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.     

Livestock Trampling Reduces the Conservation Value of Beetle Communities on High Quality Exposed Riverine Sediments

Exposed riverine sediments (ERS) are habitat for a large number of rare and threatened specialist species of invertebrates and are of considerable conservation importance. Livestock trampling is believed to be one of the most widespread causes of damage to ERS habitats in the UK, and as such, its effects were the focus of this investigation. Beetle density was measured at two points within 25 distinct patches of habitat along ∼ ∼47 km of the Afon Tywi special site of scientific interest in South Wales, which is known to support an extremely good quality ERS beetle fauna in a UK context. Partial canonical correspondence analyses were used to explore the relationship between beetle assemblage and a range of environmental variables. The percentage of fine (<8 mm) sediments, median sediment size, distance downstream, cattle stocking levels, and counts of sheep faeces were found to best relate to beetle abundance and assemblage structure. Species richness was positively associated with stocking levels, probably because of the addition of species associated with resultant elevated levels of silt and organic matter. The ERS quality score, which is a measure of conservation value based on the rarity of specialist ERS beetles, was negatively associated with measures of trampling damage. It was therefore concluded that livestock trampling reduces the conservation value of beetle communities on high quality ERS and management should restrict trampling in sites of high conservation importance.     

On the rotational brownian motion of a bacterial idle motor. II. Theory of fluorescence correlation spectroscopy

The photon flux autocorrelation function of a fluorescent label attached to a bacterial motor shaft is calculated for the case in which the bacterial motor is considered to be actively but idly rotating. It is shown that even when the fluorescent label has a very short lifetime, fluorescence correlation spectroscopy should provide a useful tool for determining the rate of revolution of the bacterial motor under various solution conditions.     

Goodness of Fit of Discriminant Functions from the Vector Space of Fixed Variates

Alternative proofs of some of KSHIRSAGAR's (1971) results on testing discriminant functions or canonical variables in the vector space of fixed variates are given. These results are derived in terms of the original variates unlike KSHIRSAGAR (1971) who derives the results by using random orthogonal transformations and triangular decompositions of the original matrix variates.     

Stereological Determination of Orientations,Second-Order Quantities and Correlations for Random Spatial Fibre Systems

This paper presents methods for the stereological analysis of spatial fibre systems on the base of planar or thin sections. Under the assumption that the cross-section figures of the tubular fibres can be measured, the orientation distribution of the fibre system and its line density L_v can be determined from one section only and without distributional assumptions. A simple way to study the degree of randomness of fibre systems consists in the statistical analysis of the point pattern of centres of intersection figures. More sophisticated methods are of stereological nature and yield the spatial reduced second moment measure. Similarly also correlations between two fibre systems can be quantified. The methods are demonstrated by two examples concerning samples of human brain.     

Effect of hyperoxidized guanine on DNA primer-template structures: Spiroiminodihydantoin leads to strand slippage

Oxidation of guanine in DNA can lead to mutagenic lesions such as 7-hydro-8-oxoguanine (oG). Upon further oxidation, a more mutagenic lesion, spirominodihydantoin (Sp), can occur. In this study, nuclear magnetic resonance (NMR) investigations were performed to determine the structural features of DNA primer-template models with 5′-GG, 5′-G(oG), 5′-G(Sp) and 5′-T(Sp) templates, that mimic the situation in which the downstream G of the template has been oxidized to oG or hyperoxidized to Sp. Our results show that misalignment occurs only in the 5′-G(Sp) and 5′-T(Sp) templates, providing structural insights into the observed differences in mutagenicity of Sp and oG during DNA replication.