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.     

The influence of environmental factors on the spatial distribution of saxicolous lichens in a Norwegian coastal community

Abstract. The effects of vegetation cover, radiation, micro‐habitat variables and maritime influence on the floristic composition of a saxicolous community in Vingen, western Norway were studied. Particular emphasis is put on the local distribution of Fuscidea cyathoides, Ochrolechia tartarea, Ophioparma ventosa and Pertusaria corallina. Very little of the variation in the lichen community composition is directly related to measured micro‐environmental variables but variance partitioning shows that vegetation cover explains more of the floristic variation than radiation, maritime influence and microhabitat variables. Logistic regression analyses nevertheless indicate that the micro‐environment influences the spatial distribution of the four species. The high fraction of unexplained floristic variation, 91%, is suggested to result from (1) lack of fit of data to the response model; (2) some influential environmental variables that have not been recorded; (3) local historical factors that affect present day distribution and/or (4) apparent randomness in colonization. The results also agree with the view that the four lichen species in this study are able to co‐exist in the long‐term because of different spatial distributions resulting from different strategies with respect to ecology, dispersion and interaction.     

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.     

Variation in dental occlusion and arches among melanesians of bougainville island,papua New Guinea. I. Methods,age changes,sex differences and population comparisons

Population studies of malocclusion lack comparability because of the subjective criteria employed in the definition of malocclusion. Alternatively, individual characteristics of occlusion can be quantified and compared within and between populations. Measurements were taken from the dental cases of 319 male an 359 female Melanesians from Bougainville, Papua New Guinea. The cross-sectional age changes from 12 to 68 years of age included an increase in intermolar arch width, a decrease in arch length and intercanine arch width, and increased crowding and malalignment. Neither age nor sex accounted for a large proportion of the differences among individuals. When compared to industrialized groups, the Bougainville population had a slight reduction in variance for most characteristics. Only the sagittal molar relationship was markedly less variable on Bougainville. The results emphasize that a quantitative evaluation of individual occlusal variables may reveal differences within and between populations not detected when simple malocclusion frequencies are reported.     

Variations in the anterior patellar groove of the human femur

An analysis of the anterior patellar groove of the human femur shows considerable variation in its medial and lateral spects. The groove itself, measured by the angle it encloses, shows considerably less variation than its individual components. The suggested functional relationship between bicondylar angle and lateral elevation of the patellar groove does not obtain for this sample.