Relative efficiency of unequal versus equal cluster sizes in cluster randomized trials using generalized estimating equation models

There is growing interest in conducting cluster randomized trials (CRTs). For simplicity in sample size calculation, the cluster sizes are assumed to be identical across all clusters. However, equal cluster sizes are not guaranteed in practice. Therefore, the relative efficiency (RE) of unequal versus equal cluster sizes has been investigated when testing the treatment effect. One of the most important approaches to analyze a set of correlated data is the generalized estimating equation (GEE) proposed by Liang and Zeger, in which the “working correlation structure” is introduced and the association pattern depends on a vector of association parameters denoted by ρ. In this paper, we utilize GEE models to test the treatment effect in a two‐group comparison for continuous, binary, or count data in CRTs. The variances of the estimator of the treatment effect are derived for the different types of outcome. RE is defined as the ratio of variance of the estimator of the treatment effect for equal to unequal cluster sizes. We discuss a commonly used structure in CRTs—exchangeable, and derive the simpler formula of RE with continuous, binary, and count outcomes. Finally, REs are investigated for several scenarios of cluster size distributions through simulation studies. We propose an adjusted sample size due to efficiency loss. Additionally, we also propose an optimal sample size estimation based on the GEE models under a fixed budget for known and unknown association parameter (ρ) in the working correlation structure within the cluster.     

A Comparison of Bone Mineral Density and Its Predictors in HIV-Infected and HIV-Uninfected Older Men

ObjectiveBone health in older individuals with HIV infection has not been well studied. This study aimed to compare bone mineral density (BMD), trabecular bone score (TBS), and bone markers between HIV-infected men and age- and body mass index (BMI)-matched HIV-uninfected men aged ≥60 years. We investigated the associations of risk factors related to fracture with BMD, TBS, and bone markers in HIV-infected men.MethodsThis cross-sectional study included 45 HIV-infected men receiving antiretroviral therapy and 42 HIV-uninfected men. Medical history, BMD and TBS measurements, and laboratory tests related to bone health were assessed in all the participants. HIV-related factors known to be associated with bone loss were assessed in the HIV-infected men.ResultsThe mean BMD, TBS, and osteopenia or osteoporosis prevalence were similar among the cases and controls. The HIV-infected men had significantly higher mean N-terminal propeptide of type 1 procollagen and C-terminal cross-linking telopeptide of type I collagen levels. Stepwise multiple linear regression analysis demonstrated that low BMI (lumbar spine, P = .015; femoral neck, P = .018; and total hip, P = .005), high C-terminal cross-linking telopeptide of type I collagen concentration (total hip, P = .042; and TBS, P = .010), and low vitamin D supplementation (TBS, P = .035) were independently associated with low BMD and TBS.ConclusionIn older HIV-infected men with a low fracture risk, the mean BMD and TBS were similar to those of the age- and BMI-matched controls. The mean bone marker levels were higher in the HIV group. Traditional risk factors for fracture, including low BMI, high C-terminal cross-linking telopeptide of type I collagen level, and low vitamin D supplementation, were significant predictors of low BMD and TBS.     

Evolutionary rescue by beneficial mutations in environments that change in space and time

A factor that may limit the ability of many populations to adapt to changing conditions is the rate at which beneficial mutations can become established. We study the probability that mutations become established in changing environments by extending the classic theory for branching processes. When environments change in time, under quite general conditions, the establishment probability is approximately twice the ‘effective selection coefficient’, whose value is an average that gives most weight to a mutant''s fitness in the generations immediately after it appears. When fitness varies along a gradient in a continuous habitat, increased dispersal generally decreases the chance a mutation establishes because mutations move out of areas where they are most adapted. When there is a patch of favourable habitat that moves in time, there is a maximum speed of movement above which mutations cannot become established, regardless of when and where they first appear. This critical speed limit, which is proportional to the mutation''s maximum selective advantage, represents an absolute constraint on the potential of locally adapted mutations to contribute to evolutionary rescue.     

Infrared spectroscopy of proteins

This review discusses the application of infrared spectroscopy to the study of proteins. The focus is on the mid-infrared spectral region and the study of protein reactions by reaction-induced infrared difference spectroscopy.     

Evaluation of integrating topographic wetness index with backscattering coefficient of TerraSAR-X image for soil moisture estimation in a mountainous region

The estimation of soil moisture by using the backscattering coefficient of radar in a mountainous region is a challenging task due to the complex topography, which impacts the distribution of soil moisture and changes the backscattering coefficient. Complicated terrain can disturb empirical moisture estimation models, thereby, the resulting estimates of soil moisture are very unlikely reliable. This article proposed an innovative way of integration of the topographic wetness index (TWI) and the backscattering coefficient of soil obtained from the TerraSAR-X image, which improves the accuracy of measurement of the soil moisture. The standard estimation error and the coefficient of determination from the model were used to evaluate the performance of TWI. Our results show that the standard estimation error was decreased from: (1) 4.0% to 3.3% cm³ cm⁻³ at a depth of 5 cm and (2) 4.5% to 3.9% cm³ cm⁻³ at a depth of 10 cm. The most reliable estimation was observed at a depth of 5 cm, when it was compared with those of 0–5 cm, 10 cm and 15 cm. The TWI from the digital elevation model (DEM) is useful as a constraint condition for modeling work. This article concludes that the integration of the backscattering coefficient of soil with TWI can significantly reduce the uncertainty in the estimation of soil moisture in a mountainous region.     

