Sharp inequalities of Bienaymé–Chebyshev and Gauß type for possibly asymmetric intervals around the mean

Sharp upper bounds are proved for the probability that a standardized random variable takes on a value outside a possibly asymmetric interval around 0. Six classes of distributions for the random variable are considered, namely the general class of ‘distributions’, the class of ‘symmetric distributions’, of ‘concave distributions’, of ‘unimodal distributions’, of ‘unimodal distributions with coinciding mode and mean’, and of ‘symmetric unimodal distributions’. In this way, results by Gauß (Commentationes Societatis Regiae Scientiarum Gottingensis Recentiores 5:1–58, 1823), Bienaymé (C R Hebd Séance Acad Sci Paris 37:309–24, 1853), Bienaymé (C R Hebd Séance Acad Sci Paris 37:309–24, 1853), Chebyshev (Journal de mathématiques pures et appliqués (2) 12:177–184, 1867), and Cantelli (Atti del Congresso Internazionale dei Matematici 6:47–59, 1928) are generalized. For some of the known inequalities, such as the Gauß inequality, an alternative proof is given

A comparison of statistical methods for age-specific reference values of discrete scales

Age-specific reference values are important in medical science to evaluate the normal ranges of subjects and to help physicians signal potential disorders as early as possible. They are applied to many types of measurements, including discrete measures obtained from questionnaires and clinical tests. These discrete measures are typically skewed to the left and bounded by a maximum score of one (or 100%). This article investigates the performances of various statistical methods, including quantile regression, the Lambda-Mu-Sigma (LMS) method and its extensions, and the generalized additive models for location, scale, and shape with zero and one-inflated distributions implemented with either fractional polynomials or splines, for age-specific reference values on discrete measures. Their large-sample performances were investigated using Monte-Carlo simulations, and the consistency of splines and fractional polynomials age profiles with quantile regression had been demonstrated as well. The advantages and disadvantages of these methods were illustrated with data on the Infant Motor Profile, a test score on motor behavior in children of 3–18 months. We concluded that quantile regression with fractional polynomials approach is a robust and computationally efficient method for setting age-specific reference values for discrete measures.</p

Unique reproduction system of invasive ants avoids genetic bottlenecks

INTRODUCTION: Advanced glycation endproducts (AGEs) may be involved in the development of atherosclerosis, beyond diabetes and renal disease. Skin autofluorescence (AF) is a non-invasive marker for AGEs. We examined whether skin AF is increased in (subclinical) atherosclerosis and associated with the degree of atherosclerosis independent of diabetes and renal function. METHODS: A cross-sectional study of 223 patients referred for primary (n = 163) or secondary (n = 60) prevention between 2006 and 2012 was performed. Skin AF was measured using the AGE-Reader. Ultrasonography was used to assess plaques in carotid and femoral arteries and computed tomography for the calculation of the coronary artery calcium score (CACS; in primary prevention only). Primary prevention patients were divided into a group with subclinical atherosclerosis defined as >1 plaque or CACS>100 (n = 67; age 53 year [interquartile range 48-56]; 49% male) and without (controls; 96; 43 [38-51]; 55%). Secondary prevention were patients with peripheral arterial disease (60; 64 [58-70]; 73%). RESULTS: Skin AF was higher in subclinical and clinical atherosclerosis compared with controls (skin AF 2.11 [interquartile range 1.83-2.46] and 2.71 [2.15-3.27] vs. 1.87 [1.68-2.12] respectively; P = 0.005 and <0.001). In a multivariate analysis, the association of skin AF with the atherosclerosis categories was independent of age, sex, diabetes, presence of the metabolic syndrome, Framingham Risk Score, and renal function. Skin AF correlated with most cardiovascular risk factors, Framingham risk score, and IMT and CACS. CONCLUSIONS: Skin AF is increased in documented subclinical and clinical atherosclerosis, independent of known risk factors such as diabetes and renal disease. These data suggest that AGEs may be associated with the burden of atherosclerosis and warrant a prospective study to investigate its clinical usability as a risk assessment tool for primary prevention

Functional disability and social participation restriction associated with chronic conditions in middle-aged and older adults

