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.     

Simulation of Y-chromosomal haplotype data

The non-recombining nature of the Y-chromosome determines the non-independence of alleles between loci. The evolution of short tandem repeat (STR) loci in the Y-chromosome is the result of different factors such as differential mutation rates, mutation modes, gene conversion, selection and demographic processes. The degree of correlation between loci is dependent on the magnitude of these processes. The simulation of data is a routine tool used for testing hypotheses in population and evolutionary studies. The most basic parameters hitherto used in lineage haplotype simulations are the allele frequency distributions and mutation rates, assuming either full independence or linkage between loci. In this study we introduce use of the Spearman correlation coefficient to estimate the degree of dependence between non-recombining loci. Then, both the interdependence between loci and the allele frequency distributions at multi-allelic loci are incorporated in an algorithm for simulating haplotypes. We illustrate the method using published and unpublished Y-chromosome STR data.     

Microsecond Dynamics During the Binding-induced Folding of an Intrinsically Disordered Protein

Tau is an intrinsically disordered protein implicated in many neurodegenerative diseases. The repeat domain fragment of tau, tau-K18, is known to undergo a disorder to order transition in the presence of lipid micelles and vesicles, in which helices form in each of the repeat domains. Here, the mechanism of helical structure formation, induced by a phospholipid mimetic, sodium dodecyl sulfate (SDS) at sub-micellar concentrations, has been studied using multiple biophysical probes. A study of the conformational dynamics of the disordered state, using photoinduced electron transfer coupled to fluorescence correlation spectroscopy (PET-FCS) has indicated the presence of an intermediate state, I, in equilibrium with the unfolded state, U. The cooperative binding of the ligand (L), SDS, to I has been shown to induce the formation of a compact, helical intermediate (IL₅) within the dead time (∼37 µs) of a continuous flow mixer. Quantitative analysis of the PET-FCS data and the ensemble microsecond kinetic data, suggests that the mechanism of induction of helical structure can be described by a U ↔ I ↔ IL₅ ↔ FL₅ mechanism, in which the final helical state, FL₅, forms from IL₅ with a time constant of 50–200 µs. Finally, it has been shown that the helical conformation is an aggregation-competent state that can directly form amyloid fibrils.     

Comparative quantitative investigations on brains of wild cavies (Cavia aperea) and guinea pigs (Cavia aperea f. porcellus). A contribution to size changes of CNS structures due to domestication

Intraspecific allometric calculations of the brain to body size relation revealed distinct differences between 127 (67; 60) ancestral wild cavies and 82 (37; 45) guinea pigs, their domesticated relatives. The dependency of both measures from one another remained the same in both animal groups but the brains of guinea pigs were by 14.22% smaller at any net body weight. Consistent with results in other species the domestication of Cavia aperea is also characterized by a decrease of brain size. Fresh tissue sizes of the five brain parts medulla oblongata, cerebellum, mesencephalon, diencephalon and telencephalon were determined for 6 cavies and 6 guinea pigs by the serial section method. Additionally the sizes of 16 endbrain structures and those of the optic tract, the lateral geniculate body and the cochlear nucleus were measured. Different decrease values resulted for all these structures concomitant with domestication as was calculated from the amount of total brain size decrease and average relative structure values in the wild as well as the domesticated brain. The size decrease of the entire telencephalon (−13.7%) was within the range of the mean overall reduction as similarly was the case for the total neocortex (−10.7%) whereas the total allocortex (−20.9%) clearly was more strongly affected. The size decrease of the olfactory bulb (−41.9%) was extreme and clearly higher than found for the secondary olfactory structures (around −11%). The primary nuclei of other sensory systems (vision, audition) were decreased to less extent (lateral geniculate: −18.1%; cochlear nucleus: −12.6%). Mass decreases of pure white matter parts were nearly twice as high in contrast to associated grey matter parts (neocortex white versus grey matter; tractus opticus versus lateral geniculate body). The relatively great decrease values found for the limbic structures hippocampus (−26.9%) and schizocortex (−25.9%) are especially notable since they are in good conformity with domestication effects in other mammalian species. The findings of this study are discussed with regard to results of similar investigations on wild and domesticated gerbils (Meriones unguiculatus), the encephalization of the wild form, the special and species-specific mode and duration of domestication and in connection with certain behavioral changes as resulted from comparative investigations in ethology, socio-biology, endocrinology and general physiology.     