Tungsten-based material as promising new lead-free gamma radiation shielding material in nuclear medicine

PurposeThe main objective of this study was to evaluate the efficacy of tungsten carbide as new lead-free radiation shielding material in nuclear medicine by evaluating the attenuation properties.Materials and methodsThe elemental composition of tungsten carbide was analysed using Field-Emission Scanning Electron Microscopy (FESEM) with energy dispersive X-ray (EDX). The purity of tungsten carbide was 99.9%, APS: 40–50 µm. Three discs of tungsten carbide was fabricated with thickness of 0.1 cm, 0.5 cm and 1.0 cm. Three lead discs with similar thickness were used to compare the attenuation properties with tungsten carbide discs. Energy calibration of gamma spectroscopy was performed by using ¹²³I, ¹³³Ba, ¹⁵²Eu, and ¹³⁷Cs. Gamma radiation from these sources were irradiated on both materials at energies ranging from 0.160 MeV to 0.779 MeV. The experimental attenuation coefficients of lead and tungsten carbide were compared with theoretical attenuation coefficients of both materials from NIST database. The half value layer and mean free path of both materials were also evaluated in this study.ResultsThis study found that the peaks obtained from gamma spectroscopy have linear relationship with all energies used in this study. The relative differences between the measured and theoretical mass attenuation coefficients are within 0.19–5.11% for both materials. Tungsten carbide has low half value layer and mean free path compared to lead for all thickness at different energies.ConclusionThis study shows that tungsten carbide has high potential to replace lead as new lead-free radiation shielding material in nuclear medicine.     

An Algorithm for Calculation of n-Dimensional Nonlinear Dependencies – Behaviour Tests on Rats

The evaluation of the data obtained during the behaviour tests always leads to the problem of multiple correlation, very often with non-linear dependencies on the target. All mathematical and statistical procedures that have been used so far are based on the assumption of an equation for the desired correlation for which parameters and related statistical equivalents are determined eventually. The MODAK system applied here (MODAK = algorithms of modelling for the calculation of multi-dimensional non-linear mathematical models) breaks down a complex correlation into individual dependencies in a mathematical and statistical way and selects suitable equations for each of them independently and determines the corresponding parameters. The numerical example evaluates data of behaviour tests on rats. First results obtained on the correlations of various behaviour tests indicate both the possibility of selecting suitable tests independent of each other and a better interpretation of the observed patterns of behaviour taking into account the interrelations between the tests. In addition, MODAK is a method which can be applied as a matter of course in a general way to all cases which call for the reduction and analysis of data occurring in process and system analysis and in the evaluation of test results requiring statistical modelling. So far, MODAK applications range from engineering sciences to medicine.     

Analysis of genetic changes in radiated and non-radiated bulk oat (Avena sativa L.) populations

Summary In both radiated and non-radiated oat populations inbreeding coefficients increased more slowly than was expected on the assumption of full selfing and equal selective values for homozygotes and heterozygotes. Assuming 1% outcrossing for oats and a selective value of 1.0 for the mean, the heterozygotes for two loci governing crown rust reaction have an advantage of 50% over the homozygotes. This study supports previous observations that the heterozygote often has a decided advantage in predominantly self-pollinated crops.     

Partition of lindane in synthetic and native membranes

Partition coefficients of the insecticide γ-1,2,3,4,5,6-hexachlorocyclohexane (trivially, lindane) were determined in model and native membranes. Partition in egg phosphatidylcholine bilayers decreases linearly with temperature, over a range (10–40°C) at which the lipid is in the liquid-crystalline state. Addition of 50 mol% cholesterol dramatically decreases partition (2100 falls to 100, at 10°C) and abolishes the temperature dependence. First-order phase transitions of dimyristoyl-, dipalmitoyl- and distearoylphosphatidylcholines (DMPC, DPPC and DSPC) are accompanied by a sharp increase in lindane partition. Apparently, the insecticide is easily accommodated in bilayers of short-aliphatic-chain lipids, since the partitions were 2450, 600 and 50 in DMPC, DPPC and DSPC, respectively, at temperatures 10 Cdeg below the midpoint of their transitions. The lindane partition sequence in native membranes is as follows: mitochondria, sarcoplasmic reticulum, myelin, brain microsomes and erythrocytes. This sequence correlates reasonably well with the relative content of cholesterol and is similar in liposomes of total extracted lipids, although the absolute partitions showed decreased values. Therefore, the presence of proteins in native membranes contributes to the insecticide partition, probably by favouring its interaction with lipids.