Abstract : Background. We examine the population impact on functional disability and social participation of physical and mental chronic conditions individually and in combination. Methods. Cross-sectional, population-based data from community-dwelling people aged 45 years and over living in the 10 Canadian provinces in 2008–2009 were used to estimate the population attributable risk (PAR) for functional disability in basic (ADL) and instrumental (IADL) activities of daily living and social participation restrictions for individual and combinations of chronic conditions, stratified by age and gender, after adjusting for confounding variables. Results. Five chronic conditions (arthritis, depression, diabetes, heart disease and eye disease) made the largest contributions to ADL-related and IADL-related functional disability and social participation restrictions, with variation in magnitude and ranking by age and gender. While arthritis was consistently associated with higher PARs across gender and most age groups, depression, alone and in combination with the physical chronic conditions, was associated with ADL and IADL disability as well as social participation restrictions in the younger age groups, especially among women. Compared to women, the combinations of conditions associated with higher PARs in men more often included heart disease and diabetes. Conclusions. Our findings suggest that in community dwelling middle-aged and older adults, the impact of combinations of mental and physical chronic conditions on functional disability and social participation restriction is substantial and differed by gender and age. Recognising the differences in the drivers of PAR by gender and age group will ultimately increase the efficiency of clinical and public health interventions

Accuracy of screening women at familial risk of breast cancer without a known gene mutation:individual patient data meta-analysis

Introduction Women with a strong family history of breast cancer (BC) and without a known gene mutation have an increased risk of developing BC. We aimed to investigate the accuracy of screening using annual mammography with or without magnetic resonance imaging (MRI) for these women outside the general population screening program. Methods An individual patient data (IPD) meta-analysis was conducted using IPD from six prospective screening trials that had included women at increased risk for BC: only women with a strong familial risk for BC and without a known gene mutation were included in this analysis. A generalised linear mixed model was applied to estimate and compare screening accuracy (sensitivity, specificity and predictive values) for annual mammography with or without MRI. Results There were 2226 women (median age: 41 years, interquartile range 35–47) with 7478 woman-years of follow-up, with a BC rate of 12 (95% confidence interval 9.3–14) in 1000 woman-years. Mammography screening had a sensitivity of 55% (standard error of mean [SE] 7.0) and a specificity of 94% (SE 1.3). Screening with MRI alone had a sensitivity of 89% (SE 4.6) and a specificity of 83% (SE 2.8). Adding MRI to mammography increased sensitivity to 98% (SE 1.8, P &lt; 0.01 compared to mammography alone) but lowered specificity to 79% (SE 2.7, P &lt; 0.01 compared with mammography alone). Conclusion In this population of women with strong familial BC risk but without a known gene mutation, in whom BC incidence was high both before and after age 50, adding MRI to mammography substantially increased screening sensitivity but also decreased its specificity.</p

Sex dependent risk factors for mortality after myocardial infarction : individual patient data meta-analysis

Background. Although a number of risk factors are known to predict mortality within the first years after myocardial infarction, little is known about interactions between risk factors, whereas these could contribute to accurate differentiation of patients with higher and lower risk for mortality. This study explored the effect of interactions of risk factors on all-cause mortality in patients with myocardial infarction based on individual patient data meta-analysis. Methods. Prospective data for 10,512 patients hospitalized for myocardial infarction were derived from 16 observational studies (MINDMAPS). Baseline measures included a broad set of risk factors for mortality such as age, sex, heart failure, diabetes, depression, and smoking. All two-way and three-way interactions of these risk factors were included in Lasso regression analyses to predict time-to-event related all-cause mortality. The effect of selected interactions was investigated with multilevel Cox regression models. Results. Lasso regression selected five two-way interactions, of which four included sex. The addition of these interactions to multilevel Cox models suggested differential risk patterns for males and females. Younger women (ag

Chip-Firing and Rotor-Routing on Directed Graphs

We give a rigorous and self-contained survey of the abelian sandpile model and rotor-router model on finite directed graphs, highlighting the connections between them. We present several intriguing open problems.Comment: 34 pages, 11 figures. v2 has additional references, v3 corrects figure 9, v4 corrects several typo