MAD (about median) vs. quantile-based alternatives for classical standard deviation, skewness, and kurtosis

In classical probability and statistics, one computes many measures of interest from mean and standard deviation. However, mean, and especially standard deviation, are overly sensitive to outliers. One way to address this sensitivity is by considering alternative metrics for deviation, skewness, and kurtosis using mean absolute deviations from the median (MAD). We show that the proposed measures can be computed in terms of the sub-means of the appropriate left and right sub-ranges. They can be interpreted in terms of average distances of values of these sub-ranges from their respective medians. We emphasize that these measures utilize only the first-order moment within each sub-range and, in addition, are invariant to translation or scaling. The obtained formulas are similar to the quantile measures of deviation, skewness, and kurtosis but involve computing sub-means as opposed to quantiles. While the classical skewness can be unbounded, both the MAD-based and quantile skewness always lies in the range [−1, 1]. In addition, while both the classical kurtosis and quantile-based kurtosis can be unbounded, the proposed MAD-based alternative for kurtosis lies in the range [0, 1]. We present a detailed comparison of MAD-based, quantile-based, and classical metrics for the six well-known theoretical distributions considered. We illustrate the practical utility of MAD-based metrics by considering the theoretical properties of the Pareto distribution with high concentrations of density in the upper tail, as might apply to the analysis of wealth and income. In summary, the proposed MAD-based alternatives provide a universal scale to compare deviation, skewness, and kurtosis across different distributions

A Decline in Renal Function is Associated With Loss of Bone Mass in Korean Postmenopausal Women With Mild Renal Dysfunction

This study was conducted to assess the relationship between estimated glomerular filtration rate (eGFR) and bone mineral density (BMD) in Korean postmenopausal women with mild renal dysfunction. A total of 328 postmenopausal women who underwent BMD measurement during health check-up was investigated. BMD was measured in lumbar spine (L1-L4), femoral neck, total proximal femur and femoral trochanteric areas by dual energy radiography absorptiometry and renal function was estimated by eGFR using Cockcroft-Gault equation. Of the 328 subjects, 317 (96.6%) had an eGFR ≥60 mL/min/1.73 m2. By using simple linear regression analysis, age, height, weight and eGFR were significantly associated with BMD for the 4 aforementioned anatomic sites, while serum levels of creatinine and blood urea nitrogen did not influence BMD. When multiple regression analyses were applied, age and body weight still had significant associations with BMD at 4 different anatomic sites (P < 0.001). A significant association of eGFR with BMD remained in the lumbar spine, femoral neck and proximal total femur (P < 0.05) but not in the trochanteric area (P = 0.300). Our study suggests that a decline of renal function is associated with lower BMD in the lumbar spine, femoral neck and total proximal femur areas in Korean menopausal women with mild renal dysfunction

Clinical and laboratory findings associated with severe scrub typhus

<p>Abstract</p> <p>Background</p> <p>Scrub typhus is a mite-borne bacterial infection of humans caused by <it>Orientia tsutsugamushi </it>that causes a generalized vasculitis that may involve the tissues of any organ system. The aim of this study was to identify factors associated to severe complications from scrub typhus.</p> <p>Methods</p> <p>We conducted this prospective, case-control study on scrub typhus patients who presented to the Department of Internal Medicine at Chosun University Hospital between September, 2004 and December, 2006. Cases were 89 scrub typhus patients with severe complications and controls were 119 scrub typhus patients without severe complications.</p> <p>Results</p> <p>There were significant differences in the absence of eschar, white blood cell (WBC) counts, hemoglobin, albumin, serum creatinine, fibrinogen, C-reactive protein (CRP), and active partial thromboplastin time (aPTT) between the two groups. Multivariate analysis demonstrated that only the following four factors were significantly associated with the severe complications of scrub typhus: (1) age ≥ 60 years (odd ratio [OR] = 3.13, <it>P </it>= 0.002, confidence interval [CI] = 1.53-6.41), (2) the absence of eschar (OR = 6.62, <it>P </it>= 0.03, CI = 1.22-35.8, (3) WBC counts > 10, 000/mm3 (OR = 3.6, <it>P </it>= 0.001, CI = 1.65-7.89), and (4) albumin ≤ 3.0 g/dL (OR = 5.01, <it>P </it>= 0.004, CI = 1.69-14.86).</p> <p>Conclusions</p> <p>Our results suggest that clinicians should be aware of the potential for complications, when scrub typhus patients are older (≥ 60 years), presents without eschar, or laboratory findings such as WBC counts > 10, 000/mm3, and serum albumin level ≤ 3.0 g/dL. Close observation and intensive care for scrub typhus patients with the potential for complications may prevent serious complications with subsequent reduction in its mortality rate.</p

Plasticity and rectangularity in survival curves

Living systems inevitably undergo a progressive deterioration of physiological function with age and an increase of vulnerability to disease and death. To maintain health and survival, living systems should optimize survival strategies with adaptive interactions among molecules, cells, organs, individuals, and environments, which arises plasticity in survival curves of living systems. In general, survival dynamics in a population is mathematically depicted by a survival rate, which monotonically changes from 1 to 0 with age. It would be then useful to find an adequate function to describe complicated survival dynamics. Here we describe a flexible survival function, derived from the stretched exponential function by adopting an age-dependent shaping exponent. We note that the exponent is associated with the fractal-like scaling in cumulative mortality rate. The survival function well depicts general features in survival curves; healthy populations exhibit plasticity and evolve towards rectangular-like survival curves, as examples in humans or laboratory animals