transient in most patients; therefore, the optimal therapy required for maintaining a successful response to a biological agent remains a challenge. We conducted a prospective study to compare the efficacy of cyclosporine (CsA) with that of mycophenolate mofetil (MMF) as maintenance therapy after a single infusion of RTX. Of 29 patients with persistent steroid-dependent NS despite the use of CsA and/or MMF, 13 without chronic nephrotoxicity continued CsA therapy, maintaining a 2-h post-dose CsA level of 400-500 ng/ml (CsA group). The remaining 16 were treated with MMF, maintaining a pre-dose level of 2-5 μg/ml of mycophenolic acid (MMF group). The median duration of CsA and MMF treatment was 18 and 19 months, respectively. Despite the mean number of relapses before RTX treatment being significantly lower in the MMF group than in the CsA group (2.3/year vs. 4.6/year, p < 0.01), treatment failure occurred more frequently in the MMF group (7/16) than in the CsA group (2/13). The rate of sustained remission was also significantly higher in the CsA group than in the MMF group (p < 0.05). Conclusion: In patients with severe steroid-dependent NS, CsA appears to be more effective than MMF for maintaining remission after a single infusion of RTX.

Concepts: Median, Arithmetic mean, Mean, Transplant rejection, Skewness, Immunosuppressants, Mycophenolic acid, Mycophenolate mofetil


Purpose To evaluate a radiomics model of Breast Imaging Reporting and Data System (BI-RADS) 4 and 5 breast lesions extracted from breast-tissue-optimized kurtosis magnetic resonance (MR) imaging for lesion characterization by using a sensitivity threshold similar to that of biopsy. Materials and Methods This institutional study included 222 women at two independent study sites (site 1: training set of 95 patients; mean age ± standard deviation, 58.6 years ± 6.6; 61 malignant and 34 benign lesions; site 2: independent test set of 127 patients; mean age, 58.2 years ± 6.8; 61 malignant and 66 benign lesions). All women presented with a finding suspicious for cancer at x-ray mammography (BI-RADS 4 or 5) and an indication for biopsy. Before biopsy, diffusion-weighted MR imaging (b values, 0-1500 sec/mm2) was performed by using 1.5-T imagers from different MR imaging vendors. Lesions were segmented and voxel-based kurtosis fitting adapted to account for fat signal contamination was performed. A radiomics feature model was developed by using a random forest regressor. The fixed model was tested on an independent test set. Conventional interpretations of MR imaging were also assessed for comparison. Results The radiomics feature model reduced false-positive results from 66 to 20 (specificity 70.0% [46 of 66]) at the predefined sensitivity of greater than 98.0% [60 of 61] in the independent test set, with BI-RADS 4a and 4b lesions benefiting from the analysis (specificity 74.0%, [37 of 50]; 60.0% [nine of 15]) and BI-RADS 5 lesions showing no added benefit. The model significantly improved specificity compared with the median apparent diffusion coefficient (P < .001) and apparent kurtosis coefficient (P = .02) alone. Conventional reading of dynamic contrast material-enhanced MR imaging provided sensitivity of 91.8% (56 of 61) and a specificity of 74.2% (49 of 66). Accounting for fat signal intensity during fitting significantly improved the area under the curve of the model (P = .001). Conclusion A radiomics model based on kurtosis diffusion-weighted imaging performed by using MR imaging machines from different vendors allowed for reliable differentiation between malignant and benign breast lesions in both a training and an independent test data set.©RSNA, 2018 Online supplemental material is available for this article.

Concepts: Cancer, Medical imaging, Magnetic resonance imaging, Diffusion MRI, Mean, Mammography, Standard deviation, Skewness


Characterization of hematomas is essential in scan reading, manual delineation, and designing automatic segmentation algorithms. Our purpose is to characterize the distribution of intraventricular (IVH) and intracerebral hematomas (ICH) in NCCT scans, study their relationship to gray matter (GM), and to introduce a new tool for quantitative hematoma delineation. We used 289 serial retrospective scans of 51 patients. Hematomas were manually delineated in a two-stage process. Hematoma contours generated in the first stage were quantified and enhanced in the second stage. Delineation was based on new quantitative rules and hematoma profiling, and assisted by a dedicated tool superimposing quantitative information on scans with 3D hematoma display. The tool provides: density maps (40-85HU), contrast maps (8/15HU), mean horizontal/vertical contrasts for hematoma contours, and hematoma contours below a specified mean contrast (8HU). White matter (WM) and GM were segmented automatically. IVH/ICH on serial NCCT is characterized by 59.0HU mean, 60.0HU median, 11.6HU standard deviation, 23.9HU mean contrast, -0.99HU/day slope, and -0.24 skewness (changing over time from negative to positive). Its 0.1(st)-99.9(th) percentile range corresponds to 25-88HU range. WM and GM are highly correlated (R (2)=0.88; p<10(-10)) whereas the GM-GS correlation is weak (R (2)=0.14; p<10(-10)). The intersection point of mean GM-hematoma density distributions is at 55.6±5.8HU with the corresponding GM/hematoma percentiles of 88(th)/40(th). Objective characterization of IVH/ICH and stating the rules quantitatively will aid raters to delineate hematomas more robustly and facilitate designing algorithms for automatic hematoma segmentation. Our two-stage process is general and potentially applicable to delineate other pathologies on various modalities more robustly and quantitatively.