Role of electrostatics in the binding of charged metallophthalocyanines to neutral and charged phospholipid membranes

Binding of the cationic tetra(tributylammoniomethyl)-substituted hydroxoaluminum phthalocyanine (AlPcN₄) to bilayer lipid membranes was studied by fluorescence correlation spectroscopy (FCS) and intramembrane field compensation (IFC) methods. With neutral phosphatidylcholine membranes, AlPcN₄ appeared to bind more effectively than the negatively charged tetrasulfonated aluminum phthalocyanine (AlPcS₄), which was attributed to the enhancement of the coordination interaction of aluminum with the phosphate moiety of phosphatidylcholine by the electric field created by positively charged groups of AlPcN₄. The inhibitory effect of fluoride ions on the membrane binding of both AlPcN₄ and AlPcS₄ supported the essential role of aluminum-phosphate coordination in the interaction of these phthalocyanines with phospholipids. The presence of negative or positive charges on the surface of lipid membranes modulated the binding of AlPcN₄ and AlPcS₄ in accord with the character (attraction or repulsion) of the electrostatic interaction, thus showing the significant contribution of the latter to the phthalocyanine adsorption on lipid bilayers. The data on the photodynamic activity of AlPcN₄ and AlPcS₄ as measured by sensitized photoinactivation of gramicidin channels in bilayer lipid membranes correlated well with the binding data obtained by FCS and IFC techniques. The reduced photodynamic activity of AlPcN₄ with neutral membranes violating this correlation was attributed to the concentration quenching of singlet excited states as proved by the data on the AlPcN₄ fluorescence quenching.     

Mean difference in live-weight per incremental difference in body condition score estimated in multiple sheep breeds and crossbreds

Body condition score (BCS) is a subjective assessment of the proportion of body fat an animal possesses and is independent of frame size. There is a growing awareness of the importance of mature animal live-weight given its contribution to the overall costs of production of a sector. Because of the known relationship between BCS and live-weight, strategies to reduce live-weight could contribute to the favouring of animals with lesser body condition. The objective of the present study was to estimate the average difference in live-weight per incremental change in BCS, measured subjectively on a scale of 1 to 5. The data used consisted of 19 033 BCS and live-weight observations recorded on the same day from 7556 ewes on commercial and research flocks; the breeds represented included purebred Belclare (540 ewes), Charollais (1484 ewes), Suffolk (885 ewes), Texel (1695 ewes), Vendeen (140 ewes), as well as, crossbreds (2812 ewes). All associations were quantified using linear mixed models with the dependent variable of live-weight; ewe parity was included as a random effect. The independent variables were BCS, breed (n=6), stage of the inter-lambing interval (n=6; pregnancy, lambing, pre-weaning, at weaning, post-weaning and mating) and parity (1, 2, 3, 4 and 5+). In addition, two-way interactions were used to investigate whether the association between BCS and live-weight differed by parity, a period of the inter-lambing interval or breed. The association between BCS and live-weight differed by parity, by a period of the inter-lambing interval and by breed. Across all data, a one-unit difference in BCS was associated with 4.82 (SE=0.08) kg live-weight, but this differed by parity from 4.23 kg in parity 1 ewes to 5.82 kg in parity 5+ ewes. The correlation between BCS and live-weight across all data was 0.48 (0.47 when adjusted for nuisance factors in the statistical model), but this varied from 0.48 to 0.53 by parity, from 0.36 to 0.63 by stage of the inter-lambing interval and from 0.41 to 0.62 by breed. Results demonstrate that consideration should be taken of differences in BCS when comparing ewes on live-weight as differences in BCS contribute quite substantially to differences in live-weight; moreover, adjustments for differences in BCS should consider the population stratum, especially breed.     

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.     

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.