Concepts: Percentile, Median, Mean, Standard deviation, Skewness, Quantitative research, Multistage rocket


Distributions of a total of 21 elements were monitored in significantly lead-zinc polluted area using moss species (Hypnum cupressiforme and Camptothecium lutescens) used interchangeably, covering a denser sampling network. Interspecies comparison was conducted using Box-Cox transformed values, due to their skewed distribution. The median concentrations of trace elements in the both mosses examined decreased in the following order: Fe>Mn>Zn>Pb>Cu>Ni∼Cr∼As>Co>Cd>Hg. For almost all analyzed elements, H. cupressiforme revealed higher bio-accumulative abilities. For arsenic contents was obtained ER-value in favor of C. lutescens. The ER for the element contents according to the distance from the pollution source in selected areas was significantly enriched for the anthropogenic introduced elements As, Cd, Cu, Pb and Zn. After Box-Cox transformation of the content values, TB was significantly different for As (4.82), Cd (3.84), Cu (2.95), Pb (4.38), and Zn (4.23). Multivariate factor analysis singled out four elemental associations: F1 (Al-Co-Cr-Fe-Li-Ni-V), F2 (Cd-Pb-Zn), F3 (Ca-Mg-Na-P) and F4 (Cu) with a total variance of 89%. Spatial distribution visualized the hazardously higher contents of “hot spots” of Cd > 1.30 mg/kg, Cu > 22 mg/kg, Pb > 130 mg/kg and Zn > 160 mg/kg. Therefore, main approach in moss biomonitoring should be based on data management of the element distribution by reducing the effect of extreme values (considering Box-Cox data transformation); the interspecies variation in sampling media does not deviate in relation to H. cupressiforme vs. C. lutescens.

Concepts: Median, Chemical element, Mean, Normal distribution, Standard deviation, Skewness, Moss, Mosses


Efforts to reduce healthcare costs have led to the development of metrics to identify unwarranted variation in care. Previous work assessing diagnostic tests is limited, despite their substantial contribution to expenditure. We explored C-reactive Protein (CRP) and Erythrocyte Sedimentation Rate (ESR) tests ordered across Oxfordshire NHS General Practices, and the proportion of tests that yielded an abnormal result, and identified practices that had a proportion of abnormal CRP and ESR results 3 standard deviations below the mean. We estimated the adjusted average proportion of abnormal CRP and ESR tests that yielded abnormal results from each practice, after adjusting for differences in practice populations. These proportions were plotted against the total CRP and ESR requests per practice. We constructed funnel plots to identify practices 3 standard deviations below the mean proportion of abnormal CRP and ESR tests. We analysed 143,745 CRP and 30,758 ESR requests from 69 practices. Twelve (17%) and 7 (10%) practices were more than 3 standard deviations below the mean for CRP and ESR testing respectively. Two practices (3%) were below the 99.8% limit for both CRP and ESR ordering. Variation in the proportion of tests with an abnormal result shows promise for auditing variation in care.

Concepts: Statistics, Red blood cell, Arithmetic mean, Mean, Standard deviation, Skewness, C-reactive protein, Erythrocyte sedimentation rate


Relative sea/land level changes are fundamental to people living in deltas. Net subsidence is complex and attributed to tectonics, compaction, sedimentation and anthropogenic causes. It can have severe impacts and needs to be quantified and where possible (for subsidence due to anthropogenic causes) avoided. For the highly populated Ganges-Brahmaputra-Meghna delta, a large range of net subsidence rates are described in the literature, yet the reasons behind this wide range of values are poorly understood. This paper documents and analyses rates of subsidence (for publications until 2014) and relates these findings to human influences (development). 205 point measurements of net subsidence were found, reported in 24 studies. Reported measurements were often repetitive in multiple journals, with some lacking detail as to precise location, cause and method, questioning reliability of the rate of subsidence. Rates differed by locality, methodology and period of measurement. Ten different measurement methods were recorded, with radio-carbon dating being the most common. Temporal and spatially, rates varied between -1.1mm/yr (i.e. uplift) and 43.8mm/yr. The overall mean reported rate was 5.6mm/yr, and the overall median 2.9mm/yr, with 7.3mm/yr representing one standard deviation. These rates were reduced if inaccurate or vague records were omitted. The highest rates were recorded in the Sylhet Plateau, Dhaka and Kolkata. Highest rates were recorded in the last 1000years, where the mean increased to 8.8mm/yr and a standard deviation of 7.5mm/yr. This could be partly due to shorter-term measurement records, or anthropogenic influence as multiple high rates are often found in urban settings. Continued development may cause rates to locally increase (e.g. due to groundwater abstraction and/or drainage). Improved monitoring is required over a wider area, to determine long-term trends, particularly as short-term records are highly variable. Focus in regions where wide spread development is occurring or is expected would be advantageous.

Concepts: Measurement, Median, Arithmetic mean, Absolute deviation, Mean, Standard deviation, Skewness, Cauchy distribution


Rigorous, informative meta-analyses rely on availability of appropriate summary statistics or individual participant data. For continuous outcomes, especially those with naturally skewed distributions, summary information on the mean or variability often goes unreported. While full reporting of original trial data is the ideal, we sought to identify methods for handling unreported mean or variability summary statistics in meta-analysis.

Concepts: Statistics, Data, Arithmetic mean, Mean, Standard deviation, Skewness